Reliability Analysis Of Uncertain Hysteretic Systems

Hysteretic system is one of the most typical nonlinear systems in engineering. Structural systems under dynamic loading usually exhibit hysteretic behavior, especially when the response becomes inelastic. The effect of hysteretic restoring force exhibits the change of stiffness and energy. Because the restoring force of a hysteretic system depends not only on the instantaneous displacement, but also on its past history. Uncertainties in material properties and structural geometry are due to measurement inaccuracies or structure complexities. Structures with random parameters are complicated to analyze, since the response is statistically correlated to these parameters. The safety of engineering structures is one of the major objectives of structure design. It can help designer to establish acceptable tolerances on structures and determine the fluctuations of the system parameters for safety operations.On the basement of the Bouc-Wen hysteretic model, an numerical method for the reliability analysis of nonlinear stochastic hysteretic system that caused by uncertain hysteretic loop itself is presented, mainly including of following three aspects:1. In the premise of the independent of failure modes, the fourth-moment technique and Edgeworth series approximation theory are employed to develop a reliability analysis method systematically. With known the first-four moment of random parameters, the corresponding statistical characters of limit state equation of system are computed. So the probability distribution of limit state equation can be express by standard normal distribution function from Edgeworth series.2. The probability purterbation method is emloyed to determine the statistical characteristic of failure modes and the correlation between them. The dynamtic sensitivity for correlation of failure modes with respect to random parameters is discussed in time domain. A numerical method of dynamic sensitivity analysis for correlation of failure modes of nonlinear random vibration system is developed. The numeric example is used to verify the present method.3. The theory of incomplete probability information, the statistical fourth-moment technique and Gram-Charlier series approximation theory are employed to develop a reliability analysis method systematically. The numerical example has revealed that in most of cases, though stochastic system is characterized by a set of independent random parameters, the responses are strong correlated and correlated failure modes is main cause of system failure. It has solved the reliability analysis of nonlinear stochastic hysteretic system that caused by uncertain hysteretic loop itself and correlated failure modes...