engleski

A B-spline meshless formulation for plate bending analysis

A meshless local Petrov-Galerkin formulation based on a mixed approach is developed for the analysis of plate structures. Using a three-dimensional solid concept, a plate continuum is discretized by the nodes located on the upper and lower plate surfaces. In contrast to the previous mixed formulations for plate and shell analysis, where the separate strain and displacement interpolations have been performed, here all stress tensor components are interpolated in terms of their nodal values which are then computed by the interpolated displacement components. A new approach using the B-spline functions as the in-plane approximations is proposed, and the results are compared with the solutions obtained by means of the moving least square approximation usually used in meshless formulations. Simple polynomials are applied for the interpolations in the transversal direction. The global discretized equations with only nodal displacement components as unknown variables are derived. The shear locking phenomenon in the thin plate limit is fully suppressed by means of the stress interpolation. The Poisson’s thickness locking effect is eliminated by using the hierarchical quadratic interpolation of the transversal displacement component. The efficiency and accuracy of the proposed formulation are illustrated by numerical examples.

plate analysis; meshless approach; B-spline interpolation; locking phenomena.

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