The Design of Michell Optimum Structures

Abstract

The fundamental problem of structural design is the determination of structures of minimum weight which safely equilibrate a given system of external forces. The classical theorem of Michell gave the basic requirements for such a structure. The first part of this paper analyses the geometrical layout of twodimensional structures which satisfy these requirements, making use of the analogy with the theory of plane plastic flow. Expressions for the calculation of sizes and the total volume of the structural members are developed. Method of graphical construction of the structural layout is also given. In the second part, the analogy with a known solution of plastic flow is used to develop solutions for a cantilever under tip shear force and a beam under uniform bending moment. Comparisons with the conventional types of construction are made and the superiority of the Michell structures are demonstrated.