The solution of elastodynamic problems using modified radial integration boundary element method (MRIBEM)

In this paper, the modified radial integration boundary elements method (MRIBEM) is applied to analyze twodimensional (2D) elastodynamic problems. The boundary and domain variables are approximated by Lagrangian shape functions and global radial basis functions (RBFs), respectively. As a key idea of this study, the domain integrals that result from implying the inertia force effect are computed by means of a modified radial integration method (MRIM). With the MRIBEM, we are able to deal with problems with concave shapes when the domain variables are approximated by global RBFs by defining an auxiliary point or, in case of complex domain shapes, two or more auxiliary points as the origin for radial integration. Two-time marching schemes, i.e. Newmark method and the Houbolt method, are implemented for the solution of governing differential equations along time. The performance of the proposed method is examined in the solution of four numerical examples.

Automated summary

This paper presents a modified radial integration boundary elements method for analyzing two-dimensional elastodynamic problems. The method can handle problems with concave shapes and uses two-time marching schemes. The performance of the method is examined through numerical examples.