Convex Programming-Based Robust Optimization Procedure for Blast-Excited Structures with Bounded Uncertainty

Abstract

Application of the robust optimization (RO) technique to ensure the least possible deviation of structural performance is gaining increasing attention in recent years. However, most RO studies have been conducted in the probabilistic domain, where sufficient uncertainty information is available to construct probability distribution functions of response parameters. But, in many cases, such as for structures under underground blast excitation, hazard parameters like charge weight and charge center distance do not have any definite probability density function. Only their ranges of variations are known to an engineer. Hence, it is more logical to model these parameters as uncertain-but-bounded (UBB) type, which requires only bounds of variations to characterize the uncertainty. The available RO studies in the UBB-domain mainly deal with static loads. Studies on time-variant dynamic loads, such as blast load, are scarce in the existing literature. Also, blast load time-histories show record-to-record variations in their signatures, even with the same setup of hazard parameters. This aspect cannot be considered by the conventional convex programming approaches of RO in the UBB domain. To address all these issues, a new RO procedure is proposed in the present study, which is based on the dual response surface method. The proposed RO procedure can transform the complex simulation-based RO procedure under dynamic blast load to an equivalent deterministic problem with explicit constraints. Thereby, the RO can be easily solved by a gradient-based optimizer. The effectiveness of the proposed approach is elucidated by the complex real-world problems of a multistory building and an underground reinforced concrete bunker. The results are compared with conventional RO approaches. The results show that the proposed approach consistently yields more economic as well as robust solutions in a computationally efficient way.