System-reliability-based design and topology optimization of structures under constraints on first-passage probability

• Published in: Structural safety Vol. 76; pp. 81 - 94
• Main Authors: Chun, Junho, Song, Junho, Paulino, Glaucio H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.01.2019; Elsevier BV
• Subjects: Design optimization; Earthquakes; Failure; First-passage probability; Ground motion; Parameter sensitivity; Probability distribution; Probability theory; Reliability analysis; Reliability engineering; Reliability-based design optimization; Reliability-based topology optimization; Seismic activity; Seismic design; Sensitivity analysis; Sequential compounding method; Stochastic excitation; Stochastic models; Structural design; Structural engineering; Structural reliability; System reliability; Topology; Topology optimization; Reliability-based design optimization; Stochastic excitation; Sequential compounding method; First-passage probability; Reliability-based topology optimization; Parameter sensitivity; System reliability
• ISSN: 0167-4730; 1879-3355
• DOI: 10.1016/j.strusafe.2018.06.006

•Structural optimization framework considering stochastic dynamic loading is proposed.•The method is developed for both structural design and topology optimization.•First-passage probability of engineering constraint is integrated into optimization.•The analytical sensitivity is derived for the first-passage probability constraint.•Numerical applications demonstrate the efficiency and effectiveness of the method. For the purpose of reliability assessment of a structure subject to stochastic excitations, the probability of the occurrence of at least one failure event over a time interval, i.e. the first-passage probability, often needs to be evaluated. In this paper, a new method is proposed to incorporate constraints on the first-passage probability into reliability-based optimization of structural design or topology. For efficient evaluations of first-passage probability during the optimization, the failure event is described as a series system event consisting of instantaneous failure events defined at discrete time points. The probability of the series system event is then computed by use of a system reliability analysis method termed as the sequential compounding method. The adjoint sensitivity formulation is derived for calculating the parameter sensitivity of the first-passage probability to facilitate the use of efficient gradient-based optimization algorithms. The proposed method is successfully demonstrated by numerical examples of a space truss and building structures subjected to stochastic earthquake ground motions.