Symbolic Computation of the Transition Matrix for Cylindrical Bending of Plates According to Reissner's Eighth-Order Theory

With the development of modern laminated structures composed of layers made of composite materials, an increasing amount of work has been devoted in the literature to the development of higher-order theories for plate bending. This is due to the fact that the influence of shear and transverse normal stress usually can not be neglected for such structures. Since Reissner's celebrated sixth-order theory of homogeneous plates, various higher order theories have been developed, and numerical implementations have been performed using finite elements. The development of analytical benchmark solutions, however, is accompanied by serious performance problems due to the complexity of the higher order theories. It is the scope of the present contribution to show that such problems can be overcome by means of modern symbolic computation. This is demonstrated using Reissner's eighth-order theory of nonhomogeneous transversely isotropic plates, which is appropriate for symmetrically layered plates.