Optimal structural design under stochastic uncertainty by stochastic linear programming methods

In the optimal plastic design of mechanical structures one has to minimize a certain cost function under the equilibrium equation, the yield condition and some additional simple constraints, like box constraints. A basic problem is that the model parameters and the external loads are random variables with a certain probability distribution. In order to get reliable/robust optimal designs with respect to random parameter variations, by using stochastic optimization methods, the original random structural optimization problem must be replaced by an appropriate deterministic substitute problem. Starting from the equilibrium equation and the yield condition, the problem can be described in the framework of stochastic (linear) programming problems with ‘complete fixed recourse’. The main properties of this class of substitute problems are discussed, especially the ‘dual decomposition’ data structure which enables the use of very efficient special purpose LP-solvers.