Method of fundamental solutions and high order algorithm to solve nonlinear elastic problems Article - Avril 2018

Omar Askour, Abdeljalil Tri, Bouazza Braikat, Hamid Zahrouni, Michel Potier-Ferry

Omar Askour, Abdeljalil Tri, Bouazza Braikat, Hamid Zahrouni, Michel Potier-Ferry, « Method of fundamental solutions and high order algorithm to solve nonlinear elastic problems  », Engineering Analysis with Boundary Elements, avril 2018, pp. 25-35. ISSN 0955-7997

Abstract

In this work, we propose an algorithm, which combines the Method of Fundamental Solutions (MFS) and the Asymptotic Numerical Method (ANM), to solve two-dimensional nonlinear elastic problems. Thanks to the development in Taylor series, nonlinear elastic problem is transformed into a succession of linear differential equations with the same tangent operator. Recognizing that the fundamental solution is not always available, the Method of Fundamental Solutions-Radial Basis Functions (MFS-RBF) is combined with the Analog Equation Method (AEM) to solve these resulting linear equations. Regularization methods such as Truncated Singular Value Decomposition (TSVD) and Tikhonov regularization associated with the L-curve or Generalized Cross Validation (GCV) criterion have been used to control the resulting ill-conditioned linear systems. The efficiency of the proposed algorithm (MFS-ANM) is validated by comparing the obtained results with those of the classical algorithm based on the finite element method (FEM-ANM)

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