Optimal Jump Nonhomogeneity of Prismatic Bars in Torsion

Abstract

The problem of optimal nonhomogeneity of a bar subjected to Saint-Venant torsion is formulated as a variational problem so that the necessary conditions for optimality may be derived. In this formulation, the shear modulus function G(x,y) which varies in a jumplike manner is to be optimized with the specified composition of two different elastic materials. It is shown in this paper that a prismatic, nonhomogeneous bar can, in fact, be optimized, and the maximum torsional rigidity is achieved by performing the proposed iterative procedure based on the derived necessary conditions. As a numerical example, the optimal solutions for prismatic bars with cross-sectional shapes of a square and an equilateral triangle are obtained by the computer program which uses the Finite Element Method formulated on the basis of the hybrid stress approach.