Structural behaviour and bending analysis of rectangular thick plate using a new 3-D modified trigonometric displacement model

Abstract

In this work, a new 3-D modified trigonometric displacement model was used to study the structural behavior and bending analysis of rectangular thick plate which was clamped in one edge and other three edges simply supported. The theoretical model whose formulation is based on static elastic principle as already reported in the literature are presented herein, obviating 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. An exact solution of deflection and rotation are obtained from the equilibrium equation using the general variational principle. The minimization, energy equation yields the general equation which was used to obtain the 3-D trigonometric displacement model of the plate. The percentage difference between the present work and those of 2-D Refined Plate Theory (RPT) with an assumed displacement and 2-D Refined plate theory (RPT) with derived function is 1.43% and 5.15% respectively. More so, percentage difference between the present work and those using polynomial shape function is 3.29%. The result showed that the 3-D trigonometric model for the present work predicts the vertical displacement and the stresses more accurately than RPT and polynomial displacement model. It is concluded that the 3-D trigonometric model gives an exact solution unlike polynomial and can be used with confidence in the analysis of thick plate under the particular initial condition.