Reliability-Based Shape Optimization Using Stochastic Finite Element Methods

Application of first-order reliability methods FORM (see Madsen, Krenk & Lind [8]) in structural design problems has attracted growing interest in recent years, see e.g. Frangopol [4], Murotsu, Kishi, Okada, Yonezawa & Taguchi [9] and Sorensen [14]. In probabilistically based optimal design of structural systems some of the quantities used in the modelling are modelled as stochastic variables. The stochastic variables are usually related to the strength, the loads or the mathematical model. However, generally a more realistic modelling of some of the uncertain quantities is obtained by using stochastic fields (e.g. loads and material parameters such as Young’s modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke [6] and Liu & Der Kiureghian [7].