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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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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

  
  

  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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