Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations

An analysis is presented for different bearing loadings of a plate resting on various linear and nonlinear foundations subjected to different boundary conditions such as the circled clamped, simply supported, and mixed boundary conditions. The highly accurate solutions of the plate deflection and the stress under different work conditions are obtained by the novel wavelet-homotopy technique, which are in full agreement with previous ones in literature. Different from previous studies, our solutions are also valid for the extra large plate bending cases, which are rarely considered before. Particularly, we consider the important case that the connection coefficients of various foundations are variational, which seems to be overlooked in previous studies owing to their extreme difficulties in mathematical treatments and programming. Besides, to overcome the limitation of existing wavelet technique of poor capability on handling complex boundary conditions, we reconstruct the boundary wavelet by the Coiflets so that it can be used to handle the governing partial differential equations subjected to nonhomogeneous boundary conditions. Moreover, we introduce the homotopy iteration technique so that the computational efficiency improves to a large extent as compared with the traditional Homotopy Analysis Method (HAM) technique. It is expected the proposed wavelet-homotopy method can be as a new generation of analytical tool for solving strong nonlinear problems subjected to complicated boundary conditions, especially for those with variable coefficients.