Application of Exact Solution Approach in the Analysis of Thick Rectangular Plate

摘要

This work evaluates the exact relationships and static analysis of an isotropic thick rectangular plate with various kinds of support conditions. In this work, the use of higher order refined shear deformation theory for thick plate analysis was applied. Total potential energy equation of a thick plate was formulated from the first principle. These relationships enable the actual displacements, stresses, stress resultants and shear deformation rotations of the traditional third order plate theory to be determined by performing general variation of the total potential energy obtained. The coordinate functions, which must satisfy the geometric and natural boundary conditions, are carefully constructed and applied into refined shear deformation plate equation. The plate equation is thus integrated by direct integration approach and the integrand minimized to obtain the unknown coefficients which when substituted back in deformation equation of mid-surface of plate gives actual displacements, stresses, stress resultants and shear deformation of plate in analytical form. This work is helpful for evaluation of in plane displacements, deflections, bending moments, shear force and shear deformation rotations at any arbitrary point on the plates unlike the numerical methods which only give these results at nodal points. The results obtained from this study was compared with those of numerical obtained from refined theory with correction factor and those obtained using numerical and other methods at various aspect ratios of the plate for rectangular plates boundary conditions with clamped on two opposite short edges and simply supported on two opposite long edges (CSCS). The results obtained are in close agreement with the results obtained from the literature.