The meshless finite point method for transient elastodynamic problems

Abstract

In this paper, the application of the meshless finite point method (FPM) to solve elastodynamic problems through an explicit velocity–Verlet time integration method is investigated. Strong form-based methods, such as the FPM, are generally less stable and accurate in terms of satisfaction of Neumann boundary conditions than weak form-based methods. This is due to the fact that in such types of methods, Neumann boundary conditions must be imposed by a series of equations which are different from the governing equations in the problem domain. In this paper, keeping all the advantages of FPM in terms of simplicity and efficiency, a new simple strategy for proper satisfaction of Neumann boundary conditions in time for elastodynamic problems is investigated. The method is described in detail, and several numerical examples are presented. Moreover, the accuracy of the method with reference to the solution of some 3D problems is discussed.