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Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. (English) Zbl 1357.74079
Summary: The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the collocation method. The traction boundary conditions are also imposed into the stress equations directly. It becomes very simple and straightforward to impose various boundary conditions, especially for the high-order PDEs. Numerical examples show that the proposed MLPG mixed collocation method possesses a stable convergence rate, and is more efficient than the other MLPG implementations, including the MLPG finite volume method.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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