On the Application of the Perturbation Method in the Buckling Optimization of a Heavy Elastic Column of Constant Aspect Ratio

S. Sadiku ()
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S. Sadiku: Federal University of Technology

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 1, No 11, 188 pages

Abstract: Abstract This paper addresses the problem of maximizing the first Euler load of a column of constant aspect ratio (moment of inertia varies with the square of the cross-sectional area), considering the column self-weight, subject to the constraint of fixed volume of column material and height. The coupled nonlinear integro-differential equations of optimality and stability, generated through variational principles, have been solved using the method of parameter perturbation. The optimal column has cross-sectional area that follows a perturbed two-thirds power law; the first Euler load is up to 87% larger than that of the corresponding column of uniform cross-section having the same volume and height.

Keywords: Elastic column; Buckling; Optimization; Perturbation method; Rayleigh’s quotient; Constant aspect ratio (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-010-9663-8

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