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• Multigrid methods and adaptive refinement techniques in elliptic problems by finite element methods

  M. Storti, N. Nigro, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1991). Vol. 93(1), pp. 13-30

  
  

  Abstract

  Multigrid and adaptive refinement techniques are powerful tools in the resolution of problems arising from computational mechanics. In structured grids the number of numerical operations needed in the resolution via the multigrid method is of order N, the number of degrees of freedom, regardless the dimensionality of the problem. In this work a multigrid technique, which works on unstructured meshes, is described. These meshes are obtained from a user defined tesselation through bisection refinement upon any element. Original techniques for nodes numbering, irregular nodes detection and nodes classification are developed in view of multigrid method implementation. The error indicator used in the refinement process is based on truncation error estimates. The refinement strategy is oriented toward error reduction at constant computational effort. Finally several numerical examples are presented.

  Abstract
  Multigrid and adaptive refinement techniques are powerful tools in the resolution of problems arising from computational mechanics. In structured grids the number of numerical [...]

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• An efficient tangent scheme for solving phase-change problems

  M. Storti, L. Crivelli, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1988). Vol. 66(1), pp. 65-86

  
  

  Abstract

  Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of equations in the nodal temperatures. The Newton-Raphson scheme is an effective procedure to cope with this type of problems; however, the choice of a good approximation to the tangent matrix is critical when the latent heat is comparatively large. In this work we derive an exact expression for the tangent matrix and analyze the behavior of its terms for different values of the physical parameters of the system. We demonstrate that this method has good convergence properties. In fact, the rate of convergence is quadratic when the trial approximation is sufficiently close to the solution. Finally, several numerical examples are given.

  Abstract
  Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of [...]

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• A reduction method for nonlinear structural dynamic analysis

  S. Idelsohn, A. Cardona

  Comput. Methods Appl. Mech. Engrg., (1985). Vol. 49(3), pp. 253-279

  
  

  Abstract

  A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a Rayleigh-Ritz analysis. The basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing. Only a few basis updatings are required during the whole time integration. The truncation error introduced at every change of basis is pointed out as the cause for a divergence-type behaviour, and some means for eliminating it are discussed. Results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations.

  Abstract
  A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from [...]

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• Pre- and post-degradation analysis of composite materials with different moduli in tension and compression

  S. Idelsohn, G. Laschet, C. Nyssen

  Comput. Methods Appl. Mech. Engrg., (1982). Vol. 30 (2), pp. 133-149

  
  

  Abstract

  An isoparametric finite element tor the analysis of multi-layer composite materials is presented. Several linear and nonlinear stress-strain relations are discussed. Special attention is given to the composite materials with different moduli in tension and compression, for which a new mathematical model is presented and tested. Different failure criteria for the matrix degradation are incorporated in the element and several post-degradation behaviors are also considered. Finally we discuss the role of the Newton-Raphson method in composite materials, especially in the presence of geometrical nonlinearities.

  Abstract
  An isoparametric finite element tor the analysis of multi-layer composite materials is presented. Several linear and nonlinear stress-strain relations are discussed. Special [...]

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• On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures

  S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1981). Vol. 26 (3), pp. 321-330

  
  

  Abstract

  This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The intention is to show when it is more suitable to use a particular approximation and to indicate the errors it introduces. Beginning with the general deep shell theory, some simplifications are introduced to obtain the shallow shell theories. The special implications of this theory for the finite element method are also examined. Finally the particular case of flat elements is discussed.

  Abstract
  This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The [...]

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• A formulation for the study, by the method of finite elements, of the deformation of marine pipes during their installation

  J. Oliver, E. Oñate

  Revista de Obras Públicas (1983). Vol. 130 (3218), pp. 747-763

  
  

  Abstract

  La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la necesidad de conocer los esfuerzos y deformaciones que se producen en el tendido de tuberías submarinas, a cuyo estudio, mediante elementos finitos en diversas condiciones de instalación, se dedica este artículo, que permite la obtención de ábacos de cálculo o formulas sencillas aplicables en los distintos casos.

  Abstract
  La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la [...]

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• Decision support system for cardiovascular problems

  E. Soudah, R. López, M. Bordone, E. Oñate

  Monograph CIMNE (2008). M108

  
  

  Abstract

  The two main lines of medical research in this project are vascular anatomy (large vessels around the heart, coronaries and peripheral arteries) and heart chambers. Geometric models will be constructed to aid clinical diagnosis or multiphysical modelling and simulation. Two levels of complexity will be considered. For heart modelling, the first level will concentrate on models of the left and right ventricular cavities for robust and efficient extraction of simple clinical indexes of geometry, volume, mass, and wall kinetics. The second level will aim at more complex, fourchambered models, which will be important in developing comprehensive solid and fluid models to assist the design of medical devices.

  Abstract
  The two main lines of medical research in this project are vascular anatomy (large vessels around the heart, coronaries and peripheral arteries) and heart chambers. Geometric [...]

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• A model of material failure for reinforced concrete via continuum strong discontinuity approach and mixing theory

  D. Linero, J. Oliver, A. Huespe

  Monograph CIMNE (2007). M106

  
  

  Abstract

  In this work a two-dimensional formulation describing the fracture process in reinforced concrete is developed, implemented and validated. The cracks in the material are captured by means of continuum strong discontinuity approach (CSDA) (Oliver 1996) and the constitutive model of composite material is defined through mixing theory (Truesdell & Toupin 1960). The composite material consists of one or two groups of long fibers or steel bars embedded within a concrete matrix. Likewise, each component is characterized by a constitutive model. The concrete is described by a damage model with degradation in tension and compression (Oliver, Cervera et al. 1990). A uniaxial plasticity model (Simó & Hughes 1998) is used for the steel. Also, phenomena as bond-slip and dowel action (Park & Paulay 1975) are included and represented by additional models of interaction between concrete and steel. The initiation and propagation of cracks are understood as a strain localization process described by means of CSDA. A bifurcation analysis of composite material is proposed to establish the bifurcation time and direction of the crack. The model has been implemented in a two-dimensional analysis program using the finite element method (FEM), where it is assumed material non-linearity and infinitesimal strains. An implicit-explicit integration scheme for the constitutive equation (Oliver, Huespe et al. 2004; Oliver, Huespe et al. 2006) ensures a positive defined stiffness matrix of the problem and increases the robustness and stability of the solution. On the other hand, a strategy to tracking discontinuity paths (Samaniego 2002; Oliver & Huespe 2004), allows that the discontinuity paths correspond among the elements. According to the proposed formulation, on each point of solid, the strain and stress fields of the reinforced concrete are described as a composite material. This has the following advantages: first, the model facilitates the implementation on the finite element method, since many ingredients of standard numerical process remain, and secondly, the macroscopic scale of analysis avoids the discretization of each component material and the interaction effects, and consequently the computational cost is reduced. The model can reproduce two different stages of cracking in the reinforced concrete. Initially, the steel capacity and the adherence in the interface produce a stable stage of distributed cracking, where appear many cracks with constant spacing and opening. Afterward, a localization cracking stage is characterized by few cracks while the structural response decreases. Reinforced concrete members subjected to tension, bending and shear are simulated. The numerical results, mainly the structural response and the crack pattern, are compared with experimental test (Leonhardt 1965; Collins, Vecchio et al. 1985; Ouyang & Shah 1994; Ruiz, Elices et al. 1998). The correlation between numerical results using the proposed formulation and actual results is quantitative and qualitatively satisfactory.

  Abstract
  In this work a two-dimensional formulation describing the fracture process in reinforced concrete is developed, implemented and validated. The cracks in the material are [...]

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• Contribuciones a la simulación numérica del fallo material en medios tridimensionales mediante la metodología de discontinuidades fuertes de continuo

  S. Blanco, J. Oliver, A. Huespe

  Monograph CIMNE (2007). M105

  
  

  Abstract

  Esta monografía presenta una reformulación de la metodología de discontinuidades fuertes de continuo para la simulación numérica del fallo material de estructuras. Los objetivos buscados han sido mejorar la robustez de este tipo de análisis numérico y proporcionar una serie de herramientas que garanticen la confiabilidad de los resultados obtenidos. La metodología de discontinuidades fuertes de continuo [50]-[51] es una aproximación numérica al fenómeno de la localización de deformaciones por ablandamiento. Al contrario de las aproximaciones discretas, utiliza un formato continuo tensión-deformación para describir todo el proceso de agotamiento del material. Gracias a una regularización (reinterpretación) de la cinemática del problema y del módulo de ablandamiento se garantiza que la disipación del modelo venga dada por la densidad superficial de energía de fractura [52]. Adicionalmente, la utilización de un algoritmo tipo térmico de captura y gestión de las superficies de localización de deformaciones permite abordar el análisis de problemas con multifisuración [57]. La mejora en la robustez del análisis numérico se ha conseguido adoptando la formulación simétrica cinemáticamente consistente y formulando un nuevo esquema de integración, denominado IMPL-EX, que garantiza la definición positiva de los operadores algorítmicos que intervienen en el problema. La confiabilidad en el resultado numérico se asegura mediante un algoritmo de control del error cometido y mediante un nuevo esquema de limitación de la longitud de arco. Estos dos algoritmos han sido desarrollados específicamente para el esquema de integración IMPL-EX. La formulación así definida ha sido aplicada en el estudio de dos fenómenos propios de la mecánica de la fractura: el estudio de la influencia del tamaño de una estructura en su resistencia nominal (efecto tamaño) y el estudio/medición de la longitud de procesamiento de fractura. Por último se presentan una serie de ensayos numéricos del fallo material en estructuras tridimensionales. Estos ensayos se dividen en tres grupos: ensayos donde el modo de fallo predominante es en modo I, ensayos donde el modo de fallo predominante es de deslizamiento (análisis de taludes) y ensayos donde el modo de fallo moviliza mecanismos resistentes tridimensionales (análisis del efecto arco en presas con simple y doble curvatura).

  Abstract
  Esta monografía presenta una reformulación de la metodología de discontinuidades fuertes de continuo para la simulación numérica del fallo [...]

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• A finite element method for solving the incompressible Navier-Stokes equations at low and high Reynolds numbers using finite calculus. Application to fluid-structure interaction

  H. Lynga, E. Oñate

  Monograph CIMNE (2007). M104

  
  

  Abstract

  The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus (FIC), which is a methodology developed by E. On˜ate and co-workers at CIMNE (International Center for Numerical Methods in Engineering),  flows with a wide range of Reynolds numbers can be modeled. The secondary objective is to test the applicability of the FIC/FEM model to fluid-structure interaction (FSI) emphasizing aero-elasticity. The implementation of the model is carried out within KRATOS, a finite element code for solving multi-physics problems developed at CIMNE.

  Abstract
  The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus [...]

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