A boundary discontinuous fourier solution for clamped transversely isotropic (pyrolytic graphite) mindlin plates

Abstract

An analytical solution to the long-standing boundary-value problem of a shear-flexible (moderately-thick) rigidly clamped transversely isotropic rectangular plate, subjected to transverse loading, is presented. A recently developed accurate yet computationally efficient boundary discontinuous Fourier series technique (BDFST) has been utilized to solve the three highly coupled second-order partial differential equations with constant coefficients that result from the Mindlin hypothesis. Numerical results presented (i) testify to the accuracy and computational efficiency of the above-mentioned solution methodology, (ii) help in understanding the nature of convergence of double Fourier series in the presence of edge discontinuities introduced by the fully clamped boundary conditions, (iii) ascertain the limit of applicability of the classical plate theory (CPT), and (iv) provide physical insight into such complex deformation behaviors as the effect of transverse shear deformability and thickness on the deformation of rigidly clamped moderately-thick plates of metallic (isotropic) and pyrolytic graphite (transversely isotropic) constructions.