Closed form buckling analysis of thin rectangular plates
Journal Title: IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) - Year 2019, Vol 16, Issue 1
Abstract
This paper presents closed form buckling analysis of rectangular thin plates. It minimizes the total potential energy functional with respect to deflection function and obtained the Euler-Bernoulli equation of equilibrium of forces for the plate. Using split-deflection method, the equilibrium equation was uncoupled into two separate equations. The function satisfying each of the two equations was determined. Exact solution of Euler-Bernoulli governing equation for the plate was obtained as a product of the functions. Nine distinct deflection functions for plates were obtained after satisfying nine different boundary conditions. The paper went further to obtain the formula for calculating the critical buckling load of the plate by minimizing the total potential energy functional with respect coefficient of deflection. Numerical examples were carried out using two plates. One of the plates has two adjacent edges clamped and the other edges simply support (ccss). The other plate has one edge clamped and the other three edges simply supported (csss). The critical buckling loads obtained for the two plates were compared with the ones from an earlier study, which used polynomial deflection equation. For square ccss the values of the non dimensional critical buckling loads are 61.706 and 64.73 for the present and past studies respectively. For csss plate the values are 56.429 and 56.807 respectively for the present and past studies. The percentage difference between the values from the present and past studies are 4.67% for ccss and 0.67% for csss. It could be seen that the differences are not too significant.
Authors and Affiliations
O. M. Ibearugbulem, H. E. Opara, C. N. Ibearugbulem, U. C. Nwachukwu
Keywords
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