engleski

Procedures for Elimination of Locking Effects in a Meshless Plate and Shell Analysis

Various procedures for the elimination of locking phenomena in the meshless shell and plate analysis using the MLPG method are presented. In contrast to the available MLPG shell formulations, here all derived algorithms are based on the concept of a three dimensional solid and discretization is carried out by the nodes located on the upper and lower surfaces of a structure. The governing equations are derived from the local weak form (LWF) of the 3-D equilibrium equations, which are written over the local sub-domains surrounding the nodes. In the fully displacement approach only the displacements are approximated. Poisson’ s thickness locking is avoided by adopting the hierarchical quadratic interpolation for the transversal displacement component and shear locking in case of thin structures is alleviated by applying a sufficiently high order of the in-plane approximation functions. In the mixed strategy appropriate strain and stress components in the LWF are approximated independently from the displacement field. The nodal strain and stress values are then expressed in terms of displacements and a global system of equations with only the unknown nodal displacement variables is obtained. In plate analysis, thickness locking is eliminated by modifying the nodal values of the normal transversal strain component, while in case of shell structures the transversal normal stress is approximated instead of the transversal normal strain. In a thin structural limit, shear locking is efficiently overcome by interpolation of the strain components. Efficiency of the proposed algorithms will be demonstrated by numerical examples.

meshless method; shells; plates; locking

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