Application of the extended Kantorovich method to the bending of variable thickness plates

The governing equations of the classical plate theory for a uniform or a unidirectional variable thickness rectangular plate under transverse applied loading are solved by means of the extended Kantorovich method. The plate may be either simply supported or clamped along the edges. The solution procedure is iterative and must be carried out numerically. This necessitates the calculation of the two missing pieces of boundary data along the edges of the plate. The missing boundary data are determined utilizing the method of adjoints of the shooting method. The numerical values of the deflection and bending moments for uniform and variable thickness plates are compared with those from the exact solutions and finite element analysis, respectively.