Multi-probability constrained reliability-based topology optimization using volume control
Xiaona Yang, Qiliang Zhang, Zongwei Hu, Jie Wang, Wei WangPurpose
To overcome the limitation of deterministic topology optimization (DTO) which ignores uncertainties, this paper proposes a multi-probability-constrained reliability-based topology optimization (MRBTO) model for structures under multiple displacement constraints.
Design/methodology/approach
The MRBTO model treats loads and material properties as random variables and uses a series system to represent multiple failure modes. System failure probability is calculated using the first-order reliability method (FORM). An outer loop adaptively adjusts the structural volume to meet a target failure probability, while an inner loop employs a modified SIMP method to optimize the material layout. A two-stage dynamic Gaussian sensitivity filtering (DGSF) method eliminates checkerboards and gray elements. The framework is validated on a 2D MBB beam and a cantilever beam using Monte Carlo simulation.
Findings
Compared with DTO, MRBTO reduces the failure probability from approximately 50% to target levels (e.g. 5% or 1%) with high precision. The volume increase is modest – 5% for the cantilever beam even at the strictest target (1%), and about 7% for the MBB beam, which is a slight increase that is acceptable given the large reliability gain. Combined with DGSF, the discreteness rate (grayness ratio) drops from over 30% to nearly 0%, producing crisp boundaries and well-controlled displacements. MRBTO successfully handles multiple independent displacement constraints and different target failure probabilities simultaneously.
Originality/value
A novel volume-controlled MRBTO model that handles system-level multi-failure probabilities is introduced, integrating DGSF to eliminate gray elements and boundary blurring. The dual-loop solution strategy efficiently couples reliability analysis with topology optimization, offering a practical and robust design tool under uncertainties.