Dynamic response and reliability analysis of structures with uncertain parameters

• Published in: International journal for numerical methods in engineering Vol. 62; no. 2; pp. 289 - 315
• Main Authors: Li, Jie, Chen, Jian-Bing
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 14.01.2005; Wiley
• Subjects: dynamic response; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Physics; precise time integration method; reliability; Solid mechanics; stochastic structures; Structural and continuum mechanics; the probability density evolution; TVD scheme; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Statistical analysis; Probabilistic approach; Initial condition; the probability density evolution; Random excitation; Initial value problem; Rupture; Evolution equation; Story(building); stochastic structures; Fracture criterion; Modeling; TVD scheme; Exact solution; Probability density; Uncertain system; Impedance matching; precise time integration method; Probability density function; Reliability; dynamic response; Random vibration; Structural analysis; Finite difference method
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1204

An original approach for dynamic response and reliability analysis of stochastic structures is proposed. The probability density evolution equation is established which implies that incremental rate of the probability density function is related to the structural response velocity. Therefore, the response analysis of stochastic structures becomes an initial‐value partial differential equation problem. For the dynamic reliability problem, the solution can be derived through solving the probability density evolution equation with an initial value condition and an absorbing boundary condition corresponding to specified failure criterion. The numerical algorithm for the proposed method is suggested by combining the precise time integration method and the finite difference method with TVD scheme. To verify and validate the proposed method, a SDOF system and an 8‐storey frame with random parameters are investigated in detail. In the SDOF system, the response obtained by the proposed method is compared with the counterparts by the exact solution. The responses and the reliabilities of a frame with random stiffness, subject to deterministic excitation or random excitation, are evaluated by the proposed method as well. The mean, the standard deviation and the reliabilities are compared, respectively, with the Monte Carlo simulation. The numerical examples verify that the proposed method is of high accuracy and efficiency. Moreover, it is found that the probability transition of structural responses is like water flowing in a river with many whirlpools, showing complexity of probability transition process of the stochastic dynamic responses. Copyright © 2004 John Wiley & Sons, Ltd.