A Meshless Local Petrov-Galerkin (MLPG) Approach Based on the Regular Local Boundary Integral Equation for Linear Elasticity

Abstract

The moving local Petrov-Galerkin (MLPG) approach based on a regular local boundary integral equation (RLBIE) to solve problems in elasto-statics is developed. The present method is a truly meshless method, as absolutely no mesh connectivity is required for interpolating the solution variables and for integrating the weak form. Compared to the original MLPG method, the present method does not need the derivatives of the shape functions in constructing the stiffness matrix for those nodes with no displacement specified on their local boundaries. The numerical examples presented in the paper show that high rates of convergence with mesh refinement for the displacement and energy norms are achievable.

Keywords:

• Meshless Methods
• Local Boundary Integral Equation
• MLPG
• Moving Least Squares Approximation