Exact truss topology optimization: allowance for support costs and different permissible stresses in tension and compression—extensions of a classical solution by Michell

摘要

The aim of this paper is twofold. It introduces a theory of Michell trusses taking support (reaction) costs into consideration, which is illustrated with a modified version of Michell’s best known example. Then eight other variations on this example are presented, with (i) equal or unequal permissible stresses in tension and compression, (ii) the structural domain consisting of a half-plane or a full plane, and (iii) the supports being two pins, or a pin and a roller. Previously noted shortcomings of Michell’s theory are highlighted and several fundamental properties of non-selfadjoint topology optimization problems discussed. The analytical solutions are verified to a high degree of accuracy by numerical results.