Makrodimopoulos, A., Bhaskar, A. and Keane, A.J.
A compliance based design problem of structures under multiple load cases
Structural and Multidisciplinary Optimization, 42, . (doi:10.1007/s00158-010-0524-8).
There are two popular methods concerning
the optimal design of structures. The first is the min-
imization of the volume of the structure under stress
constraints. The second is the minimization of the com-
pliance for a given volume. For multiple load cases an
arising issue is which energy quantity should be the
objective function. Regarding the sizing optimization of trusses, Rozvany proved that the solution of the es-
tablished 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 1. In this paper, we intro-
duce 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 non-
indeterminate2 trusses, this compliance method gives
the same optimal design as the stress based design method.
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