Efficient algorithm for probability-based design optimisation of complex structures and related issues

Abstract

The probabilistic structural design optimisation problem can be carried out using either the conventional reliability index approach (RIA) or the performance measure approach (PMA). The direct approach for either RIA or PMA is to form a two-level optimisation by simply connecting algorithms of probabilistic calculation and design optimisation, which is computationally prohibitive for complex structures. The authors used the sequential approximate programming (SAP) strategy for RIA and extended to PMA. Examples show that SAP for both RIA and PMA reduce the total number of function evaluations notably, whereas PMA with SAP is more efficient and less dependent on probabilistic distributions and thus serves as a promising approach for complex structures. This study introduces the two SAP approaches in a unified way and shows that in these approaches, Taylor linear approximation is applied to both design variables and random variables. Two kinds of variables are treated in the same way from the mathematical viewpoint.