A strain tensor method for three-dimensional Michell structures

Abstract

In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by Michell (1904) and has been mostly used for two-dimensional structures so far. This paper develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two- and three-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three-dimensional cases.