A compliance based design problem of structures under multiple load cases

There are two popular methods concerning the optimal design of structures. The first is the minimization of the volume of the structure under stress constraints. The second is the minimization of the compliance for a given volume. For multiple load cases an arising issue is which energy quantity should be the objective function. Regarding the sizing optimization EPSRC grant EP/E004547/1. A. Makrodimopoulos (corresponding author) School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-595194 Fax : ++44-(0)2380-594813 E-mail: [email protected] A. Bhaskar School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-593825 Fax : ++44-(0)2380-594813 E-mail: [email protected] A.J. Keane School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-592944 Fax : ++44-(0)2380-594813 E-mail: [email protected] of trusses, Rozvany proved that the solution of the established compliance based problems leads to results which are awkward and not equivalent to the solutions of minimization of the volume under stress constraints, unlike under single loading . In this paper, we introduce the “envelope strain energy” problem where we minimize the volume integral of the worst case strain energy of each point of the structure. We also prove that in the case of sizing optimization of statically nonindeterminate trusses, this compliance method gives the same optimal design as the stress based design method.