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• Lagrangian formulations to solve free surface incompressible inviscid fluid flows

  S. Idelsohn, M. Storti, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2001). Vol. 191 (6–7), pp. 583-593

  
  

  Abstract

  A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used in "meshless" approximations and the time integration is introduced in a semi-implicit way by a fractional step method. In this manner, both classical stabilization terms used in incompressible Euler equations are unnecessary: numerical diffusion for convective terms are unnecessary due to the Lagrangian formulation, and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method.

  Abstract
  A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used [...]

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• On the simulation of flows with violent free surface motion

  R. Lohner, C. Yang, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 5597–5620

  
  

  Abstract

  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from smoothed particle hydrodynamics (SPH) calculations. These and a series of other examples demonstrate that the present CFD method is capable of simulating violent free surface flows with strong nonlinear behavior.

  Abstract
  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]

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• To mesh or not to mesh. That is the question. . .

  S. Idelsohn, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 4681–4696

  
  

  Abstract

  In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh (such as those made of tetrahedra or hexahedra), from those that do not need a standard mesh, namely the meshless methods. For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. This paper discusses this issue to show that this choice is not, in the large majorities of the cases, the right question.

  Abstract
  In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification [...]

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• A critical displacement approach for predicting structural instability

  E. Oñate, W. Matias

  Comput. Methods Appl. Mech. Engrg., (1996). Vol. 134 (1-2), pp. 135-161

  
  

  Abstract

  A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this procedure are given together with explicit forms of the secant stiffness matrix for finite element analysis of solids and trusses. The accuracy and effectiveness of the method are clearly shown in a number of examples of two- and three-dimensional bar structures.  

  Abstract
  A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement [...]

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• A stabilized finite point method for analysis of fluid mechanics problems

  E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

  Comput. Methods Appl. Mech. Engrg., (1996). Vol. 195, pp. 6750-6777

  
  

  Abstract

  flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.

  Abstract
  flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]

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• Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems

  E. Oñate

  Comput. Methods Appl. Mech. Engrg., (1998). Vol. 151 (1-2), pp. 233-265

  
  

  Abstract

  The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow problems is revised in this paper. It is shown that the standard forms of the balancing diffusion terms, usually chosen in a heuristic manner, can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.

  Abstract
  The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow [...]

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• An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites

  E. Car, S. Oller, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 185, pp. 245-277

  
  

  Abstract

  In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material.  The elastic anisotropic behavior  is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The  approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order  tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.

  Abstract
  In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials [...]

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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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