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• A Finite Element formulation for the numerical solution of the convection-diffusion equation

  R. Codina

  Monograph CIMNE (1993). M14

  
  

  Abstract

  In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, tha is, when diffusion is very small. The basic finite element formulation employed here is the Streamline-Upwind-Petrov-Galerkin (SUPG). A thorough description of this approach is presented in Chapter 1. Chapter 2 deals with the application of the generalized trapezoidal rule to advance in time for the transient equation. A complete stability and accuracy analysis is performed for the explicit Euler scheme, both using linear and quadratic finite elements. Chapter 3 is concerned with the problem of removing the localized oscillations that remain about abrupt layers of the solution.

  Abstract
  In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, tha is, when diffusion is very [...]

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• Mechanics of a continuum medium. Vol. III

  A. Fusco

  Monograph CIMNE (1993). M20

  
  

  Abstract

  This work presents the fundamental assumptions and the successive mathematical developments which allow to establish the complete field equations of a continuum. The aim is to be sufficiently general and self-content using, however, mathematical procedures which can be always understook by an engineer with a common background of Linear Algebra and elementary Differential Calculus.

  Abstract
  This work presents the fundamental assumptions and the successive mathematical developments which allow to establish the complete field equations of a continuum. The aim is [...]

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• A Finite Element formulation for viscous incompressible flows

  R. Codina

  Monograph CIMNE (1993). M16

  
  

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• Modelado de la fisuración en estructuras de hormigón

  J. Oliver

  Monograph CIMNE (1993). M15

  
  

  Abstract

  En este trabajo, se presenta una perspectiva general de los modelos de fisuración existentes y de algunas aportaciones de la línea de investigación que se desarrollan, tanto en el dominio de la formulación teórica de dichos modelos como de su aplicación práctica.

  Abstract
  En este trabajo, se presenta una perspectiva general de los modelos de fisuración existentes y de algunas aportaciones de la línea de investigación que [...]

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• Particle finite element method in fluid-mechanics including thermal convection-diffusion

  R. Aubry, S. Idelsohn, E. Oñate

  Computers and Structures (2005). Vol. 83 (17-18), pp. 1459-1475

  
  

  Abstract

  A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed.

  Abstract
  A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due [...]

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• A Lagrangian meshless finite element method applied to fluid–structure interaction problems

  S. Idelsohn, E. Oñate, F. Del Pin

  Computers and Structures (2003). Vol. 81 (8-11), pp. 655-671

  
  

  Abstract

  A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.

  Abstract
  A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are [...]

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• Lectures on nonlinear finite element analysis of concrete shells

  E. Oñate

  Monograph CIMNE (1991). M7

  
  

  Abstract

  This monograph presents 4 lectures on non linear analysis of concrete shells by the finite element method. The lectures were prepared by the author for the course on "Non linear analysis of shells by finite elements" held at the International Center for Mechanics Sciences in Udine, Italy on June 24-28th 1991. The content of the lectures presents an overview of the different aspects involved in the analysis of concrete shells by finite elements. Thus, Lecture 1 introdeuces the basic concepts of the analysis of reinforced concrete shell structures using flat shell and curved degenerated layered shell finite elements. Both the geometric and kinematic assumptions are described in detail together with the respective finite element formulation and the numerical algorithm for non linear elasto-plastic analysis including the effect of moderately large displacements. Lecture 2 presents an overview of the constitutive behaviour of concrete and steel in a form suitable for numerical computations using the finite element models described in previous lecture. The reinforcing steel bars are modelled with a simple elasto-plastic model. Hovewer, two conceptualy different concrete models are presented. The first model is based on elasto-plastic theory to describe the compressive behaviour of concrete, whereas a linear orthotropic elasto-brittle model is used for modelling the cracking behaviour under tensile conditions. This ``elasto-platic-brittle model has been extensively used by Owen and Figueiras and most of the concepts presented emanate from reference [18] of this chapter. The second model is based on the assumptions that both the tensile and compressive behaviour of concrete can be treated under the unified framework of elasto-plasticity theory. This model termed ``plastic-damage model has ben proposed by Lubliner, Oller, Oliver and O\~nate in different publications which main concepts are summarized in the lecture (see refs. [33-38] of this chapter). In Lecture 3 the basic finite element formulation for the analysis of stiffened concrete shells via the use of eccentric beams is described. Finally, in Lecture 4 some examples of applications of the finite element formulations presented to the non-linear analysis of different reinforced concrete shell structures analyzed by different authors are described. Examples included range from the analysis of plain and pre-stressed concrete deep beams, to more sophisticated shell type structures including the nonlinear behaviour of a composite steel-concrete girder bridge and a cryogenic concrete liquid gas tank under severe thermal conditions. This monograph has been written exclusively with didactic purposes. Most of the ideas included in the text have been extracted from research publications by the author and many others. The interested reader will be able to find details on the different subjects treated in the many references included at the end of each chapter.

  Abstract
  This monograph presents 4 lectures on non linear analysis of concrete shells by the finite element method. The lectures were prepared by the author for the course on "Non [...]

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• Análisis dinámico de presas

  J. Miquel, E. Oñate, J. Buil, E. Herrero

  Monograph CIMNE (1991). M5

  
  

  Abstract

  Se desarrolla en este trabajo un estudio numérico-experimental acerca del comportamiento dinámico de las presas bóvedas considerando su interacción con el agua del embalse. Para ello, se ha realizado un análisis de los factores que inciden más directamente en el comportamiento dinámico de tales tipos de estructuras. Dicho análisis se realiza mediante e lmétodo de los elementos finitos, estudiando distintas alternativas de formulación. Asimismo, se ha realizado un esayo a escala real de una presa bóveda existente, mediante una serie de explosiones y midiendo la respuesta obtenida.

  Abstract
  Se desarrolla en este trabajo un estudio numérico-experimental acerca del comportamiento dinámico de las presas bóvedas considerando su interacción [...]

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• Simulación Numérica de Patologías en Presas de Hormigón

  M. Cervera, J. Oliver, M. Galindo

  Monograph CIMNE (1991). M4

  
  

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• Stress, strain and energy splittings for anisotropic elastic solids under volumetric constraints

  C. Felippa, E. Oñate

  Computers and Structures (2003). Vol. 81 (13), pp. 1343-1357

  
  

  Abstract

  We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.

  Abstract
  We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, [...]

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