UBC-constrained non-probabilistic reliability-based optimization of structures with uncertain-but-bounded parameters

A new UBC-constrained (ultimate-bearing-capacity-constrained) non-probabilistic reliability-based optimization method for structures with uncertain-but-bounded parameters is proposed. Different from the traditional stress-constrained optimization, the ultimate bearing capacity (UBC) is taken as the constraints in the non-probabilistic reliability-based optimization, which reflect the system safety of structures. Based on the interval mathematics, the UBC constraint is transformed into the format of non-probabilistic reliability, in which a novel measuring index, namely, the UBC, is defined by an interval interference model. Thus, structural optimization is converted by the lightweight design problem with UBC reliability constraints. Moreover, the gradient-based Taylor expansion method is employed to obtain the lower and upper bounds of the UBC, which transforms a double-layer optimization into an efficient single-layer one. Finally, 2D and 3D structural examples are given to illustrate the effectiveness of the proposed method.