A multivariable wavelet-based finite element method and its application to thick plates

A multivariable wavelet-based finite element method (FEM) is presented to resolve the bending problems of thick plates. The interpolating wavelet functions based on boundary conditions are constructed to represent the generalized field functions of thick plates. The formulation of multivariable wavelet-based FEM is derived by the Hellinger-Reissner generalized variational principle with two kinds of independent variables. The proposed formulation can be solved directly when the stress-strain relations and the differential calculations are not utilized in determining the variables. The applicability of the multivariable wavelet-based FEM is demonstrated by determining the bending solutions of a single thick plate and of an elastic foundation plate. Comparisons with corresponding analytical solutions are also presented. The wavelet-based approach is highly accurate and the wavelet-based finite element has potential to be used as a numerical method in analysis and design.