STO-DAMV: Sequential topology optimization and dynamical accelerated mean value for reliability-based topology optimization of continuous structures

Abstract

In deterministic topology optimization (TO), due to not taking into account the uncertainties of the structural system, explicitly, resulting optimal layouts may conclude in low reliable levels or unreliable optimum design conditions. The objective of reliability-based topology optimization (RBTO) is to integrate the reliability concept into topology optimization, finding the optimized structures priori by the designer through a mathematical framework guaranteeing that the least reliability level is achieved. In the present investigation under a constant volume fraction, the bisection algorithm is implemented for approximating the optimal feature of the structure in the TO framework by applying the moving iso-surface threshold (MIST) topology optimization approach. The results from the previous step are employed to consider uncertainties by a reliability analysis algorithm. A reliability analytical method based on dynamical accelerated formulation is combined with the TO-based bisection algorithm as a novel sequential topology optimization and reliability analysis (STORA) for RBTO. The descent condition is guaranteed in the dynamical accelerated mean value method to search the most probable point which is applied in TO for finding optimum layouts of continuous structure problems. A dynamical step factor in the reliability loop of the STORA and the MIST integration are applied to find the optimum layouts in the optimization loop. Illustrative examples are presented for validation and to maintain the capability of the proposed sequential topology optimization and dynamical accelerated mean value (STO-DAMV). Based on the results, it is demonstrated that the application of reliability analysis with the integration of bisection in topology optimization can produce a robust reliability analysis with stable results in RBTO which facilitates a more reliable design than that acquired by TO. It is also concluded that, under identical accuracy, STO-DAMV for STORA is improved in view of computational robustness.