Optimal design and sensitivity of large scale plane frames for the case of uncertainty

This paper deals with the optimal design and the robustness of large scale plane frames in dependence of their height. Using the first collapse theorem, the necessary and sufficient survival conditions of an elasto-plastic structure consist of the yield condition and the equilibrium condition. The basis for our consideration is provided by a plane n-storey frame which will be increased successively, and which is affected by applied random forces and moments. Taking into account these random applied loads, we get a stochastic structural optimization problem which cannot be solved using the traditional methods. Instead of that, an appropriate (deterministic) substitute problem is formulated. First, the recourse problem will be formulated in general and in the standard form of stochastic linear programming (SLP), and after the formulation of the stochastic optimization problem, the Recourse Problem based on Discretization (RPD) is introduced as a representative of substitute problems. The resulting (large scale) linear program (LP) can be solved efficiently by means of usual LP-solvers. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)