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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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• 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

  
  

  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

  
  

  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

  
  

  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 [...]

  • 18
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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

  
  

  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

  
  

  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

  
  

  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

  
  

  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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