The extrinsic enriched finite element method based on RBFs for linear elastic solid dynamic analysis

A novel extrinsic enriched finite element method (EFEM) based on radial basis functions (RBFs) is proposed for dynamic analysis of linear elastic solids to obtain accurate numerical solutions and avoid the potential linear dependence (LD) problem. In the proposed method, the RBFs are used in conjunction with the linear polynomial functions from the conventional finite element method (FEM) to construct the nodal interpolation functions. Moreover, the approximation space formed by the RBFs is enriched using enrichment functions based on the partition of unity (PU) concept without requiring any extra nodes. The LD issue commonly encountered in PU-based methods is effectively avoided by the present RBF formulation. In this paper, free and forced vibrations of a series of classical numerical models are simulated using both the proposed method and the conventional FEM. The results demonstrate that the proposed method achieves better computational accuracy and efficiency. Additionally, sufficiently accurate numerical solutions are obtained even when distorted meshes are used. With the proposed approach, essential and natural boundary conditions can be directly imposed as in the conventional FEM. Therefore, the proposed method may offer a promising alternative to the conventional FEM for dynamic analysis of linear elastic solids.