Analytical bending solutions of thin plates by two‐dimensional generalized integral transform method

In this paper, analytical bending solution of a rectangular thin plate with different boundary conditions was obtained by using the two‐dimensional generalized finite integral transform method. During the solution procedure, the vibrating beam functions satisfying different boundary conditions of the plate are taken as integral kernels to form the integral transform pairs. This two‐dimensional integral transform is used to the partial differential governing equations of the plate, to transform them to a system of linear algebraic equations from which the accurate analytical solution is obtained easily. The superiority of the present method is that it does not need to seek the deformation function in advance, and avoids the complex superposition processes. Thus, the proposed method is reasonable and feasible. The good agreement of present results and the analytical solution from the literature shows the validity of the method. In this paper, analytical bending solution of a rectangular thin plate with different boundary conditions was obtained by using the two‐dimensional generalized finite integral transform method. During the solution procedure, the vibrating beam functions satisfying different boundary conditions of the plate are taken as integral kernels to form the integral transform pairs. This two‐dimensional integral transform is used to the partial differential governing equations of the plate, to transform them to a system of linear algebraic equations from which the accurate analytical solution is obtained easily….