Elastic Bending Analysis Exact Solution of Plate using Alternative I Refined Plate Theory

Abstract

Plate materials play a significant role in civil engineering and its application is found in building, bridges, marine, nuclear and structural engineering. Plates are three-dimensional (3-D) structural elements and normal practice in its analysis as two-dimensional (2-D) element has produced unreliable design which is a major problem in the construction industry. In this paper, a 3-D exact elastic plate theory (alternative I refined plate theory) is developed and applied to the bending analysis of an isotropic rectangular plate with free support at the third edge and the other edges clamped (CCFC) under uniformly distributed transverse load. The energy equation is formulated using the three-dimensional constitutive relations thereafter, the compatibility equation was obtained through general variation. The solution of the compatibility equation gave an exact deflection function of the plate as presented in the trigonometric form. This deflection function which is a product of the coefficient of deflection and shape function of the plate are substituted back into the energy equation, and simplified through minimization with respect to the coefficients of deflection and shear deformation to get a realistic formula for calculating the deflection, rotations and stresses of thick rectangular plate. The results of deflections and stresses obtained at aspect ratio of 2 were compared with those of previous studies available in the literature. It was observed that the present theory varied more with those of 2-D refined plate theory (RPT) with an assumed deflection function by 6.2% whereas it varied with exact 2-D RPT by 3.1%. This shows the inefficiency of assuming the deflection function in the analysis of thick plate. Meanwhile, the recorded total percentage differences showed that 2-D RPT over predicted the bending characteristics of the plate with 4.7%. This finding provides in-depth insight about the coarseness of 2-D RPT in the thick plate analysis.