Structural optimization of non-linear systems under stochastic excitation

• Published in: Probabilistic engineering mechanics Vol. 21; no. 4; pp. 397 - 409
• Main Author: Jensen, Hector A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2006; Elsevier Science
• Subjects: Applied sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical engineering. Machine design; Non-linear systems; Physics; Response statistics; Solid mechanics; Static elasticity (thermoelasticity...); Statistical equivalent linearization; Stochastic response; Structural and continuum mechanics; Structural optimization; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Stochastic response; Statistical equivalent linearization; Structural optimization; Response statistics; Non-linear systems; Statistical analysis; Probabilistic approach; Statistical moment; Random excitation; Optimization; Engineering design; Design process; Uncertain system; Function minimization; Random load; Non linear effect; Non deterministic system; Random vibration; Structural analysis; Linearization
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2006.02.002

This work concentrates on the structural optimization of a class of non-linear systems with deterministic structural parameters subject to stochastic excitation. The optimization problem is formulated as the minimization of an objective function subject to constraints on the response level. The stochastic response is characterized by its first two statistical moments, which are computed by a statistical equivalent linearization technique. The implicit structural optimization problem is replaced by a sequence of explicit sub-optimization problems. The sub-problems are constructed by using a conservative first-order approximation of the objective and constraint functions. The applicability of the proposed design process is demonstrated in three numerical examples where the methodology is applied to systems with nonlinearity of hardening and hysteretic type. The effects of the nonlinearity on the general performance of the final designs are discussed. At the same time, some engineering implications of the results obtained in this work are addressed.