Non-iterative method for reliability-based topology optimization of static and dynamic problems with uncertain-but-bounded parameters

The non-probabilistic reliability-based topology optimization (NRBTO) method offers a powerful tool for achieving high-performance and high-safety layout designs under uncertain-but-bounded (UBB) parameters. However, the practical application of NRBTO is limited by unaffordable computational burden associated with repeated non-probabilistic reliability iterations. To address this issue, a new non-iterative reliability-based topology optimization method for static and dynamic problems with UBB parameters is established to avoid the non-probabilistic reliability iteration, in which a novel non-iterative method (NIM) is proposed by strict proving the monotonicity conditions with respect to UBB parameters. The complex NRBTO model is transformed into an equivalent deterministic topology optimization model, thereby reducing computational costs. Moreover, the sensitivities with respect to design variables are derived using the adjoint method. The effectiveness of proposed NIM for NRBTO is validated through two static and two dynamic examples, where the compliance, displacement, stress, frequency, and frequency-band problems are addressed.