A Meshless Local Petrov-Galerkin (MLPG) Formulation for Static and Free Vibration Analyses of Thin Plates
Y. T. Gu and G. R. Liu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 2, No. 4, pp. 463-476, 2001
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Keywords Meshless Method; Meshless Local Petrov-Galerkin (MLPG) method; Kirchhoff plates; Free Vibration; Numerical Analysis
Abstract A meshless method for the analysis of Kirchhoff plates based on the Meshless 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 domains from the 4th order partial differential equation of Kirchhoff plates. The integration of the local weak form is performed in a regular-shaped local domain. The Moving Least Squares (MLS) approximation is used to constructed shape functions. The satisfaction of the high continuity requirements is easily met by MLS interpolant, which is based on a weight function with high continuity and a quadratic polynomial basis. The validity and efficiency of the present MLPG method are demonstrated through a number of examples of thin plates under various loads and boundary conditions. Some important parameters on the performance of the present method are investigated thoroughly in this paper. The present method is also compared with EFG method and Finite Element Method in terms of robustness and performance.
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