Minimum-Weight Design of Thin-Walled Cylinders Subject to Flexural and Torsional Stiffness Constraints

Abstract

We consider the problem of determining the cross-sectional shape of a thin-walled cylinder of constant (unknown) wall thickness and given contour length that uses the least possible material to achieve prescribed minimum stiffness in torsion and bending. The corresponding variational problem is shown to belong to a class with nonadditive functionals whose Euler equation is an integrodifferential equation. Cross-sectional shapes are presented for various stiffness ratios and compared with circular and elliptical cylinders.