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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

  
  

  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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• Multiscale computational analysis in mechanics using finite calculus. An introduction

  E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2003). Vol. 192 (28-30), pp. 3043-3059

  
  

  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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• Study of Composite Materials using Zigzag Theory on Timoshenko Beams

  M. Masó, E. Oñate, F. Zarate

  (2013). Research Report, Nº PI397

  
  

  Abstract

  This final studies work target is to contribute two new beam theories to MAT-fem [6], an educational developed program by CIMNE [5]. Until now the MAT-fem Beams program only offered the Euler-Bernoulli and Timoshenko beam theories for homogeneous materials. With this work, the Timoshenko theory for composite materials and the refined zigzag theory are added. MAT-fem Beams application works by discretizing beams into two noded elements. This work offers a beam theories opportunity of contrasting with up to four kinematic variables. Timoshenko theory for composite materials works with three kinematics variables per node and zigzag theory works with four variables. Finally, the accuracy of zigzag theory must be remarked in comparison to other classic beam theories.

  Abstract
  This final studies work target is to contribute two new beam theories to MAT-fem [6], an educational developed program by CIMNE [5]. Until now the MAT-fem Beams program only [...]

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• Desarrollo y aplicación de un modelo de elementos finitos para cálculo de vigas con materiales compuestos laminados basado en la teoría de Timoshenko

  A. Llanos, E. Oñate, F. Zarate

  Personal Repository of Francisco Zarate (2013). 13

  
  

  Abstract

  Actualmente existen programas de MAT-fem para calcular vigas de material homogéneo, según la teoría de Euler-Bernoulli o de Timoshenko. El objetivo de la presente tesina es conseguir un nuevo programa capaz de calcular vigas de materiales compuestos con la teoría de Timoshenko.

  Abstract
  Actualmente existen programas de MAT-fem para calcular vigas de material homogéneo, según la teoría de Euler-Bernoulli o de Timoshenko. El objetivo [...]

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• New Rotation Free Shell Triangle for Crash-Worthiness Analysis in Parallel PC Networks

  E. Oñate, F. Zarate, L. Neamtu

  Personal Repository of Francisco Zarate (1999). 6

  
  

  Abstract

  A new three node shell triangular element with translational degree of freedom as the only nodal variables is presented. The element formulation is based on combining a standard linear finite element interpolation with a cell centered finite volume scheme. Details of the implementation of the element in an explicit dynamic code operating in parallel on networks of PC's are presented. The efficiency and applicability of the new rotation free shell triange is shown in the solution of some contact/impact and crash worthiness problem.

  Abstract
  A new three node shell triangular element with translational degree of freedom as the only nodal variables is presented. The element formulation is based on combining a standard [...]

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• Rotation Free Triangular Plate and Shell Elements

  E. Oñate, F. Zarate

  Personal Repository of Francisco Zarate (1999). 9

  
  

  Abstract

  The paper describes how 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 variable. The simplest element of the two families based on combining a linear interpolation of displacements with cell centered 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 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 [...]

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• Estudio de estimación de parámetros constitutivos en el método de elementos discretos o de partículas

  C. Recarey Morfa, E. Oñate, J. Canet, F. Zarate, J. Rojek

  Personal Repository of Francisco Zarate (2005). 4

  
  

  Abstract

  Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación de rocas, suelos, medios granulares otros materiales. El movimiento de elementos esféricos se describe por medio de las ecuaciones de dinámica del cuerpo rígido, Se emplea en la formulación una integración explicita, la cual., brinda una buena eficiencia computacional. Los elementos esféricos interactúan recíprocamente ente si a través de las fuerzas del contacto, en la direccion normal y tangencial. 

  Abstract
  Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación [...]

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• Discrete Element Modelling of Rock Cutting Processes Interaction with Evaluation of Tool Wear

  J. Rojek, E. Oñate, F. Zarate, C. Recarey Morfa

  Monograph CIMNE (2003). M87

  
  

  Abstract

  The document presents a numerical model of rocks and soils using spherical Discrete Elements, also called Distinct Elements. The motion of spherical elements is described by means of equations of rigid body dynamics. Explicit integration in time yields high computational efficiency. Spherical elements interact among one another with contact forces, both in normal and tangential directions. Efficient contact search scheme based on the octree structures has been implemented. Special constitutive model of contact interface taking into account cohesion forces allows us to model fracture and decohesion of materials. Numerical simulation predicts wear of rock cutting tools. The developed numerical algorithm of wear evaluation allows us us to predict evolution of the shape of the tool caused by wear. Results of numerical simulation are validated by comparison with experimental data.

  Abstract
  The document presents a numerical model of rocks and soils using spherical Discrete Elements, also called Distinct Elements. The motion of spherical elements is described [...]

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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

  
  

  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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• Advances in the formulation of the rotation-free basic shell triangle

  E. Oñate, F. Flores

  Comput. Methods Appl. Mech. Engrg., (2005). Vol. 194 (21-24), pp. 2406-2443

  
  

  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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