A modified wavelet approximation of deflections for solving PDEs of beams and square thin plates

This paper presents a modified wavelet approximation for deflections of beams and square thin plates, in which boundary rotational degrees of freedom are included as independent wavelet coefficients. Based on the modified approximations and Hamilton's principle, variational equations for dynamical, statical and buckling problems of square plates are established, without requiring the wavelet approximations or the wavelet basis to satisfy any specific boundary condition in advance. Further, both homogeneous and non-homogeneous boundary conditions, as well as general boundary conditions, of square plates can be treated in the same way as conventional finite element methods' (FEMs') way. These properties are advantages over current wavelet-Galerkin methods and wavelet-FEMs. Illustrative examples are presented at the end of this paper, and the results show that the modified wavelet approximations can achieve satisfactory accuracy for both homogeneous and non-homogeneous boundary conditions of square plates.