Elastodynamic problems by meshless local integral method: Analytical formulation

In this paper, analytical forms of integrals in the meshless local integral equation method in the Laplace space are derived and implemented for elastodynamic problems. The meshless approximation based on the radial basis function (RBF) is employed for implementation of displacements. A weak form of governing equations with a unit test function is transformed into local integral equations. A completed set of the local boundary integrals are obtained in closed form. As the closed form of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically. Several examples including dynamic fracture mechanics problems are presented to demonstrate the accuracy of the proposed method in comparison with analytical solutions and the boundary element method.