Une technique sans maillage pour simuler l'écoulement d'un fuide compressible à surface libre

Dans cette communication, nous présentons une méthode sans maillage couplée avec une technique implicite d'ordre élevé pour la simulation des écoulements de fuides compressibles. Les dificultés de la mise en oeuvre numérique sont axées sur les équations du mouvement et les conditions aux limites. Cet algorithme combine les procédures mathématiques suivantes: une discrétisation en temps, une méthode des moindres carrés mobiles MLS, une transformation d'homotopie, un développement en séries de Taylor et d'une méthode de continuation [1, 2, 3]. L'algorithme proposé permet d'obtenir un grand nombre de pas de temps qui minimise le nombre de décompositions de matrices tangentes. La formulation forte est considérée pour éviter l'inconvénient d'intégration numérique. Les conditions aux limites de la surface libre sont traitées par la technique de collocation qui est la plus appropriée pour les grandes déformations sans la nécessité de redénir le maillage

Numerical model based on meshless method to simulate FSW

In the present work, a numerical models based on the meshless method “the smoothed particle hydrodynamics (SPH)” is developed to simulate the Friction Stir Welding (FSW). This technique type is well adapted to modeling of mixing zone which is subjected to high strain rate. We limit ourselves to two dimensional problems

A 2D Fourier double scale analysis of global-local instability interaction in sandwich structures

In sandwich structures, with a soft core and stiff skins, under in-plane compressive loading, global buckling of the whole structure and local wrinkling on the skin can occur. Several works have been developed to investigate the buckling and post-buckling behavior of sandwich structures (Léotoing, Drapier and Vautrin, IJSS, EJM-A 2002). The bifurcation analysis according to the Landau–Ginzburg equation can be used to study these instabilities, which follows from an asymptotic double scale analysis. This bifurcation equation is valid only close to the critical state and it is not able to account for the coupling between a global non-linear behavior and the appearance of wrinkles. A new approach has been presented by Damil and Potier-Ferry (EJCM 2008, JMPS 2010) that is based on the concept of Fourier series with slowly varying coefficients. The obtained models are consistent with the Landau–Ginzburg theory, but they may also remain valid away from the bifurcation point and the coupling between global and local instabilities can be accounted for. In this work, we present a new Fourier double scale analysis to study the interaction of local wrinkling and global buckling of 2D sandwich structures. By this way, a 2D microscopical sandwich model is transformed into 2D macroscopical one and only the envelopes of instability patterns are numerically evaluated. This new non-linear macroscopic 2D model of sandwich structures is then solved by the Asymptotic Numerical Method (Cochelin, Damil and Potier-Ferry, IJNME 1994). The proposed 2D Fourier double scale model of sandwich structures is validated by comparison with the 1D Fourier double scale model of sandwich structures of Liu, Yu, Hu, Belouettar, Potier-Ferry and Damil, IJSS 2012 and the 2D microscopical model. Accurate results have been obtained

COUPLING OF MFS AND ANM FOR SOLVING NONLINEAR ELASTICITY PROBLEMS

In this work, we propose an algorithm that combines the Method of Fundamental Solutions (MFS) with the Asymptotic Numerical Method (ANM) for solving nonlinear elasticity problems. The ANM allows one to transform the nonlinear differential equations into a sequence of linear differential equations having the same tangent operator. Each linear resulting problem is then solved by using MFS. This last technique belongs to meshless collocation methods which has attracted considerable attention in recent years. It consists in constructing the solution by considering a linear combination of fundamental solutions of the differential operator. Regularization methods such as Truncated Singular Value Decomposition (TSVD) associated with the Generalized Cross Validation (GCV) criterion have been used to solve the ill-conditioned resultant linear systems. Two examples of nonlinear elasticity problems have been studied and have shown the robustness of the proposed algorithm