Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE)

The Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) is an online archive aimed at collecting, preserving, and disseminating digital copies of scientific papers published by researchers of the International Center for Numerical Methods in Engineering (CIMNE).

The goal of the repository is to widely disseminate the results of the research performed at CIMNE, by sharing the preprints or postprints -depending on the article sharing policies of the original ... show more

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An adaptive finite point method for the shallow water equations
E. Ortega, E. Oñate, S. Idelsohn, C. Buachart

Int. J. Numer. Meth. Engng. (2011). Vol. 88 (2), pp. 180-204; doi: 10.1002/nme.3171

Abstract
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on clouds of points, adopts an upwind‐biased discretization for dealing with the convective terms in the governing equations. The viscous and source terms are discretized in a pointwise manner and the semi‐discrete equations are integrated explicitly in time by means of a multi‐stage scheme. Moreover, with the aim of exploiting meshless capabilities, an adaptive h‐refinement technique is coupled to the described flow solver. The success of this approach in solving typical shallow water flows is illustrated by means of several numerical examples and special emphasis is placed on the adaptive technique performance. This has been assessed by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost‐effective tool for solving practical shallow water problems. Copyright © 2011 John Wiley & Sons, Ltd.
Abstract
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations [...]
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Fluid–structure interaction problems with strong added‐mass effect
S. Idelsohn, F. Del Pin, R. Rossi, E. Oñate

Int. J. Numer. Meth. Engng. (2009). Vol. 80, (10), pp. 1261-1294; doi: 10.1002/nme.2659

Abstract
In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid–structure interaction problems, which has good convergent characteristics even for biomechanical application, where the added‐mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods. Copyright © 2009 John Wiley & Sons, Ltd.
Abstract
In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is [...]
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An advancing front technique for filling space with arbitrary separated objects
R. Löhner, E. Oñate

Int. J. Numer. Meth. Engng. (2009). Vol. 78 (13), pp. 1618-1630; doi: 10.1002/nme.2548

Abstract
An advancing front technique for filling space with arbitrary, separated objects has been developed. The input required consists of the specification of the desired object type, the mean object size, the distance between objects in space, as well as an initial triangulation of the surface. The objects are assumed to be described by a coarse mesh of tetrahedra. One face at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active faces are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Several examples are included that demonstrate the capabilities of the technique. Copyright © 2009 John Wiley & Sons, Ltd.
Abstract
An advancing front technique for filling space with arbitrary, separated objects has been developed. The input required consists of the specification of the desired object [...]
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ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems
J. García-Espinosa, A. Valls, E. Oñate

Int. J. Numer. Meth. Engng. (2008). Vol 76 (9), pp. 1297-1327; doi: 10.1002/nme.2348

Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary Lagrangian–Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235–249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier–Stokes equations are solved using an iterative monolithic predictor–corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence‐free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd.
Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary [...]
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Neural networks for variational problems in engineering
R. Lopez, E. Balsa-Canto, E. Oñate

Int. J. Numer. Meth. Engng. (2008). Vol. 75 (11), pp. 1341-1360; doi: 10.1002/nme.2304

Abstract
In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function, which is an extremal for some functional. Therefore, a variational formulation for NNs provides a direct method for the solution of variational problems. This proposed method is then applied to distinct types of engineering problems. In particular a shape design, an optimal control and an inverse problem are considered. The selected examples can be solved analytically, which enables a fair comparison with the NN results. Copyright © 2008 John Wiley & Sons, Ltd.
Abstract
In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning [...]
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A rotation‐free shell triangle for the analysis of kinked and branching shells
F. flores, E. Oñate

Int. J. Numer. Meth. Engng. (2007). Vol. 69 (7), pp. 1521-1551; doi: 10.1002/nme.1823

Abstract
This paper extends the capabilities of previous BST and EBST rotation‐free thin shell elements to the analysis of kinked and branching surfaces. The computation of the curvature tensor is first redefined in terms of the angle change between the normals at the adjacent elements. This allows to deal with arbitrary large angles between adjacent elements and to treat kinked surfaces. A relative stiffness between elements is introduced to consider non‐homogeneous surfaces. This idea is latter generalized to deal with branching shells. Several linear and non‐linear examples are presented showing that the formulation leads to the correct results. Copyright © 2006 John Wiley & Sons, Ltd.
Abstract
This paper extends the capabilities of previous BST and EBST rotation‐free thin shell elements to the analysis of kinked and branching surfaces. The computation of the curvature [...]
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CBS‐based stabilization in explicit solid dynamics
J. Rojek, E. Oñate, R. Taylor

Int. J. Numer. Meth. Engng. (2006). Vol. 66 (10), pp. 1547-1568; doi: 10.1002/nme.1689

Abstract
The characteristic‐based split (CBS) stabilization procedure developed originally in fluid mechanics has been adapted successfully to solid mechanics problems. The CBS algorithm has been implemented within a finite element program using an explicit time integration scheme. Volumetric locking of linear triangular and tetrahedral elements has been successfully eliminated. The performance of the numerical algorithm is illustrated with numerical results. Comparisons with an alternative stabilization technique based on the finite calculus method also are given. Copyright © 2006 John Wiley & Sons, Ltd.
Abstract
The characteristic‐based split (CBS) stabilization procedure developed originally in fluid mechanics has been adapted successfully to solid mechanics problems. The CBS algorithm [...]
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Obituary
N. Wiberg, E. Oñate, O. Zienkiewicz, R. Taylor, J. Hult

Int. J. Numer. Meth. Engng. (2006). Vol. 67 (2), pp. 158-159; doi: 10.1002/nme.1511

Abstract
Professor E. M. Alf Samuelsson from Chalmers University, Göteborg, Sweden, died on the 3rd of June 2005 at the age of 75 after a lengthy illness. Professor Samuelsson was an engineer with Professor Sven-Olof Asplund’s ConstructionCompany from 1952 to the time he joined Chalmers University in September 1954. In 1963 he completed his doctoral thesis with Professor Asplund on the subject of analysis of framedstructures by use of algebraic topology. He was beloved by students, colleagues and co-workersand was known as ‘Alf’ by all. Through his foresight and deep knowledge in many fields Alfcreated a strong group in Computational Mechanics at Chalmers University, which he led until his retirement in July 1994. Under his leadership the Department of Structural Mechanics flourished and has been widely recognized for its many scientific contributions. Alf supervised a large number of doctoral students of which nine have become professors. Alf was, formany years, the Dean of Research at Chalmers and has contributed much to the University’s development. Copyright 2006 John Wiley & Sons, Ltd.
Abstract
Professor E. M. Alf Samuelsson from Chalmers University, Göteborg, Sweden, died on the 3rd of June 2005 at the age of 75 after a lengthy illness. Professor Samuelsson [...]
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Simple modifications for stabilization of the finite point method
B. Boroomand, A. Tabatabaei, E. Oñate

Int. J. Numer. Meth. Engng. (2005). Vol. 63 (3), pp. 351-379; doi: 10.1002/nme.1278

Abstract
A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill‐conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non‐monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd.
Abstract
A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. [...]
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Simulation of light‐weight membrane structures by wrinkling model
R. Rossi, M. Lazzari, R. Vitaliani, E. Oñate

Int. J. Numer. Meth. Engng. (2005). Vol. 62 (15), pp. 2127-2153; doi: 10.1002/nme.1266

Abstract
The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo‐dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub‐iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo‐dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd.
Abstract
The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. [...]
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Possibilities of finite calculus in computational mechanics
E. Oñate

Int. J. Numer. Meth. Engng. (2004). Vol. 60 (1), pp. 255-281; doi: 10.1002/nme.961

Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space–time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection–diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations.
Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a [...]
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Finite calculus formulation for incompressible solids using linear triangles and tetrahedra
E. Oñate, J. Rojek, R. Taylor, O. Zienkiewicz

Int. J. Numer. Meth. Engng. (2004). Vol. 59 (11), pp. 1473-1500; doi: 10.1002/nme.922

Abstract
Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented.
Abstract
Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach [...]
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A general advancing front technique for filling space with arbitrary objects
R. Löhner, E. Oñate

Int. J. Numer. Meth. Engng. (2004). Vol. 61 (12), pp. 1977-1991; doi: 10.1002/nme.1068

Abstract
An advancing front space‐filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance in space and an initial triangulation of the surface. One object at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active objects are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Different deposition or layering patterns can be achieved by selecting the order in which objects are eliminated from the active front. Timings show that for simple objects like spheres the scheme is considerably faster than volume mesh generators based on the advancing front technique, making it possible to generate large (> 106) yet optimal clouds of points in a matter of minutes on a PC. For more general objects, the performance may degrade depending on the complexity of the penetration checks. Several examples are included that demonstrate the capabilities of the technique.
Abstract
An advancing front space‐filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance [...]
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The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves
S. Idelsohn, E. Oñate, F. Del Pin

Int. J. Numer. Meth. Engng. (2004). Vol. 61 (7), pp. 964-989; doi: 10.1002/nme.1096

Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology.
Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]
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The meshless finite element method
S. Idelsohn, E. Oñate, N. Calvo, F. Del Pin

Int. J. Numer. Meth. Engng. (2003). Vol. 58 (6), pp. 893-912; doi: 10.1002/nme.798

Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the finite element method such as: (a) the simplicity of the shape functions in a large part of the domain; (b) C0 continuity between elements, which allows the treatment of material discontinuities, and (c) ease of introduction of the boundary conditions.
Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, [...]
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A finite point method for compressible flow
R. Löhner, C. Sacco, E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Engng. (2002). Vol. 53 (8), pp. 1765-1779; doi: 10.1002/nme.334

Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive.
Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique [...]
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A basic thin shell triangle with only translational DOFs for large strain plasticity
F. flores, E. Oñate

Int. J. Numer. Meth. Engng. (2001). Vol. 51 (1), pp. 57-83; doi: 10.1002/nme.147

Abstract
A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non‐linear isotropic hardening is adopted. The element is an extension of a previous similar rotation‐free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro‐) code adequate to simulate sheet‐stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation.
Abstract
A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large [...]
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Rotation‐free triangular plate and shell elements
E. Oñate, F. Zárate

Int. J. Numer. Meth. Engng. (2000). Vol. 47 (1-3), pp. 557-603; doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<557::AID-NME784>3.0.CO;2-9

Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.
Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with [...]
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Finite element solution of free‐surface ship‐wave problems
S. Idelsohn, E. Oñate, C. Sacco

Int. J. Numer. Meth. Engng. (1999). Vol. 45 (5), pp. 503-528; doi: 10.1002/(SICI)1097-0207(19990620)45:5<503::AID-NME570>3.0.CO;2-E

Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.
Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes [...]
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Solving structural optimization problems with genetic algorithms and simulated annealing
S. Botello, J. Marroquín, E. Oñate

Int. J. Numer. Meth. Engng. (1999). Vol. 45 (8), pp. 1069-1084; doi: 10.1002/(SICI)1097-0207(19990720)45:8<1069::AID-NME620>3.0.CO;2-E

Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar structures. We show that it is possible to embed these two schemes into a single parametric family of algorithms, and that optimal performance (in a parallel machine) is obtained by a hybrid scheme. Examples of applications to the optimization of several real steel bar structures are presented.
Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar [...]
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A homogeneous constitutive model for masonry
J. Lopez, S. Oller, E. Oñate, J. Lubliner

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1651-1671; doi: 10.1002/(SICI)1097-0207(19991210)46:10<1651::AID-NME718>3.0.CO;2-2

Abstract
Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non‐linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design efficient repair and maintenance has motivated the work of many structural analysts in this field. Here the finite element method has emerged as one of the most powerful procedures for linear and non‐linear analysis of masonry structures. The main problem pending is the development of accurate and efficient constitutive models capable of predicting the behaviour of masonry in the non‐linear range and this has been the motivation of this work. The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The effect of anisotropy is introduced by means of fictitious isotropic stress and strain spaces. The material properties in the fictitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth‐order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non‐linear behaviour in the isotropic spaces. Details of the model for masonry structures and its implementation in a general non‐linear finite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the efficiency of the model.
Abstract
Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity [...]
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A large strain explicit formulation for composites
J. Ruberts, S. Oller, E. Casas, S. Proença, E. Oñate

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1595-1607; doi: 10.1002/(SICI)1097-0207(19991210)46:10<1595::AID-NME715>3.0.CO;2-Z

Abstract
A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.
Abstract
A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small [...]
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A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis
A. Morán, E. Oñate, J. Miquel

Int. J. Numer. Meth. Engng. (1998). Vol. 42 (2), pp. 219-236; doi: 10.1002/(SICI)1097-0207(19980530)42:2<219::AID-NME355>3.0.CO;2-E

Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non‐linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application
Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness [...]
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Boundary conditions for finite element simulations of convective flows with artificial boundaries
J. Heinrich, S. Idelsohn, E. Oñate, C. Vionnet

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (6), pp. 1053-1071; doi: 10.1002/(SICI)1097-0207(19960330)39:6<1053::AID-NME896>3.0.CO;2-N

Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. [...]
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Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients
S. Idelsohn, J. Heinrich, E. Oñate

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (9), pp. 1455-1473; doi: 10.1002/(SICI)1097-0207(19960515)39:9<1455::AID-NME912>3.0.CO;2-0

Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method.
Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally [...]
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A temperature‐based formulation for finite element analysis of generalized phase‐change problems
D. Celentano, E. Oñate, S. Oller

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (20), pp. 3441-3465; doi: 10.1002/nme.1620372004

Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it [...]
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A simple triangular element for thick and thin plate and shell analysis
E. Oñate, F. Zárate, F. flores

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (15), pp. 2569-2582; doi: 10.1002/nme.1620371505

Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field [...]
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A finite volume format for structural mechanics
E. Oñate, M. Cervera, O. Zienkiewicz

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (2), pp. 181-201; doi: 10.1002/nme.1620370202

Abstract
A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non‐Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
Abstract
A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements [...]
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A penalty finite element method for non‐Newtonian creeping flows
R. Codina, M. Cervera, E. Oñate

Int. J. Numer. Meth. Engng. (1993). Vol. 36 (8), pp. 1395-1412; doi: 10.1002/nme.1620360808

Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.
Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference [...]
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A general methodology for deriving shear constrained Reissner-Mindlin plate elements
E. Oñate, O. Zienkiewicz, B. Suarez, R. Taylor

Int. J. Numer. Meth. Engng. (1992). Vol. 33 (2), pp. 345-367; doi: 10.1002/nme.1620330208

Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted [...]
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Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation
E. Oñate, C. Agelet de Saracibar

Int. J. Numer. Meth. Engng. (1990). Vol. 30 (8), pp. 1577-1593; doi: 10.1002/nme.1620300815

Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.
Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements [...]
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Plastic and viscoplastic flow of void‐containing metals. Applications to axisymmetric sheet forming problems
E. Oñate, M. Kleiber, C. Agelet de Saracibar

Int. J. Numer. Meth. Engng. (1988). Vol. 25 (1), pp. 227-251; doi: 10.1002/nme.1620250118

Abstract
A formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.
Abstract
A formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. [...]
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On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
E. Dvorkin, E. Oñate, J. Oliver

Int. J. Numer. Meth. Engng. (1988). Vol. 26 (7), pp. 1597-1613; doi: 10.1002/nme.1620260710

Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness [...]
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Benchmarks for geotechnical modeling
E. Alarcón, E. Alonso, D. Aubry, K. Axelsson, E. Oñate, E. al.

Int. J. Numer. Meth. Engng. (1988). Vol. 26 (11), pp. 2559-2568; doi: 10.1002/nme.1620261113

Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive that the type of approach outlined is important in a serious numerical study of all problems in geomechanics and indeed is valid in other areas.
Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive [...]
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A total lagrangian formulation for the geometrically nonlinear-analysis of structures using finite-elements. Part II: arches, frames and axisymmetric shells
J. Oliver, E. Oñate

Int. J. Numer. Meth. Engng. (1986). Vol. 23 (2), pp. 253-274, 1986 doi: 10.1002/nme.1620230209

Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows for large displacement-large rotations of the structure. Shear deformation effects have also been taken into account. It has been shown how the formulation can be presented in a unified manner to treat simultaneously the three types of structures.
Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows [...]
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A total lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two‐dimensional problems: Shell and plate structures
J. Oliver, E. Oñate

Int. J. Numer. Meth. Engng. (1984). Vol. 20 (12), pp. 2253-2281; 10.1002/nme.1620201208

Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co‐ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of [...]
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A general formulation for coupled thermal flow of metals using finite elements
O. Zienkiewicz, E. Oñate, J. Heinrich

Int. J. Numer. Meth. Engng. (1981). Vol. 17 (10), pp. 1497-1514; doi: 10.1002/nme.1620171005

Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic flow approach and the solution technique for the coupled problem implies a simultaneous solution for velocities and temperatures. Some aspects of the numerical solution of the problem are given and in the last part of the paper some examples of steady‐state extrusion and rolling problems showing the applicability of the method are shown.
Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic [...]
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Simple and efficient element for axisymmetric shells
O. Zienkiewicz, J. Bauer, K. Morgan, E. Oñate

Int. J. Numer. Meth. Engng. (1977). Vol. 11 (10), pp. 1545-1558; doi: 10.1002/nme.1620111006

Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.
Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point [...]
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Simple and efficient element for axisymmetric shells
O. Zienkiewicz, J. Bauer, K. Morgan, E. Oñate

Int. J. Numer. Meth. Engng. (1978). Vol. 12 (7), pp. 1197; doi: 10.1002/nme.1620111006

Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.
Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point [...]
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Multi-fluid flows with the particle finite element method
S. Idelsohn, M. Mier-Torrecilla, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2009). Vol. 198, pp. 2750–2767; doi: 10.1016/j.cma.2009.04.002

Abstract
Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology.
Abstract
Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]
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New rotation-free finite element shell triangle accurately using geometrical data
P. Fuentes, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2010). Vol. 199, pp. 383–391; doi: https://doi.org/10.1016/j.cma.2009.01.006

Abstract
A new triangle shell element is presented. The advantages of this element are threefold: simplicity, generality and geometrical accuracy. The formulation is free from rotation degrees of freedom. The triangle here presented can be used regardless of the mesh topology, thus generality is conserved for any meshrepresented surface. From an original first order approach we evolve to a third order geometric description. The higher degree geometric description is based on the Bézier triangles concept, a very well known geometry in the domain of CAGD [G. Farin, Curves and Surfaces for CAGD. A Practical Guide, fifth ed., Morgan Kaufmann Publishers, San Francisco, CA, 2002]. Using this concept we show the path to reconstruct a general third order interpolating surface using only the three coordinates at each node. This work takes as starting point the nodal implementation of a basic triangle shell element [E. Oñate, F. Zárate, Rotation-free triangular plate and shell elements, Int. J. Numer. Methods Engrg. 47 (2000) 557– 603]. In order to use an exact formula for the curvature, the normal directions at each node and the way to characterize them are proposed. Then, the geometrical properties and the mechanical behavior of the surface created are introduced. Finally, different examples are presented to depict the versatility and accuracy of the element.
Abstract
A new triangle shell element is presented. The advantages of this element are threefold: simplicity, generality and geometrical accuracy. The formulation is free from rotation [...]
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A high-resolution Petrov-Galerkin method for the convection-diffusion-reaction problem. Part II-A multidimensional extension
P. Nadukandi, E. Oñate, J. García-Espinosa

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213-216, pp. 327-352; doi: 10.1016/j.cma.2011.10.003

Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions. This is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1D reaction–diffusion problem. The nondimensional element number is then defined using this fictitious reaction coefficient, the diffusion coefficient and an appropriate element size. Next, we introduce anisotropic element length vectors li and the stabilization parameters αi, βi are calculated along these li. Except for the modification to include the new dimensionless number that quantifies the characteristic layers, the definitions of αi, βi are a direct extension of their counterparts in 1D. Using αi, βiand li, objective characteristic tensors associated with the HRPG method are defined. The numerical artifacts across the characteristic layers are manifested as the Gibbs phenomenon. Hence, we treat them just like the artifacts formed across the parabolic layers in the reaction-dominant case. Several 2D examples are presented that support the design objective—stabilization with high-resolution
Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies [...]
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Large time-step explicit integration method for solving problems with dominant convection
S. Idelsohn, N. Nigro, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 217-220, pp. 168-185; doi: 10.1016/j.cma.2011.12.008

Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated by convection, independently of the spatial discretization. The idea is to use the information existing at time t=tn in the velocity streamlines as well as in the acceleration streamlines to update the particle position as well as the velocity in an updated Lagrangian frame. The method may be used with moving or fixed meshes.
Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated [...]
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A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles
K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 255 (1), pp. 210-225; doi: 10.1016/j.cma.2012.11.018

Abstract
A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is verified by several benchmarks which evaluate the behavior of the numerical scheme for severe compression and expansion cases. This model is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. We observe that the conditions within the bubble are nearly uniform until the converging pressure wave is strong enough to create very large pressures near the center of the bubble. These bubble dynamics occur on very small spatial (0.3 mm), and time (0.1 ms) scales. During the final stage of the collapse Rayleigh–Taylor instabilities appear at the interface and then disappear when the rebounce starts. At the end of the rebounce phase the bubble radius reaches 50% of its initial value and the bubble recover its circular shape. It is when the second collapse starts, with higher mode shape instabilities excited at the bubble interface, that leads to the rupture of the bubble. Several graphs are presented and the pressure pulse detected in the water is compared by experiment.
Abstract
A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible [...]
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Validation of numerical flow simulations against in vitro phantom measurements in different type B aortic dissection scenarios
E. Soudah, P. Rudenick, M. Bordone, D. García-Dorado, A. Evangelista, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 18 (8), pp. 805-815; doi: 10.1080/10255842.2013.847095

Abstract
An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment and follow-up are clinical challenges due to the progressive aortic dilatation and potentially severe complications during follow-up. It is well known that the direction and rate of dilatation of the artery wall depend on haemodynamic parameters such as the local velocity profiles, intra-luminal pressures and resultant wall stresses. These factors act on the FL and true lumen, triggering remodelling and clinical worsening. In this study, we aimed to validate a computational fluid dynamic (CFD) tool for the haemodynamic characterisation of chronic (type B) ADs. We validated the numerical results, for several dissection geometries, with experimental data obtained from a previous in vitro study performed on idealised dissected physical models. We found a good correlation between CFD simulations and experimental measurements as long as the tear size was large enough so that the effect of the wall compliance was negligible.
Abstract
An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment [...]
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A locally extended finite element method for the simulation of multi-fluid flows using the particle level set method
K. Kamran, R. Rossi, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 294, pp. 1-18; doi: 10.1016/j.cma.2015.05.017

Abstract
The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations. First of all, a spatial enrichment is employed to improve the approximation properties of the Eulerian mesh. This is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface. Then, the Lagrangian Particle Level Set (PLS) method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method. While the local enrichment can be understood in the general context of the XFEM, we employ an element-local variant, which allows preserving the matrix graph, and hence highly improving the computational efficiency.
Abstract
The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This [...]
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The intrinsic time for the streamline upwind Petrov-Galerkin formulation using quadratic elements
R. Codina, E. Oñate, M. Cervera

Comput. Methods Appl. Mech. Engrg., (1992). Vol. 94, pp. 239-262; doi: 10.1016/0045-7825(92)90149-E

Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic elements. Some related issues such as the computation of the characteristic element length and the introduction of source terms in the one-dimensional model problem are also addressed.
Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic [...]
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A finite element formulation for incompressible flow problems using a generalized streamline operator
M. Cruchaga, E. Oñate

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143, pp. 49-67; doi: 10.1016/S0045-7825(97)84579-3

Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. Methods Appl. Mech. Engrg. (1986) 58 305-328) for compressible flows is adapted to the incompressible Navier-Stokes equations. This new methodology allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, the definition of the ‘upwinding tensor’ does not require parameters defined outside this model. This formulation has been checked in classical tests with satisfactory results. Finally, a moving surface problem (Cruchaga et al., Comput. Numer. Methods Engrg. (1986) 59: 85-99) is also presented.
Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. [...]
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A hierarchical finite element method based on the partition of unity
R. Taylor, O. Zienkiewicz, E. Oñate

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 152, pp. 73-84; doi: 10.1016/S0045-7825(97)00182-5

Abstract
In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added to base finite element interpolations which, for Co approximations, are a particular case of the partition of unity. We also show how the functions may be constructed to preserve the interpolation property of the base finite element functions. An application to linear elasticity is used to illustrate the properties and stability of the approximation.
Abstract
In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added [...]
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A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem
P. Nadukandi, E. Oñate, J. García-Espinosa

Comput. Methods Appl. Mech. Engrg. (2010). Vol. 199, pp. 525–546; doi: 10.1016/j.cma.2009.10.009

Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi /partial t + u partial phi /partial x - k partial^2 phi /partial x^2 +s phi -f where k; s > o = 0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov– Galerkin (CAU/PG) method [A.C. Galeão, E.G. Dutra do Carmo, A consistent approximate upwind Petrov– Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83–95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Oñate, Derivation of stabilized equations for numerical solution of advective–diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233–265; E. Oñate, J. Miquel, G. Hauke, Stabilized formulation for the advection–diffusion– absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926–3946] by an appropriate definition of the characteristic length. The prefix ‘high-resolution’ is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L2-projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u; k; s and f . Finally, some remarks are made on the extension of the HRPG method to multidimensions.
Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi [...]
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A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces
M. Cruchaga, E. Oñate

Comput. Methods Appl. Mech. Engrg. (1999). Vol. 173, pp. 241-255; doi: 10.1016/S0045-7825(98)00272-2

Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.
Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this [...]
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Shape variable definition with C0 , C1 and C2 continuity functions
G. Chiandussi, G. Bugeda, E. Oñate

Published in Comput. Methods Appl. Mech. Engrg. (2000). Vol. 188, pp. 727-742; doi: 10.1016/S0045-7825(99)00358-8

Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).
Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of [...]
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Lagrangian formulations to solve free surface incompressible inviscid fluid flows
S. Idelsohn, M. Storti, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2001). Vol. 191 (6-7), pp. 583-593; doi: 10.1016/S0045-7825(01)00303-6

Abstract
A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used in "meshless" approximations and the time integration is introduced in a semi-implicit way by a fractional step method. In this manner, both classical stabilization terms used in incompressible Euler equations are unnecessary: numerical diffusion for convective terms are unnecessary due to the Lagrangian formulation, and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method.
Abstract
A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used [...]
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On the simulation of flows with violent free surface motion
R. Lohner, C. Yang, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2006). Vol. 195, pp. 5597–5620; doi: 10.1016/j.cma.2005.11.010

Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from smoothed particle hydrodynamics (SPH) calculations. These and a series of other examples demonstrate that the present CFD method is capable of simulating violent free surface flows with strong nonlinear behavior.
Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]
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To mesh or not to mesh. That is the question. . .
S. Idelsohn, E. Oñate

Comput. Methods Appl. Mech. Engrg. (1996). Vol. 195, pp. 4681–4696; doi: :10.1016/j.cma.2005.11.006

Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh (such as those made of tetrahedra or hexahedra), from those that do not need a standard mesh, namely the meshless methods. For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. This paper discusses this issue to show that this choice is not, in the large majorities of the cases, the right question.
Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification [...]
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A critical displacement approach for predicting structural instability
E. Oñate, W. Matias

Comput. Methods Appl. Mech. Engrg. (1996). Vol. 134 (1-2), pp. 135-161; doi: 10.1016/0045-7825(96)01032-8

Abstract
A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this procedure are given together with explicit forms of the secant stiffness matrix for finite element analysis of solids and trusses. The accuracy and effectiveness of the method are clearly shown in a number of examples of two- and three-dimensional bar structures.
Abstract
A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement [...]
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Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems
E. Oñate

Comput. Methods Appl. Mech. Engrg. (1998). Vol. 151 (1-2), pp. 233-265, 1998 doi: 10.1016/S0045-7825(97)00119-9

Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow problems is revised in this paper. It is shown that the standard forms of the balancing diffusion terms, usually chosen in a heuristic manner, can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.
Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow [...]
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A stabilized finite point method for analysis of fluid mechanics problems
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

Comput. Methods Appl. Mech. Engrg. (1996). Vol. 139 (1-4), pp. 315-346; doi: 10.1016/S0045-7825(96)01088-2

Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.
Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]
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An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites
E. Car, S. Oller, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2000). Vol. 185, pp. 245-277; doi: 10.1016/S0045-7825(99)00262-5

Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material. The elastic anisotropic behavior is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.
Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials [...]
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A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation
E. Oñate

Comput. Methods Appl. Mech. Engrg. (2000). Vol. 182 (3-4), pp. 355-370; doi: 10.1016/S0045-7825(99)00198-X

Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus (FIC) procedure. Application of the standard finite element Galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier-Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.
Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the [...]
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A finite element method for fluid-structure interaction with surface waves using a finite increment calculus formulation
E. Oñate, J. García

Comput. Methods Appl. Mech. Engrg. (2001). Vol. 191, pp. 635-660; doi: 10.1016/S0045-7825(01)00306-1

Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous fluid and the free surface are derived at a differential level via a finite increment calculus procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.
Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized [...]
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Multiscale computational analysis in mechanics using finite calculus. An introduction
E. Oñate

Comput. Meth. Appl. Mech. Engng. (2003). Vol. 192 (28-30), pp. 3043-3059; doi: 10.1016/S0045-7825(03)00340-2

Abstract
The paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus (FIC) formulation. The FIC approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size. This introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters. The discrete nodal values obtained with the FIC formulation and the finite element method (FEM) can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched FEM. Typical multiscale problems in mechanics which can be solved with the FIC method include convection-diffusion-reaction problems with high localized gradients, incompressible problems in solid and fluid mechanics, localization problems such as prediction of shear bands in solids and shock waves in compressible fluids, turbulence, etc. The paper presents an introduction of the treatment of multiscale problems using the FIC approach in conjunction with the finite element method (FEM). Examples of application of the FIC/FEM formulation to the solution of simple multiscale convection-diffusion problems are given.
Abstract
The paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus (FIC) formulation. The FIC [...]
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Advances in the formulation of the rotation-free basic shell triangle
E. Oñate, F. Flores

Comput. Meth. Appl. Mech. Engng. (2005). Vol. 194 (21-24), pp. 2406-2443; doi: 10.1016/j.cma.2004.07.039

Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and a constant membrane field computed from the standard linear interpolation of the displacements within each triangle. An enhanced version of the element is obtained by using a quadratic interpolation of the geometry in terms of the six patch nodes. This allows to compute an assumed linear membrane strain field which improves the in-plane behaviour of the original element. A simple and economic version of the element using a single integration point is presented. The efficiency of the different rotation-free shell triangles is demonstrated in many examples of application including linear and non linear analysis of shells under static and dynamic loads, the inflation and de-inflation of membranes and a sheet stamping problem.
Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in [...]
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Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems
E. Oñate, J. Rojek

Comput. Methods Appl. Mech. Engrg. (2004). Vol 193, 3087-3128; doi: 10.1016/j.cma.2003.12.056

Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system. The DEM is a suitable tool to model soil/rock materials while the FEM in many cases can be a better choice to model other parts of the system considered. A typical example can be an idealization of rock cutting with a tool discretized with finite elements and rock or soil samples modelled with discrete elements. The FEM presented in the paper allows large elasto-plastic deformations in the solid regions. Such problems require the use of stabilized FEM to deal with the incompressibility constraint in order to eliminate the volumetric locking defect, especially when using triangular and tetrahedra elements with equal order interpolation for the displacement and the pressure variables. In the paper a stabilization based on the Finite Calculus (FIC) approach is used. Both theoretical algorithms of DEM and stabilized FEM are implemented in an explicit dynamic code. The paper presents some details of both formulations. A combined numerical algorithm is described finally. Selected numerical results illustrate the possibilities and performance of discrete/finite element analysis in geomechanics problems.
Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical [...]
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Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach
F. Flores, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2005). Vol. 194, pp. 907-932; doi: 10.1016/j.cma.2003.08.012

Abstract
In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain-stress pair. A plane stress behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed CBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhnaced rotation-free shell triangle.
Abstract
In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) [...]
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Advances in stabilized finite element and particle methods for bulk forming processes
E. Oñate, J. Rojek, M. Chiumenti, S. Idelsohn, F. Pin, R. Aubry

Comput. Methods Appl. Mech. Engrg. (2006). Vol. 195, pp. 6750-6777; doi: 10.1016/j.cma.2004.10.018

Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized linear triangles and tetrahedra using finite calculus and a new procedure combining particle methods and finite element methods. Applications of the new numerical methods to casting, forging and other bulk metal forming problems and mixing processes are shown.
Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized [...]
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Polyhedrization of an arbitrary 3D point set
S. Idelsohn, N. Calvo, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2003). Vol. 192, pp. 2649–2667; doi:10.1016/S0045-7825(03)00298-6

Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several physical problems need to define volume domains, boundary surfaces and approximating functions from a given point distribution. This is for instance the case of particle methods, in which all the information is the particle positions and there are not boundary surfaces definition. Until recently, all the FEM mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with a generalization of the Delaunay tessellation presented in this paper, gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here is not a standard mesh generation. The problem here is: for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method. To include new nodes or change their positions is not allowed.
Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several [...]
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Rotation-free finite element for the non-linear analysis of beams and axisymmetric shells
F. Flores, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2006). Vol. 195, pp. 5297–5315; doi:10.1016/j.cma.2005.08.021

Abstract
In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbour (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic-plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic-plastic materials and large strains.
Abstract
In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions [...]
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Stabilized formulation for the advection-diffusion-absorption equation using finite calculus and linear finite elements
E. Oñate, J. Miquel, G. Hauke

Comput. Meth. Appl. Mech. Engng. (2006). Vol. 195, pp. 3926–3946; doi: 10.1016/j.cma.2005.07.020

Abstract
A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. The basis of the method is detailed for the 1D problem. It is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter. A critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given. More accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives. A straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. The extension to the multi-dimensional case is briefly described. Numerical results for 1D and 2D problems are presented showing the efficiency and accuracy of the new stabilized formulation.
Abstract
A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing [...]
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Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus
E. Oñate, F. Zarate, S. Idelsohn

Comput. Meth. Appl. Mech. Engng. (2006). Vol. 195 (13-16), pp. 1793–1825;
doi: 10.1016/j.cma.2005.05.036

Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.
Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]
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A unified monolithic approach for multi-fluid flows and Fluid-Structure Interaction using the Particle Finite Element Method with fixed mesh
P. Becker, S. Idelsohn, E. Oñate

Computational Mechanics (2015). Vol. 55, pp. 1091–1104; 10.1007/s00466-014-1107-0

Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . Our approach is an extension of the fluid-only PFEM-2 [1,2] which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh [...]
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Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches
E. Oñate, J. García, S. Idelsohn, F. Pin

Comput. Meth. Appl. Mech. Engng. (2006). Vol. 195 (23-24), pp. 3001-3037; doi: 10.1016/j.cma.2004.10.016

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The standard Eulerian formulation is described first. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus (FIC) method. A simple extension of the fluid flow equations to an arbitrary Lagrangian-Eulerian (ALE) frame adequate for treating fluid-structure interaction problems is briefly presented. A fully Lagrangian formulation called the Particle Finite Element Method (PFEM) is also described. The PFEM is particularly attractive for fluid-structure interaction problems involving large motions of the free surface and breaking waves. Examples of application of the Eulerian, the ALE and the fully lagrangian PFEM formulations are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The standard Eulerian formulation is described first. The necessary [...]
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Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion
F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 21

Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classiﬁ cations d ue to the competing ef fects of gasiﬁca ti on, charring, ﬂame inhibition and melt ﬂow/dripping. For numerical investigation, the particle ﬁnite element method (PFEM) is used. Its capability to model the complex ﬁre behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efﬁcie nt p lasticiser; adding PTFE p reve nts dripping by causing a ﬂo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasiﬁcation and dripping. The thermal impact of both the burner and the ﬂame is approximated taking into account ﬂame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the ﬁre behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi ﬁ cations and t he exti nc tion times are well predicted.
Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol [...]
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Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

Comput. Meth. Appl. Mech. Engng. (2008). Vol. 197 (19-20), pp. 1777–1800; doi: 10.1016/j.cma.2007.06.005

Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.
Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]
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Fluid-structure interaction using the Particle Finite Element Method
S. Idelsohn, E. Oñate, F. Pin, N. Calvo

Comput. Meth. Appl. Mech. Engng. (2006). Vol. 195 (17-18), pp. 2100-2123; doi: 10.1016/j.cma.2005.02.026

Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.
Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]
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Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach
E. Oñate, J. Arteaga, J. García-Espinosa, R. Flores

Comput. Meth. Appl. Mech. Engng. (2006). Vol. 195, pp. 339-200; doi: 10.1016/j.cma.2004.07.054

Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on the evaluation of the energy rate (the power) of the FE residuals of the momentum and incompressibility equations. The residuals are computed using recovered values of the derivatives of the velocity and pressure variable obtained via a nodal derivative recovery technique. Two mesh adaptation procedures based on: a) the equi-distribution of the residual power among the elements in the mesh and b) the equi-distribution of the density of the total residual power are presented. The stabilized form of the Navier-Stokes equations using a finite calculus (FIC) formulation is solved with a fractional step FE scheme. This allows the use of linear triangles and tetrahedra with an equal order interpolation for the velocity and pressure variables. A nodal-based approach is used for computing the residual power integrals. The examples show the ability of the error estimation and the mesh adaptation process to capture the high gradients of the solution in the vecinity of boundary layers and in zones of high vorticity of the fluid for both steady state and transient flow situations.
Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on [...]
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Simple and accurate two-noded beam element for composite laminated beams using a refined zigzag theory
E. Oñate, A. Eijo, S. Oller

Comput. Methods Appl. Mech. Engrg. (2012). Vol. 213–216, pp. 362–382; doi: 10.1016/j.cma.2011.11.023

Abstract
In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical Timoshenko beam theory and the refined zigzag kinematics proposed by Tessler ''et al.'' [[#cite-22|[22]]]. The element has just four kinematic variables per node. Shear locking is eliminated by reduced integration. The accuracy of the new beam element is tested in a number of applications to the analysis of composite laminated beams with simple supported and clamped ends under point loads and uniformly distributed loads. An example showing the capability of the new element for accurately reproducing delamination effects is also presented.
Abstract
In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical [...]
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Unified Lagrangian formulation for elastic solids and incompressible fluids. application to fluid-structure interaction problems via the PFEM
S. Idelsohn, J. Marti, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg. (2008). Vol. 197, pp. 1762–1776; doi: 10.1016/j.cma.2007.06.004

Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. In our work the FSI problem is solved via the Particle Finite Element Method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.
Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and [...]
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P1/P0+ elements for incompressible flows with discontinuous material properties
E. Oñate, P. Nadukandi, S. Idelsohn

Comput. Meth. Appl. Mech. Engng. (2015). Vol. 293, pp. 191-206, 10.1016/j.cma.2013.12.009

Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant pressure field'' and ''a prescribed linear field'' that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behaviour for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf-sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier-Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper. The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.
Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant [...]
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Lagrangian versus Eulerian integration errors
S. Idelsohn, E. Oñate, N. Nigro, P. Becker

Comput. Methods Appl. Mech. Engrg. (2015). Vol. 293, pp. 191–206; 10.1016/j.cma.2015.04.003

Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.
Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible [...]
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A unified Lagrangian formulation for solid and fluid dynamics and its possibility for modelling submarine landslides and their consequences
X. Zhang, E. Oñate, S. Galindo, J. Bleyer

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 13

Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect impact via the generated tsunami. The simulation of submarine landslides and their consequences has been a long-standing challenge majorly due to the strong coupling among sliding sediments, seawater and infrastructure as well as the induced extreme material deformation during the complete process. In this paper, we propose a unified finite element formulation for solid and fluid dynamics based on a generalised Hellinger–Reissner variational principle so that the coupling of fluid and solid can be achieved naturally in a monolithic fashion. In order to tackle extreme deformation problems, the resulting formulation is implemented within the framework of the particle finite element method. The correctness and robustness of the proposed unified formulation for single-phase problems (e.g. fluid dynamics problems involving Newtonian/Non-Newtonian flows and solid dynamics problems) as well as for multi-phase problems (e.g. two-phase flows) are verified against benchmarks. Comparisons are carried out against numerical and analytical solutions or experimental data that are available in the literature. Last but not least, the possibility of the proposed approach for modelling submarine landslides and their consequences is demonstrated via a numerical experiment of an underwater slope stability problem. It is shown that the failure and post-failure processes of the underwater slope can be predicted in a single simulation with its direct threat to a nearby pipeline and indirect threat by generating tsunami being estimated as well.
Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect [...]
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3D numerical simulation of free-surface Bingham Fuids interacting with structures using the PFEM
A. Franci, X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 12

Abstract
This paper presents a purely Lagrangian approach for the 3D simulation of Bingham free-surface uids and their interaction with deformable solid structures. In the proposed numerical strategy, the fluid is handled using the Particle Finite Element Method (PFEM) to tackle the issues resulting from extreme changes of geometry, such as mesh distortion and free-surface evolution. Additionally, the Papanastasiou model is employed as a regularization technique to overcome the computational difficulties associated with the classical Bingham model. The solid structure, on the other hand, is represented by the hypoelastic constitutive model and simulated using the conventional Finite Element Method (FEM). The coupling between the fluid and the structure is achieved via a monolithic approach, called Unified formulation. Several numerical examples are presented to illustrate the correctness and the robustness of the proposed formulation, in 2D and in 3D. Special attention is devoted to the analysis of the convergence behavior of the proposed computational framework, the effect of the regularization on the numerical results and the 3D effects. Moreover, detailed comparisons between the simulated results and experimental data are performed so that the concerned problems and results can serve as benchmarks.
Abstract
This paper presents a purely Lagrangian approach for the 3D simulation of Bingham free-surface uids and their interaction with deformable solid structures. In the proposed [...]
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Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity
X. Zhang, S. Sloan, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 11

Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐ out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.
Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out [...]
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Surface tension problems solved with the Particle Finite Element Method using large time-steps
J. Giménez, N. Nigro, S. Idelsohn, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 10

Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [3] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.
Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology [...]
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Data-MSCA-IF: Collapse Velocity
X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 7

Abstract
Variations of horizontal and vertical velocities of retrogressive landslides
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Data-MSCA-IF: Sensitive clays
X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 6

Abstract
Properties of Norwegian clays, Canadian clays and offshore clays
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Particle finite element modelling of retrogressive slope failure in sensitive clays
X. Zhang, D. Sheng

(2017). paper no 868

Abstract
In this paper, the slope failure in sensitive clays is studied numerically using the particle finite element method which is a novel approach capable of tackling extreme deformation problems. The sensitive clay is described using an elastoviscoplastic model with strain softening. This model can be considered a mixture of the Tresca model with strain softening and the classical Bingham model. The former is used to capture the solid-like behaviour, for example when the clay is intact, whereas the latter is to describe the semi-fluid behaviour of the fully remolded clay. The complete process of the collapse of a sensitive clay deposit is captured successfully and the widely-observed retrogressive failure mode is reproduced. The mechanism behind the failure is also discovered.
Abstract
In this paper, the slope failure in sensitive clays is studied numerically using the particle finite element method which is a novel approach capable of tackling extreme deformation [...]
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A non-linear finite element method on unstructured meshes for added resistance in waves
J. García-Espinosa, B. Servan Camas

Ships and offshore structures (2018). (preprint) DOI: 10.1080/17445302.2018.1483624

Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration (SLI); and the second one based on the Streamline-Upwind Petrov-Galerking (SUPG) stabilization. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.
Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured [...]
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Some algorithms to correct a geometry in order to create a finite element mesh
R. Ribó, G. Bugeda, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2002).

Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non proper geometrical definitions coming from CAD systems. Typically, CAD systems do not take care of the proper definition of the geometries for the analysis purposes. In addition, the use of standard CAD files (IGES, VDA,...) for the transfer of geometries between different systems introduce some additional difficulties. In this work, a collection of algorithms to repair and/or to improve the geometry definitions are provided. The aim of these algorithms is to make as easy as possible the generation of a mesh over complex geometries given some minimum requirements of quality and correctness. The geometrical model will be considered as composed of a set of NURBS lines and trimmed surfaces. Some examples of application of the algorithms and of the meshes generated from the corrected geometry are also presented in this work
Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non proper geometrical definitions coming from CAD systems. Typically, CAD systems do not take [...]
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Accelerated 3D multi-body seakeeping simulations using unstructured finite elements
B. Servan Camas, J. García-Espinosa

J. Comput. Phys. (2013). 252, 382-403 (preprint)

Abstract
Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industry. However, most computer programs used in the industry work in the frequency domain, with the subsequent limitation in the accuracy of their model predictions. The main objective of this work is the development of a time domain solver based on the finite element method capable of solving multi-body seakeeping problems on unstructured meshes. In order to achieve such an objective, several techniques are combined: the use of an efficient algorithm for the free surface boundary conditions, the use of deflated conjugate gradients, and the use of a graphic processing unit for speeding up the linear solver. The results obtained results by the developed model showed good agreement with analytical solutions, experimental data for an actual offshore structure model, as well as numerical solutions obtained by other numerical method. Also, a simulation with sixteen floating bodies was carried out in a affordable CPU time, showing the potential of this approach for multi-body simulation.
Abstract
Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industry. However, most computer programs used in the [...]
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A coupled FEM-DEM procedure for predicting blasting operations in tunnels
F. Zarate, J. Gonzalez, J. Miquel, R. Lohner, E. Oñate

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2017).

Abstract
We present recent developments in the coupling of the finite element method (FEM) and the discrete element method (DEM) for analysis of rock blasting operations in tunnels. The coupled FEM-DEM technique has proven to be an efficient technique for predicting the multi-fracture of rock induced by the loads generated in blasting situations. The coupled FEM-DEM procedure is applied in the tunnel construction, as well as to gas pressure blasting pyrotechnics situations to break rock for excavation of the tunnel front. In the latter case the effect of gas explosion is modelled by solving with the FEM the equations of gas dynamics in the analysis domain. The effect of the gas forces in the underlying rock mass is modelled with an embedded fluid-structure interaction method. This allows us to accurately predicting the progressive multi-fracture of the rock accounting for the penetration of the gas in the fractured domain modelled with the FEM-DEM procedure. The efficiency of the coupled FEM-DEM technique is demonstrated in several examples of fracture tests and rock blasting problems related to tunnel engineering'''.''' The examples presented show that the combination of the DEM with simple 3-noded linear triangular elements correctly captures the onset of fractures and their evolution [1].
Abstract
We present recent developments in the coupling of the finite element method (FEM) and the discrete element method (DEM) for analysis of rock blasting operations in tunnels. [...]
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Time domain simulation of coupled sloshing–seakeeping problems by SPH–FEM coupling
B. Servan Camas, J. Cercós-Pita, J. Colom Cobb, J. García-Espinosa, A. Souto-Iglesias

Ocean Engineering (2016). 123, 383-396 (preprint)

Abstract
The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this aim, a Smooth Particle Hydrodynamics (SPH) solver for simulating internal flows in tanks is coupled in the time domain to a Finite Element Method (FEM) diffraction-radiation solver developed for seakeeping problems. Validations are carried out comparing against available experimental data. Good agreement between obtained numerical results and experimental data is found.
Abstract
The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this [...]
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Lagrangian finite element model for the 3D simulation of glass forming processes
P. Ryzhakov, J. García-Espinosa, E. Oñate

Computers and Structures (2016). 117, 126-140 (preprint)

Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product's wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.
Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we [...]
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A FEM fluid-structure interaction algorithm for analysis of the seal dynamics of a Surface-Effect Ship
J. García-Espinosa, B. Servan Camas, E. Oñate, D. Di Capua, P. Ubach de Fuentes

Comp. Meth. App. Mech. Eng. (2015). 295, 290-304 (preprint)

Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The paper focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water. The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method. Several validations against experimental results have been carried out to demonstrate the developed algorithm.
Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver [...]
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Computer Programming of free GUIs for the Analysis of the Behaviour of Marine Structures
J. Gutiérrez Romero, Z. B, J. García-Espinosa, M. Peyrau Rubio

Ships and Offshore Structures (2015). 11(5), 471-481 (preprint)

Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on the analysis of the behaviour of offshore structures, especially of offshore wind turbines. The first one is related to the aeroelastic analysis of wind turbines, and the second is concerned with the seakeeping of marine structures. The development of these tools has been carried out using a powerful software called ''Lognoter''. This tool is free software for Knowledge Management in Technology (KMT), which integrates computer programming for allowing the development of GUIs. These GUIs give an open platform for conducting a parametric study of the structural and dynamic behaviour of marine structures. Their coupling permits the user to set a suitable way to evaluate new concepts in marine structures. Finally, an application for the intensive analysis of offshore wind turbines is shown.
Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on [...]
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Non-linear dynamic analysis of the response of moored floating structures
J. Gutiérrez Romero, J. García-Espinosa, B. Servan Camas, B. Zamora-Parra

Marine Structures (2017). Vol. 49 pp. 116-137 49, 116-137 (preprint)

Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. The aim of this work is to present a time-domain model for solving the dynamics of floating marine devices, subjected to non-linear environmental loads and paying special attention on the mooring dynamics. First, the formulation of the hydrodynamic approach for solving the wave-floater interaction is introduced. Second, the solver of the mooring dynamics, based on a non-linear Finite Element Method approach, is presented. Third, a procedure for coupling the hydrodynamic along with other external loads, with the floating structure and mooring dynamics is described. Fourth, some validation examples and comparisons among different mooring approaches are presented. Fifth, an analysis of the OC3 floating wind turbine concept is performed to study the influence of different mooring models, the effects of non-linear waves on the platform, and the tension in the mooring system. The dynamic mooring model along with the second-order wave model produce realistic simulations of the floating wind turbine performance.
Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these [...]
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