Stress Analysis of Transversely Loaded Isotropic Three-Dimensional Plates Using a Polynomial Shear Deformation Theory

Abstract

 A 3-D total potential energy was developed.  A derived shape function of the plate was obtained.  An expression for stress and moment of the plate was formulated.An exact solution for the bending attributes of a thick rectangular plate under transverse loading is modeled herein using three-dimensional (3-D) elasticity plate theory and fourth-order polynomial shear deformation function. Precluding coefficients of shear correction, this model captured the effect of shear deformation along with the transverse normal strain stress. The expression for total potential energy was derived from a 3-D kinematic and constitutive relation the equilibrium equation was developed and employed from the energy functional transformation to get the relationship between slope and deflection. Exact polynomial functions were obtained from the outcome of the equilibrium equation and with the aid of the direct variation approach, the coefficient of deflection of the plate was generated from the governing equation. The expression for computing the displacement, bending moments, and stress components along the three axes of the plate was established from these solutions for the assessment of the bending characteristics of a rectangular plate. The result of a simply supported at one edge, free at one edge and clamped at the two outer edges (SCFC) was evaluated using the obtained functions in this study. The report of this study confirms the exactness and consistency of the 3-D model unlike the refined plate theories applied by previous authors in the available literature. The value of 8.05% is the comprehensive average percentage variation of the values for center deflection obtained by Onyeka and Okeke (2020) and Gwarah (2019). It is established that at the 92 % confidence level, this model is worthy of adoption for safe, cost-effective and accurate bending analysis of thick plates of any support condition.

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

“…Onyeka et al, [23][24][25] have used energy methods for thick plate problems under buckling and bending. Recent studies by Onyeka et al, [26][27][28] considered thick rectangular plates with various edge support conditions. Onah et al, [29] used the stress function method to derive elastostatic solutions to thick circular plate bending problems.…”