Optimal Design for Stability under Multiple Loads

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Abstract
Optimal design of elastic structures for maximum buckling load is investigated. The structures considered are subjected to two or more independent loads, and the objective is to enlarge the stability region in the loading space as much as possible by distributing the mass of the structure in an optimal manner. The cross-sectional area is assumed to be piecewise constant along the length of the structure. Buckling loads are determined with the use of the finite element method, and optimization is carried out by an iterative procedure utilizing the optimality criterion. The following problems are analyzed: a column attached to an elastic foundation and subjected to an axial end load, and axial distributed load due to self-weight; a rotating shaft with axial load; a pipe conveying fluid and compressed by an axial load; a one-bay frame subjected to two vertical loads; and a two-bay frame subjected to three vertical loads.

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