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

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  • S. Sadiku

    (Federal University of Technology)

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.

Suggested Citation

  • S. Sadiku, 2010. "On the Application of the Perturbation Method in the Buckling Optimization of a Heavy Elastic Column of Constant Aspect Ratio," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 181-188, July.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:1:d:10.1007_s10957-010-9663-8
    DOI: 10.1007/s10957-010-9663-8
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