A New Optimization Approach for the Tallest Column Design
Authors: Dragan T. Spasić, Teodor M. Atanacković
Keywords: tallest column, generalized elastica with shear and axial strain, optimal control problem with a free end point
Abstract:
Motivated by the classical brachistochrone we present a new pattern of finding the shape of a vertical column that attains the maximum height if its material and volume are prescribed. It comprises the optimal control problem with a free end point. Besides, the constitutive equation of the column is such that it can suffer flexure, compression and shear. The critical load of a heavy compressed column for the finite values of shear and extensional rigidity and the novel use of the Pontryagin maximum principle with the corresponding first integral yielding the non-vanishing optimal cross section as a solution of a quadratic equation are main novelties of this work. The classical solution for the tallest column under selfweight is covered as a special case for infinite values of shear and extensional rigidity.
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