A meshless local Petrov-Galerkin (MLPG) formulation for static and free vibration analyses of thin plates

A meshless method for the analysis of Kirchhoff plates based on the Meshles s Local Petrov-Galerkin (MLPG) concept is presented. A MLPG formulation is developed for static and free vibration analyses of thin plates. Local weak form is derived using the weighted residual method in local supported doma ins from the 4th order partial differential equation of Kirchhoff plates. T he integration of the local weak form is performed in a regular-shaped loca l domain. The Moving Least Squares (MLS) approximation is used to construct ed shape functions. The satisfaction of the high continuity requirements is easily met by MLS interpolant, which is based on a weight function with hi gh continuity and a quadratic polynomial basis. The validity and efficiency of the present MLPG method are demonstrated through a number of examples o f thin plates under various loads and boundary conditions. Some important p arameters on the performance of the present method are investigated thoroug hly in this paper. The present method is also compared with EFG method and Finite Element Method in terms of robustness and performance.