engleski

A locking free thin plate meshless formulation based on stress interpolation

A meshless local Petrov-Galerkin formulation based on the mixed approach is developed for the analysis of plate structures. Using a 3-D solid concept, the plate continuum is discretized by the nodes located on the upper and lower plate surfaces. In contrast to other formulations for plate and shell analysis, where the independent strain and displacement interpolations have been performed, here all stress tensor components are interpolated in terms of the nodal values which are than replaced by the interpolated displacement components. The approximation in the in-plane directions is carried out by using both Moving Least Square (MLS) and B-spline functions, while linear polynomials are used in the transversal direction. In order to obey Kronecker delta property, the MLS modification is performed, and a transformation procedure is applied in the B-spline interpolation to establish the true nodal values. The global discretized equations with the 6 nodal displacement components as unknown variables over the thickness are derived. The shear locking phenomenon in thin plate limit is fully suppressed by means of the stress interpolation. The thickness locking is eliminated by using the hierarchical quadratic interpolation of transversal displacement components. The efficiency and accuracy of the proposed formulations are illustrated by numerical examples.

MLPG method; thin plates; mixed formulation; stress approximation

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