Three-dimensional elastodynamic analysis employing the generalized finite difference method with arbitrary-order accuracy

Abstract

This study introduces an efficient numerical methodology for the analysis of three-dimensional (3D) elastodynamics, featuring high-order precision in the temporal and spatial domains. In the temporal discretization process using the Krylov deferred correction (KDC) technique, the second-order time derivative is treated as a new variable in the governing equations. Spectral integration is then employed to mitigate the instability associated with numerical differentiation operators. Additionally, an improved numerical implementation of boundary conditions based on time integration is incorporated into the KDC approach. The boundary value problems at time nodes resulting from the above discretization process are resolved by employing generalized finite difference method (GFDM), providing the flexibility to choose the Taylor series expansion order. We present four numerical examples to indicate the performance of the developed method in the accuracy and stability. The obtained numerical results are meticulously compared with either analytical solutions or those calculated using COMSOL software.