LAUSR

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).