Bending analysis of thick laminated plates using extended Kantorovich method

This study is concerned with bending of moderately thick rectangular laminated plates with clamped edges. The governing equations, based on Reissner first-order shear deformation plate theory; in terms of deflection and rotations of the plate include a system of three second-order, partial differential equations (PDEs). Application of extended Kantorovich method (EKM) to the system of partial differential equations reduces the governing equations to a double set of three second-order ordinary differential equations in the variables x and y. These sets of equations were then solved in an iterative manner until convergence was achieved. Normally three to four iterations are enough to get the final results with desired accuracy. It is demonstrated that, unlike other weighted residual methods, in the extended Kantorovich method initial guesses to start iterations are arbitrary and not even necessary to satisfy the boundary conditions. Results of this study also reveal that the convergence of the EKM is rapid and the method is an efficient way to solve system of PDEs of the same type. To compare the results of this study, the problem was also analyzed using commercial finite element software, ANSYS. Results show reasonably good agreement with the finite element analysis.