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Author: ONYEDIKACHI ALOYSIUS OGUAGHAMBA

Title: Analysis of Buckling and Postbuckling Loads of Isotropic Thin Rectangular Plates.

Affiliation: Civil Engineering Department
School of Engineering and Engineering Technology
Federal University of Technology, Owerri Imo State

Date: November, 2015

ABSTRACT
This study investigated the analysis of buckling and postbuckling loads of isotropic thin rectangular plates. The study derived the governing differential equations defining the postbuckling behaviour of isotropic thin rectangular plates, known as von Karman’s equilibrium and compatibility large deflection equations; as well as the governing differential equation of plates’ buckling. In view of the complex nature of these equations, it is not possible to obtain their closed-form solutions. Hence, the study used the direct integration method to solve the governing differential equation of plates’ buckling and the von Karman’s compatibility large deflection equation of plates to obtain their deflections and stresses functions respectively for different support conditions. Then, the study applied these functions in the von Karman’s equilibrium large deflection equation to solve for the buckling and postbuckling loads of these plates using work principle technique. The displacement parameters, Wuv, stress coefficients, Wuv2 and load factors, Kcx for the various support conditions of plates were determined using the Johasen yield line theory, leading to the critical buckling and postbuckling loads and stresses of these plates. The study’s numerical analysis among other things revealed that thin rectangular plates possess postbuckling reserve of strength upon buckling. That is, they do not fail at mere critical buckling loads. Their postbuckling reserve of strength upon buckling loads are due to the transverse and longitudinal fibers of the plates which undergo stress redistribution with consequential tensile stress build up in the plates. Another finding of the study is that plates’ reduction in axial stiffness upon buckling is due to the in-plane load postbuckling bending stresses developed in the plates, in the cause of buckling. These bending stresses lower the axial stiffness of plates. Other revelation of the study is that plates would reach yield stress at different out of plane deflections, depending on their support conditions. SSSS, CCCC, CSCS, CSSS, CCSS, CCSC, SCFC and CCFC, plates reach yield stress at out of plane deflection coefficient of 4.1, 0.1, 1.4, 3.1, 1.8, 1.1, 3.0, and 2.80 of their plates’ thicknesses, h respectively. These group of thin rectangular plates could be adequately be designed for in – plane loads using their critical buckling and postbuckling loads and stresses. While SSFS, CSFS and SCFS plates possess yield stresses far below the yield stress of steel material (250MPa), even at 5.0h out of plane deflection. In the design of such plates, the deflections criteria should be implored as their yield stresses would result to inadmissible deflections. This study has made useful contribution towards solving the problem of dearth of literature on the analysis of buckling and postbuckling loads of isotropic thin rectangular plates, especially with regard to the use of direct integration method and work principle to solve these differential equations. Other novel feat of the study is the use of Johasen yield line theory to deduce the displacement parameters, Wuv, stress coefficients, Wuv2 and load factors, Kcx for the various support conditions of thin rectangular plates.