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Study on Stability Analysis of Rectangular Plates Section Using a Three-Dimensional Plate Theory with Polynomial Function

: In this paper, a polynomial displacement function is developed to evaluate the stability of rectangular thick plate that is freely supported at the third edge and other three edges simply supported (SSFS). Employing three-dimensional (3-D) constitutive relations which consist of entire stress components, the functional for total potential energy was obtained. The governing equations plate was obtained through the variation of the 3-D theory of elasticity to get the slope and deflection relations. The solution of equilibrium equations gives an exact polynomial deflection and rotation function which was gotten after replacement of the variables of total potential energy while the solution of the governing equation gave the expression for the deflection coefficient of the plate. The direct variation method through deflection coefficient was applied to get the formula for calculation of the critical buckling load. Furthermore, the model followed strictly from the first principle of 3-D theory of elasticity without state of stress assumption through the thickness axis of the plate, so that it is able to eliminate the stress under-estimation problem from the approximation and 2-D refined plate theory approach, when the thickness becomes thicker. The result of the present study using the established 3-D model yields an exact solution which shows that it can be used with confidence in the stability analysis of any type of plate boundary condition.