Genie Mecanique

ABSTRACT Kinematical approach by limit analysis is one of the fundamental methods used to predict the plastic limit state and it is applied successfully to deal with engineering problems in solid mechanics. The kinematical approach consists of minimizing the plastic dissipation power throughout the body, produced by plasticity, which involves functional with norm integrand. Besides, to derive the stress field within the body, one uses the inverse plastic law that is a subdifferential of the dissipation power. The complexity and possible singularity in the derivatives of functionals become a source of many numerical troubles. To overcome these encountered difficulties, we propose a solving algorithm by using a regularization procedure on the basis of the inf-convolution operation. Some numerical applications by plane strain or axisymmetric finite element method are presented to illustrate the algorithm. Copyright © 2003 John Wiley & Sons, Ltd.

ABSTRACT We present a theoretical and numerical analysis of incremental elasto-plastic problems based on the meshless method and the mathematical programming. This study is done on an elasto-plastic material with isotropic hardening obeying to the von Mises criterion. The transformation method is adopted to impose the essential boundary condition. The Coulomb's dry friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential method which leads to only one principle of minimum in displacement. The numerical analysis results obtained by the method proposed in this paper are in good agreement with those obtained by FEM.

ABSTRACT Limit analysis is one of the most fundamental methods of plasticity. For the nonstandard model, the concept of the bipotential, representing the dissipated plastic power, allowed us to extend limit analysis theorems to the nonassociated flow rules. In this work, the kinematic approach is used to find the limit load and its corresponding collapse mechanism. Because the bipotential contains in its expression the stress field of the limit state, the kinematic approach is coupled with the static one. For this reason, a solution of kinematic problem is obtained in two steps. In the first one, the stress field is assumed to be constant and a velocity field is computed by the use of the kinematic theorem. Then, the second step consists to compute the stress field by means of constitutive relations keeping the velocity field constant and equal to that of the previous step. A regularization method is used to overcome problems related to the nondifferentiability of the dissipation function. A successive approximation algorithm is used to treat the coupling question. A simple compression-traction of a nonassociated rigid perfectly plastic material and an application of punching by finite element method are presented in the end of the paper.

ABSTRACT Que ce soit dans un objectif de conception de structures ou de mise en forme par déformation plastique, l’analyse limite est parmi les méthodes directes d’estimation des états limites plastiques les plus connues. En se basant sur l’approche cinématique au sens de l’analyse limite et en se servant de la méthode des éléments finis, l’objectif principal de ce travail consiste à aborder les grandes déformations plastiques du modèle de von Mises en considérant l’écrouissage isotrope. Afin de surmonter la difficulté engendrée par la nondifférentiabilité de la dissipation plastique, nous avons particularisé une méthode de régularisation initialement développée pour les matériaux compressibles. Dans le but de suivre les séquences de grandes déformations, la notion d’analyse limite séquentielle qui consiste en la mise à jour des propriétés des matériaux et de la géométrie de configuration après chaque séquence est appliquée.