New Analytic Shear Buckling Solution of Clamped Rectangular Plates by a Two-Dimensional Generalized Finite Integral Transform Method

A first attempt is made in this paper to explore new analytic shear buckling solution of clamped rectangular thin plates by a two-dimensional generalized finite integral transform method. The problem is classical but challenging due to the mathematical difficulty in handling the complex boundary value problem of the governing higher-order partial differential equation (PDE). Taking the vibrating beam functions as the integral kernels, and imposing the double transform, the problem comes down to solving a system of linear algebraic equations, thereby the analytic solution is obtained in a straightforward way. The present method is confirmed to be highly accurate with fast convergence, which agrees very well with both the finite element method (FEM) and energy method from the literature. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods.