Component and system reliability-based topology optimization using a single-loop method

• Published in: Structural and multidisciplinary optimization 2010-02, Vol.41 (1), p.87-106
• Main Authors: Silva, Mariana, Tortorelli, Daniel A., Norato, Julian A., Ha, Christopher, Bae, Ha-Rok
• Format: Article
• Language: English
• Subjects: Component reliability; Computational Mathematics and Numerical Analysis; Computer simulation; Engineering; Engineering Design; Reliability analysis; Research Paper; System reliability; Theoretical and Applied Mechanics; Topology optimization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-009-0401-5

We perform reliability-based topology optimization by combining reliability analysis and material distribution topology design methods to design linear elastic structures subject to random inputs, such as random loadings. Both component reliability and system reliability are considered. In component reliability, we satisfy numerous probabilistic constraints which quantify the failure of different events. In system reliability, we satisfy a single probabilistic constraint which encompasses the component events. We adopt the first-order reliability method to approximate the component reliabilities and the inclusion-exclusion rule to approximate the system reliability. To solve the probabilistic optimization problem, we use a variant of the single loop method, which eliminates the need for an inner reliability analysis loop. The proposed method is amenable to implementation with existing deterministic topology optimization software, and hence suitable for practical applications. Designs obtained from component and system reliability-based topology optimization are compared to those obtained from traditional deterministic topology optimization and validated via Monte Carlo simulation.