engleski

On the enforcement of Neumann boundary conditions in the mixed MLPG collocation method for 2-D linear elastic problems

The mixed MLPG collocation strategy is studied, where the stress and displacement fields are approximated separately by using same trial functions. Compatibility between the approximated stresses and displacements is enforced at certain points, most often the discretization nodes, in order to eliminate the nodal stress variables from the discretized governing equations. For equal number of nodes, collocation methods are faster than the methods based on the integration of weak forms, but they suffer from numerical instabilities and the lack of accuracy caused by the inaccurate imposition of Neumann boundary conditions. In this contribution, different procedures for the enforcement of the Neumann boundary conditions (BCs) are used, including the direct collocation approach, the penalty method and the application of the local weak forms near the boundary with prescribed Neumann BCs. The approximation schemes used in this work include the interpolating Moving Least Squares (IMLS)and polynomial Point Interpolation Method (PPIM). They possess the interpolation property at the nodes, which enables a simple enforcement of the essential BCs, like in FEM. The accuracy and numerical efficiency of the proposed approaches for the enforcement of natural BCs are demonstrated by a set of suitable numerical examples and the results are compared to a corresponding mixed meshless approach based on the integration of a local weak form.

mixed MLPG collocation method ; Neumann boundary conditions ; direct collocation ; penalty method

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