Stochastic Response Determination and Reliability Assessment of a Nonlinear Cable Net Structural System

Abstract eng:
A multi-degree-of-freedom (MDOF) symmetric cable net system with fixed cable ends under Gaussian white noise excitation is considered. First, a dimension reduction approach based on similarity relations is employed to cast the original MDOF system into an equivalent single-degree-of-freedom (SDOF) nonlinear oscillator of the hardening Duffing kind. Next, a numerical path integral (NPI) approach is utilized for determining the reduced system non-stationary response amplitude probability density function (PDF). The main concept of the approach relates to the evolution of the response PDF in short time steps, assuming a Gaussian form for the conditional response PDF. Further, the NPI approach is employed for determining first-passage kind reliability statistics of the Duffing oscillator; these are associated with the probability of cable tensile failure for specific mechanical and geometrical characteristics of the original cable net system. It is noted that the main advantages of the approximate deterministic approach of dimension reduction relate to a) the detection of nonlinear phenomena, such as the occurrence of sub/super-harmonic resonances, jump phenomena, etc, and b) the reduction of the computational effort associated with the nonlinear dynamic analysis of the original MDOF system. The latter advantage becomes significantly more important in the case of stochastic excitation where Monte Carlo simulation (MCS) methodologies can be computationally prohibitive, especially for cases of large scale complex systems. Hopefully, the herein developed approximate stochastic approach can be used as a convenient tool for preliminary reliability based design of the original MDOF structural system.

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