Abstract
In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF
Highlights
The captivating properties; light weight, economy, and ability to withstand loads, etc. of plate materials have made them to be widely used in different engineering field [1]
As an indication of the error involved in using the classical plate theory, first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) for thick plate analysis, consider the problem of all edges supported square plate subjected to a uniformly distributed uniaxial compressive load presented in the Figure 3
For the non-dimensional values obtained in Tables 2, it reveals that the values of critical buckling load increase as the span- thickness ratio increases
Summary
The captivating properties; light weight, economy, and ability to withstand loads, etc. of plate materials have made them to be widely used in different engineering field [1]. The plates are usually under the action of axially compressive or tensile loads acting in the mid-plane of the plate. This axial load at the boundary perpendicular to the mid-surface and distributed through the plate’s thickness is known as the in-plane compressive load [4]. The in-plane loading in an elastic plate material beyond its critical values generates structural instability thereby result to the buckling of the plate when a very large stresses are induced [5]. Critical buckling load becomes the greatest load which causes an axially loaded plate to lose its stability [6]. To avoid failure of the plate due to buckling of the plate structure, relatively more accurate and practical studies on stability analysis of plate is required
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