MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD

Abstract

Meshfree methods are effective tools for solving partial differential equations. The radial point interpolation method, a partial differential equation solver based on a meshfree approach, enables accurate imposition of displacement boundary conditions and has been successfully applied to elastostatic analysis of various kinds of three-dimensional solids. In this method, stiffness matrix construction accounts for the majority of CPU time required for the entire process, resulting in high computational costs, especially when higher-order numerical integration is applied for accurate matrix construction. An alternative method, modified radial point interpolation, was proposed to overcome this shortcoming and has accomplished fast computation of elastostatic solid analysis. The purpose of this study is to develop an algorithm for time-dependent simulation of three-dimensional elastic solids. We show that the modified radial point interpolation method also accelerates the construction of the mass matrix required for time-dependent analysis in addition to that of the stiffness matrix. In our approach, the problem domain is assumed to have an implicit function representation that can be constructed from a set of surface points measured using a three-dimensional scanning system. Several numerical tests for elastodynamic analysis of complex shape models are presented.