Simple and Exact Approach to Post Buckling Analysis of Rectangular Plate

International Journal of Civil Engineering

© 2020 by SSRG - IJCE Journal

Volume 7 Issue 6

Year of Publication : 2020

Authors : Ibearugbulem,O. M, Adah, E. I., Onwuka, D. O., Okere, C. E.

10.14445/23488352/IJCE-V7I6P107

How to Cite?

Ibearugbulem,O. M, Adah, E. I., Onwuka, D. O., Okere, C. E., "Simple and Exact Approach to Post Buckling Analysis of Rectangular Plate," SSRG International Journal of Civil Engineering, vol. 7,  no. 6, pp. 54-64, 2020. Crossref, https://doi.org/10.14445/23488352/IJCE-V7I6P107

Abstract:

This paper presents a new, simple, and exact approach to the post-buckling analysis of thin rectangular plates. In the stud, the Airy's stress functions are not incorporated as the middle surface axial displacement equations are determined as direct functions of middle surface deflection. With this, the bending and membrane stresses and strains, which are direct functions of middle surface deflection are obtained. These stresses and strains are used to obtain the total potential energy functional. The minimization of the total potential energy gives the governing equation and compatibility equation for rectangular thin plates buckling with large deflection. The compatibility equations and the governing equation are solved to obtain the deflection function for the problem. Direct variation is applied to the total potential energy function to get the formula to calculate the buckling loads. A numeric analysis is performed for a plate with all the four edges simply-supported (SSS plate). It is observed that when the deflection to thickness ratio (w/t) is zero the buckling load obtained coincides with the critical buckling from small deflection (linear) analysis. Another observation is that the values of buckling load for given values of w/t obtained in the present study do not vary significantly with those obtained by Samuel Levy. The recorded average percentage difference is 12.65%. It is also observed that the maximum w/t to be considered when small deflection analysis is to be used is 0.225. When w/t is more than 0.225, using small deflection analysis will give erroneous results. Thus, a large deflection analysis is recommended when w/t is above 0.25. We conclude and recommend that this new equation for the analysis of thin plates is a better alternative to the popular von Karman equation.

Keywords:

Post-buckling buckling load, membrane strains, total potential energy, minimization, direct variation

References:

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