Efficient evaluation of probabilistic constraints using an envelope function

Probabilistic design optimization deals with uncertainties quantitatively and can be characterized by probabilistic constraints. As evaluating the probabilistic constraints requires quite large computational cost, reduction of the number of the probabilistic constraints by using an envelope function can improve the efficiency of the optimization process. Several numerical examples are tested adopting the reliability index approach and the performance measure approach with or without the envelope function. The results show that the proposed method requires fewer function evaluations. Efficiency improvement would be remarkable for large structural problems.