A Study on Stability Analysis of 3-D Shear Deformable Isotropic Plate Elastically Restrained against Rotation and Simply Supported in the two Adjacent Edges using Exact Displacement Potential
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In this paper, a three-dimensional (3-D) stability analysis of rectangular deformable plate was performed to find the solution to the buckling problem of a uniaxially compressed plate in which the two adjacent loaded edges is clamped and the other, simply supported (CSCS). A three dimensional kinematics and constitutive relations were used to obtain the equation of total energy functional. The general and direct variation of the total potential energy function was done to get the general and direct governing equation of the plate by considering the effect of shear deformation. The solution of the general governing equation gave the deflection of the plate which is a product of the coefficient of deflection and shape function of the plate. The shape function is derived in terms of polynomial and trigonometric function and solved to get the exact deflection of the plate. The expression for the critical buckling load and other formulae was obtained by the direct variation of the total potential energy equation. This was done by minimizing the energy functional with respect to the coefficients of deflection after including the deflection and shear deformation rotation functions in it. The span to thickness ratio and aspect ratios were varied to ascertain the buckling behavior of different type of plate under uniformly distributed load. The outcome of the numerical analysis revealed that increase in the span- thickness ratio led to the increased value of the critical buckling load which implies that the plate structure is safe when the plate thickness is increased. The result showed that the critical buckling loads from the present study using polynomial are slightly higher than those obtained using trigonometric theories signifying the more exactness of the latter. The overall average percentage differences between the two functions recorded are 2.4%. This shows that at about 98% both approaches are the same and can be applied with confidence in the stability analysis of any type of plate with such boundary condition. The result of the present study using the established 3-D model for both functions is satisfactory and were found to follow an identical pattern, but quite distinct in validation which shows the credibility of the derived relationships.
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