A Fully Explicit Point Collocation Meshless Method for Analyses of Elasto-Dynamic Problems

This paper describes a numerical approach to analyze elasto-dynamic problems using a point collocation meshless method. This method is based on the explicit time integration of equilibrium equations to compute the velocity domain of the deformed area. The stress and strain domains are updated by stress and strain rates obtained from velocity domains using Cauchy strain relations. Reproducing kernel particle method (RKPM)is used to derive meshless shape functions and their derivatives. This meshless point collocation explicit method does not require any special treatment for either essential boundary conditions or natural boundary conditions and can analyze any damping equation. In this research strain rate based damping is used. Some tests are analyzed and the results are presented. Numerical test results showed that this fully explicit meshless approach is a powerful method to analyze dynamic deformations

Keywords:

Explicit time integration , Point collocation , Reproducing kernel particle method , Strain rate based damping