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.

An Abaqus UEL implementation of the smoothed finite element method

“…To alleviate some of the aforementioned challenges, recent research has been focused on alternative approaches, viz., meshfree methods [2][3][4][5][6], partition of unity methods (PUM) [7][8][9][10][11], strain smoothing techniques [12,13] and polygonal finite element method (PFEM) [14][15][16][17]. The meshfree methods does not have a priori topology which makes it suitable for large deformation problems and moving boundary problems [18][19][20].…”