On Basic Properties of Michell’s Structures

Abstract

The paper is an introduction towards Michell’s optimum design problems of pin-jointed frameworks. Starting from the optimum design problem in its discrete setting we show the passage to the discrete-continuous setting in the kinematic form and then the primal stress-based setting. The classic properties of Hencky nets are consistently derived from the kinematic optimality conditions. The Riemann method of the net construction is briefly recalled. This is the basis for finding the analytical solutions to the optimum design problems. The paper refers mainly to the well known solutions (e.g. the cantilevers) yet discusses also the open problems concerning those classes of solutions in which the kinematic approach cannot precede the static analysis.