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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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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.

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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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