A wavelet method for large-deflection bending of irregular plates

Abstract

A very rare sixth-order multiresolution method based on wavelet theory for solving irregular domain problems is proposed and applied to the large-deflection bending of irregular plates. High accuracy approximation of multiple integrals of functions defined in the irregular domain is realized by suggesting a new method of boundary extension of functions, which is associated with a boundary node removal technique to avoid singular matrices in the integration process. Each derivative of the unknown function is defined as a new function in the solution of the governing differential equations of the problem. The original equations containing derivatives of different orders can then be transformed into a system of algebraic equations with only discrete nodal values of the highest-order derivative, based on integral relations between these functions and excellent accuracy features on the wavelet approximation of multiple integrals. Various boundary conditions for irregular domains can be automatically and almost exactly included in the integration operation. The proposed method is applied to the solution of large-deflection bending of various irregular plates. The displacement and stress results demonstrate that the accuracy of the proposed method is still as high as the rare sixth order even when the problems are strongly nonlinear and defined in irregular regions, showing a much better accuracy and efficiency than those of classical methods such as the finite element method.