Displacement and Stress Analysis in Shear Deformable Thick Plate

摘要

This paper presents exact solution of displacement fields of thick rectangular plate which was obtained using traditional third order refined theory for the bending of rectangular plates with different support cases under general boundary conditions. The aim of study is static bending analysis of an isotropic rectangular thick plate using analytical method. Total potential energy equation of a thick plate was formulated from the first principle. This equation was subjected to direct variation to obtain three simultaneous direct governing equations for determination of displacement coefficients. The main assumption here is that the vertical line that is initially normal to the middle surface of the plate before bending is no longer straight nor normal to the middle surface after bending, as a result the shear deformation profile F (z) is used in the place of z. The shear deformation profile equation for vertical shear stress through the thickness of the plate was formulated mathematically in line with Timoshenko work. From this profile equation, the deformation line equation (called function of z or s) was obtained and compared to other four model. These models in comparison includes one polynomial and three trigonometric model. A numerical problem for a rectangular plate simply supported around all the edges was used to test the sufficiency of this study. It was observed that the values of non-dimensional forms of displacements and stresses from the present study agree with the values from previous studies. Also observed is that the values of the in-plane quantities did not vary with span-depth ratio (ρ) 6 and above. They are all equal to the values from classical plate theory (CPT) for the values of (ρ) 6 and above. However, the out-of-plane quantities varied with span-depth ratio from (ρ) equal to 4 up to (ρ) equal to 30, after which they become constant and approximately equal to values from CPT. This shows that the present method is reliable and sufficient for thick plate analysis.