Extension of Heyman's and Foulkes' theorems to structures with linear segmentation

Abstract

Heyman [Q. J. Mech. appl. Maths 12, 314-324 (1959)] and Foulkes [Proc. R. Soc. Lond. A233, 482-494 (1954)] introduced optimality criteria for structures with freely varying and segment-wise constant cross-sections, respectively. The present paper deals with an extension of the above theorems to structures in which the cross-sections vary linearly over each segment and in which there are no discontinuities in the cross-sectional area at segment boundaries. These geometrical restrictions have practical advantages in actual design problems. In addition, allowance for self-weight and dual formulation are discussed, and it is shown through several examples that the proposed optimality criteria are simpler to use than other optimization methods. © 1989.