Boundary‐Continuous Fourier Solution for Clamped Mindlin Plates

Abstract

A hitherto unavailable analytical or strong (differential) form of solution to the boundary‐value problem of a shear‐flexible (moderately thick) rigidly clamped isotropic homogeneous rectangular plate, subjected to transverse loading, is presented. A novel generalized Navier solution technique is developed to solve the three highly coupled second‐order partial differential equations (with constant coefficients) resulting from the application of the first‐order shear deformation theory (FSDT), based on Mindlin hypothesis, in conjunction with the Dirichlet boundary conditions. The assumed solution functions are in the form of double Fourier series, which satisfy the rigidly clamped boundary conditions a priori in a manner similar to Navier's method. Numerical results presented include convergence characteristics of transverse displacement (deflection) and bending moment, and variation of these quantities with respect to aspect ratios. Comparison with the available classical plate theory (CPT) and FSDT‐based boundary‐discontinuous Fourier and numerical (finite elements and finite difference) solutions helps validate the accuracy of the present analytical solution, and also delineates the upper limit (with respect to the thickness‐to‐length ratio) of validity of the CPT.