Meshless local integral equation method for two-dimensional nonlocal elastodynamic problems

Abstract

Abstract. This paper presents the meshless local integral equation method (LIEM) for nonlocal analyses of two-dimensional dynamic problems based on the Eringen's model. A unit test function is used in the local weak-form of the governing equation and by applying the divergence theorem to the weak-form, local boundary-domain integral equations are derived. Radial Basis Function (RBF) approximations are utilized for implementation of displacements. The Newmark method is employed to carry out the time marching approximation. Two numerical examples are presented to demonstrate the application of time domain technique to deal with nonlocal elastodynamic mechanical problems.

The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems

“…A meshless local integral method for two-dimensional elastodynamic fracture problems by the Laplace transform technique is proposed [43]. The Newmark method is generally selected as an approximation scheme to deal with time-dependent cases [44][45][46].…”