An efficient local RBF-based method for elasticity problems involving multiple material phases

Abstract

This work concerns a numerical solution for two-dimensional elasticity problems involving multiple material phases. We consider a localized collocation method based on radial basis functions (RBFs), namely RBF-generated finite difference (RBF-FD). The mesh-free RBF-FD method based on polyharmonic spline (PHS) RBFs with polynomial augmentation has been proved to be an effective tool for solving partial differential equations (PDEs) on irregular domains. The PHS+poly based RBF-FD method provides highly accurate results while bypassing the stagnation errors and the limitations imposed by stability concerns associated with the shape parameter values. We utilize the present method to treat the elasticity problems with arbitrary interfaces in multiply connected domains. To find the appropriate solution near the material interfaces, we employ the domain decomposition technique. In this technique, we construct the approximation in each domain separately and then impose proper jump conditions along the interfaces separating multiple material phases. Several problems involving arbitrary interfaces are solved to illustrate the effectiveness of the proposed method for this class of multi-domain coupled systems. Its performance is also discussed in comparison with that of other methods in the recent literature.