Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

Abstract

Regular domain collocation method based on barycentric rational interpolation for solving irregular thin plate bending problems on Winkler foundation is presented in this article. Embedding the irregular plate into a regular domain, the barycentric rational interpolation is used to approximate the unknown function. The governing equation and the boundary conditions of thin plate bending problems on Winkler foundation in a rectangular region can be discretized by the differentiation matrices of barycentric rational interpolation. The additional method or the substitute method is used to impose the boundary conditions. The overconstraint equations can be solved by using the least square method. Numerical solutions of bending deflection for the irregular plate bending problems on Winkler foundation are obtained by interpolating the data on rectangular region. Numerical examples illuminate that the proposed method for irregular thin plate bending problems on Winkler foundation has the merits of simple formulations, efficiency, and relative error precision of 10−9 orders of magnitude.

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

“…Trefftz method does not contain singular integrals and it is more exact in comparison with other methods. Variant of collocation method is worked in paper [36] for a plate inscribed in rectangular contour. Collocation points are Chebyshev nodes.…”

“…The obtained results are in perfect agreement with known analytical and numerical solutions. Thin rectangular cantilever plate [28] and irregular thin plate on Winkler foundation [36] were also solved with this method.…”