an:01156493
Zbl 0896.90106
Kuschel, Norbert; Rackwitz, R??diger
Two basic problems in reliability-based structural optimization
EN
Math. Methods Oper. Res. 46, No. 3, 309-333 (1997).
00044526
1997
j
90B25 74P99 90C90
reliability-oriented optimization; probabilistic reliability constraints; one-level optimization; structural failure; semi-infinite programming
Summary: Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper, two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation.