Equivalence of a Constrained Minimum Weight and Maximum Column Buckling Load Problem With Solution

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Abstract
Packaged computer programs are available for solving the two-point boundary-value problems resulting from well-posed structural optimization problems. These methods generally require a standard form of representation of the structure’s equations and the other necessary conditions for optimization. At the same time there is a duality between minimum weight designs of structures and maximum load designs. If the maximum load design problem is an eigenvalue problem associated with the mini-max problem of the Rayleigh quotient, standard forms of representation are complex. This complexity has lead to a simple equivalence statement of the problems of minimum column weight and maximum buckling load; and, has produced a straight forward solution technique for maximum load problems.

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