Abstract
Optimal design problems for structural elements in equilibrium often come in pairs in which the cost function for one problem becomes a constraint for the second. In particular, the problem of minimizing structural volume or weight under size and stress constraints has a dual in which potential energy is minimized for fixed volume of material. These dual problems are solved here for a linearly elastic rod hanging from a rigid support. The design variable is the cross-sectional area of the rod. The method used is the Maximum Principle of Pontryagin and Hestenes, rather than the function space methods used by others for similar problems.
Published Version
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