15. Three-Dimensional Stability Analysis of A Uniaxially Compressed Polynomially Thick Rectangular Plates Using Energy Method

by Onyeka F C.1, 3, Nwa-David C D.2 and Okeke T E.3*
1 Department of Civil Engineering, Edo State University Uzairue, Edo State.
2Department of Civil Engineering, University of Nigeria, Nsukka.
3Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike.

Abstract
This study presents the three-dimensional (3-D) stability analysis of a uniaxially compressed thick rectangular isotropic plate that is clamped in one edge and the other three edges simply supported (CSSS). The energy method was applied in the coupling the three dimensional kinematics and constitutive relations to formulate the total potential energy equation. The formulated the total potential energy for the plate was transformed into equilibrium equation and used to obtain the shape function of the plate. The shape function derived was analysed through variational principle to get an exact polynomial displacement function which is a product of the coefficient of deflection and shape function 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 to produce a reliable solution for stability analysis of any type of plate rectangular plate. 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 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. The overall average percentage differences between the two functions recorded are 2.06%. 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.

Keywords: CSSS rectangular plate, stability analysis 3-D plate, exact polynomial function, critical buckling load.