Meshless generalized finite difference method for two- and three-dimensional transient elastodynamic analysis - Sun, Wenxiang; Qu, Wenzhen; Gu, Yan; Zhao, Shengdong (Engineering analysis with boundary elements, 2023)
In this paper, a meshless collocation method is introduced for two-dimensional (2D) and three-dimensional (3D) transient elastodynamic problems by applying the generalized finite difference method (GFDM) in conjunction with the Houbolt scheme. Coupled equilibrium equations with a time-dependent loading are transformed into the static equations at time nodes by adopting the Houbolt method. After then, the solution of the static equations is achieved with the GFDM with second-order and fourth-order expansions. Several numerical examples involving complicated geometries and different initial and boundary conditions are simulated to validate the performance of the present approach.