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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 [...]

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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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• 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

  
  

  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

  
  

  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

  
  

  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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