Static Elastic Bending Analysis of a Three-Dimensional Clamped Thick Rectangular Plate using Energy Method

Abstract

Analytical formulations and solutions for the thick rectangular plate static analysis with clamped support based on a three-dimensional (3-D) elasticity theory is developed using the energy method. The theoretical model, whose formulation is based on the static elastic principle as already reported in the literature, is presented herein to obviate the shear correction coefficients while considering shear deformation effect and transverse normal strain/stress in the analysis. The equilibrium equations are obtained using 3-D kinematic and constitutive relations. The deflection and rotation functions, which are the solutions of the equilibrium equation, are obtained in closed form using a general variational technique for solving the boundary value problem. The minimization energy equation yields the general equation which was used to obtain the theoretical model for the deflection and stresses of the plate. The results are compared with the available literature and the results-computed trigonometric displacement function shows that this 3-D predicts the vertical displacement and the stresses more accurately than previous studies considered in this paper. The result showed that the percentage difference between the present work and those of 2-D Mindlin FSDT, 2-D numeric analysis, and 2-D HSDT of polynomial shape functions was about 3.02%, 0.62%, and 0.33%, respectively. It is concluded that the 3-D trigonometric model gives an exact solution, unlike other 2-D theories, and can be used for clamped-supported thick plate analysis. Doi: 10.28991/HIJ-2022-03-03-03 Full Text: PDF

Keywords

• exact static theory
• equilibrium equation
• bending of 3-d clamped plate
• trigonometric model.