Wavelet solution for large deflection bending problems of thin rectangular plates

Abstract

In this study, we introduce a modified wavelet Galerkin method proposed recently by us to analyze the large deflection bending problems of thin rectangular plates, which are governed by the well-known von Karman equations, consisting of two coupled fourth-order two-dimensional nonlinear partial differential equations. This adopted wavelet method is established based on a modified wavelet approximation scheme to interval-bounded L 2-functions, in which each series-expansion coefficient can be explicitly expressed by a single-point sampling of the functions, and corresponding boundary values and derivatives can be embedded in the modified scaling function bases. By incorporating this approximation scheme into the conventional Galerkin method, the resulting algorithm can make the solution of the von Karman equations become very effective and accurate, as demonstrated by the case studies that the wavelet solutions on the deflection–load relations have better accuracy and less consumed computing time than that of other numerical methods including the finite element method and the meshless method.