Abstract
By using Pontryagin's principle we study the optimal shape of an elastic compressed column with clamped ends and restrictions on cross-sectional area. The restrictions are imposed on either maximum or both minimal and maximum value of the cross-sectional area. We analyzed a column on elastic foundation of Winkler type and a column without foundation. It is shown that the optimization can be both bimodal and unimodal. We determine the transition value between unimodal and bimodal optimization for specified values of parameters.
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