Analytical buckling solutions of rectangular thin plates by straightforward generalized integral transform method

In this study, the generalized integral transform method is applied for the first time to get the exact analytical buckling solution of a rectangular thin plate. In solution procedure, according to the boundary conditions of the plate the vibrating beam functions are adopted as the integral kernels to construct the integral transform pairs. Then the integral transformation is applied on the basic governing high order partial differential equation of plate, utilizing some inherent properties of beam function and transformed the title problem into a system of a linear algebraic equation where the exact analytical solution is obtained elegantly. The main advantage of this analytical method is that it is simple and general and does not require any pre-determined deformation function. Therefore, the solution obtained is reasonable and theoretical. To illuminate the correctness of the method the present results are compared with finite element analysis by the commercial software (ABAQUS) as well as the analytical results from the literature which shows good agreement.