Reliability-based topology optimization of interval parameters structures with dynamic response constraints

An improved equivalent static loads method (ESL) for interval parameters structures is proposed based on local equivalence. In this method, the reliability-based dynamic response topology optimization is solved in the time domain. While calculating the improved ESLs, two measures are taken to prevent the uncertainty from increasing in the process of interval arithmetic. Firstly, only the uncertainty of the critical degrees of freedom is considered. Secondly, the uncertain ESLs are expressed by set. Through the measures above, the interval static response by uncertain ESLs has the same median with the interval dynamic response by dynamic loads, and their deviations in the critical degree of freedom are same. Based on the definition of the non-probabilistic reliability index and structural optimization principle of ESL, the static reliability-based topology optimization model is constructed. The adjoint variable schemes for sensitivity analysis of non-probabilistic reliability constraints are discussed. The method of moving asymptotes is adopted to solve the structural optimization problem. The validity of the model and proposed numerical techniques was verified by examples.