Analyze of 3D Elasto-Static Problems by Meshless Local Petrov-Galerkin Method

A truly meshless local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the Heaviside function. The moving least squares (MLS) are chosen to construct the shape functions, for the MLPG method. The penalty approximation is used to impose essential boundary condition. Several numerical examples are included to demonstrate that the present method is very promising for solving the elastic problems.