We show that a problem of finding the truss of minimum expected compliance under stochastic loading conditions is equivalent to the dual of a special convex minimax problem, and therefore may be efficiently solved. This equivalence makes it possible to provide classic multiload compliance minimization problems with interpretations in a probabilistic setting. In fact, we prove that minimizing the expected compliance amounts to solving a multiload-like problem associated with a particular finite set of loading scenarios, which depend on the mean and the variance of the perturbations.
- Expected compliance
- Multiload compliance minimization
- Stochastic loading
- Structural mechanics
- Topology optimization