Meshless generalized finite difference method for two- and three-dimensional transient elastodynamic analysis

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 equa-tions 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.

Automated summary

This paper introduces a meshless collocation method for 2D and 3D transient elastodynamic problems. The method combines the generalized finite difference method (GFDM) with the Houbolt scheme to transform the coupled equilibrium equations into static equations at time nodes. The GFDM with second-order and fourth-order expansions is then used to solve the static equations and obtain the solution.