Displacement and Stress Analysis of Thick Rectangular Clamped Plates Using Third-Order Energy Functional

Abstract

This study analysed the stress and displacement responses of an all-clamped rectangular thick plate subjected to a uniformly distributed load using polynomial displacement functions. A polynomial shear deformation function was incorporated in the determination of the general governing equations; hence, there is no need for shear correction factors. Approximate Polynomial Displacement Functions w, u, and v for all the clamped thick rectangular plates subject to transverse loading were obtained. Numerical results were obtained using displacement equations obtained from the literature for the non-dimensional form of displacements and stresses of an all clamped (CCCC) plate at different aspect and span-depth ratios to determine the efficiency of this theory. The results obtained were validated as they showed good agreement with the results obtained by other researchers available in literature. Hence, this theory can be used as a reliable, concise, easy and dependable means for the stress and displacement analysis of thick plates. The results obtained also indicate that at a span-depth ratio of 100 and above, the classical plate theory (CPT) can be used to analyse plates, as the numerical values obtained are approximately equal to that of the CPT.