There are two popular methods concerning<br/>the optimal design of structures. The first is the min-<br/>imization of the volume of the structure under stress<br/>constraints. The second is the minimization of the com-<br/>pliance for a given volume. For multiple load cases an<br/>arising issue is which energy quantity should be the<br/>objective function. Regarding the sizing optimization of trusses, Rozvany proved that the solution of the es-<br/>tablished compliance based problems leads to results<br/>which are awkward and not equivalent to the solutions<br/>of minimization of the volume under stress constraints,<br/>unlike under single loading 1. In this paper, we intro-<br/>duce the “envelope strain energy” problem where we<br/>minimize the volume integral of the worst case strain<br/>energy of each point of the structure. We also prove<br/>that in the case of sizing optimization of statically non-<br/>indeterminate2 trusses, this compliance method gives<br/>the same optimal design as the stress based design method.<br/
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