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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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• Diseño de aliviaderos de bloques en forma de cuña

  J. Mauro, M. Toledo

  Monograph CIMNE (2018). M180

  
  

  Abstract

  Los aliviaderos de bloques en forma de cuña son una tipología innovadora que permite el sobrevertido sobre el cuerpo de presas de materiales sueltos de una manera segura, con la consiguiente ventaja económica que presenta frente a las soluciones habituales de aliviaderos exentos de hormigón. Sin embargo apenas se ha aplicado esta solución de aliviadero por algunas incertidumbres que plantea, fundamentalmente en cuanto al desarrollo de presiones intersticiales en la capa granular de apoyo de los bloques y sus efectos sobre la estabilidad de los mismos, así como por la ausencia de procedimientos técnicos de diseño. En esta monografía se ha propuesto un procedimiento completo para el diseño de aliviaderos con bloques en forma de cuña, el cual se ha automatizado mediante el desarrollo de un código informático propio. Como base para el desarrollo del procedimiento de diseño se han desarrollado varias campañas de modelación numérica, respaldadas por ensayos de validación en modelo físico. De tal forma que se caracterizó el comportamiento de la capa de drenaje y sus condiciones de saturación, se desarrolló un método para el ajuste numérico-experimental de leyes de pérdida de carga parabólica en medios porosos, así como una formulación para el cálculo del coeficiente de seguridad a deslizamiento de una capa de drenaje parcialmente saturada. También se calibró y validó un método numérico para reproducir el fenómeno de infiltración entre bloques. Finalmente se caracterizó la estabilidad de los bloques en forma de cuña ante acciones de vandalismo y frente a solicitaciones hidráulicas debidas al sobrevertido. Según los resultados obtenidos en las campañas de modelación se propone un procedimiento de cálculo que permite definir la geometría apropiada de aliviadero, garantizando la estabilidad del cuerpo de presa, de la capa de drenaje y de los propios bloques, evitando la subpresión en el apoyo granular de los mismos con las incertidumbres que ello acarrea.

  Abstract
  Los aliviaderos de bloques en forma de cuña son una tipología innovadora que permite el sobrevertido sobre el cuerpo de presas de materiales sueltos de una manera [...]

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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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