Generalized finite integration method for 2D elastostatic and elastodynamic analysis

In this paper, the elastostatic and elastodynamic problems are analyzed by using the meshless generalized finite integration method (GFIM). The idea of the GFIM is to construct the integration matrix and the arbitrary functions by piecewise polynomial with Kronecker product, which leads to a significant improvement in accuracy and convenience. However, the traditional direct integration in the GFIM is difficult to deal with a large number of arbitrary functions generated in elastic problems. In order to tackle this problem, a special technique is proposed to construct relationships among arbitrary functions in this paper. Also, the Laplace transform method and the Durbin's inversion technique are adopted to deal with the variables of time in the elastodynamic problem. Several numerical examples are presented to demonstrate the accuracy and stability of the GFIM. © 2024 International Association for Mathematics and Computers in Simulation (IMACS)