A modified meshless local Petrov–Galerkin method to elasticity problems in computer modeling and simulation

A modified meshless local Petrov–Galerkin (MLPG) method is presented for elasticity problems using the moving least squares (MLS) approximation. It is a truly meshless method because it does not need a mesh for the interpolation of the solution variables or for the integration of the energy. In this paper, a simple Heaviside test function is chosen to overcome the computationally expensive problems in the MLPG method. Essential boundary conditions are imposed by using a direct interpolation method based on the MLPG method establishes equations node by node. Numerical results in several examples show that the present method yielded very accurate solutions. And the sensitivity of the method to several parameters is also studied in this paper.