Minimum-weight design of hollow cylinders for given lower bounds on torsional and flexural rigidities

Abstract An approximate analytical solution is obtained for the problem of minimizing the cross-sectional area of elastic, doubly-connected cylindrical bars for given lower bounds on torsional and flexural rigidities. The bars are designed to withstand either a twisting or a bending moment, but not both, at any given time. The shape of the inner contour of the doubly-connected (hollow) cross-section is specified while that of the outer contour is determined as a result of the optimization. The economy achieved by optimization is estimated.