engleski

A mixed MLPG formulation for plate analysis using a quadtree-based discretization

The Meshless Local Petrov-Galerkin (MLPG) Method does not require any kind of element mesh or background cells for either interpolation or integration. However, certain issues, such as the generation of a proper set of nodes, determination of optimal parameters for numerical analysis and high computational costs, are still a matter of debate, especially in case of non-uniform discretizations. In this contribution the mixed MLPG formulatio is applied for the analysis of plate structures. All independent variables are approximated by using polynomials in the transversal direction, while the Moving Least Square (MLS) functions are employed in the in-plane directions. Non-uniform discretization is based on the hierarchical recursive quadtree subdivision of the global domain. This procedure is guided by the configuration of the global boundary and the user-specified criteria. One couple of nodes positioned on the upper and lower plate surface is inserted into each quadtree leaf cell. The governing equations are derived from the local weak form (LWF) of the 3-D equilibrium equations, written over the local sub-domains surrounding the nodes. The sizes of the local sub-domains and the MLS support domains are determined depending on the local topology of the space subdivision around the node couples. Here the cylindrical and hexagonal local sub-domains are considered. By using the face neighbor pointers, node searching is performed locally, improving the numerical efficiency of the algorithms. Performance of the proposed discretization approach will be demonstrated by numerical examples.

MLPG; mixed approach; quadtree; nonuniform discretization

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