Solution of Linear Elastostatic Plane Problems by the Meshless Local Petrov-Galerkin Method

The Meshless Local Petrov-Galerkin (MLPG) method is adopted to solve plane strain/stress solid mechanics problems. The MLPG method requires only a set of nodes both for the interpolation of the solution variables and the evaluation of various integrals appearing in the problem formulation. The MLPG formulation including the moving least squares method, the choice of the weight function, the local symmetric weak form (LSWF), and the discretization of the weak form are presented. A code based on the MLPG method is developed, and three numerical examples, namely, a cantilever beam loaded by tangential tractions at the unclamped edge, an infinite plate with a circular hole subjected to a uniform tensile force at infinity, and a hollow circular cylinder subjected to a pressure on the inner surface are demonstrated to validate the developed code.