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The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. (English) Zbl 0976.74078
From the summary: We develop the meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. The present method is a truly meshless method, as it need not use a “finite element mesh”, either for purposes of interpolation of solution variables, or for the integration of energy. All integrals in the formulation can be easily evaluated over regularly shaped domains (in general, spheres in three-dimensional problems) and their boundaries. The essential boundary conditions in the present formulation are imposed by a penalty method, as the essential boundary conditions cannot be enforced directly when the non-interpolative moving least squares approximation is used. Several numerical examples are presented to illustrate the performance of the method.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
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