A MOVING KRIGING INTERPOLATION-BASED MESHLESS LOCAL PETROV–GALERKIN METHOD FOR ELASTODYNAMIC ANALYSIS

A meshless local Petrov–Galerkin method (MLPG) based on the moving Kriging interpolation for elastodynamic analysis is presented in this paper. The present method is developed based on the moving Kriging interpolation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each subdomain to avoid the need for domain integral in symmetric weak form. Since the shape functions constructed by this moving Kriging interpolation have the delta function property, the essential boundary conditions can be implemented easily, and no special treatment techniques are required. The discrete equations of the governing elastodynamic equations for two-dimensional solids are obtained using the local weak-forms. The Newmark method is adopted for the time integration scheme. Some numerical results are compared to that obtained from the exact solutions of the problem and other (meshless) methods. This comparison illustrates the efficiency and accuracy of the present method for solving the static and dynamic problems.