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Failure Probability Assessment of Single-layer Reticulated Dome Considering Dynamic Instability

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**Jun Xu**

Rice University

United States

**Jie Li**

Tongji University

China

*Abstract:*

Single-layer reticulated dome is widely observed in engineering practice. Dynamic instability is of great concern in such type of structure subjected to dynamic excitations. However, dynamic instability may not manifest the failure of dome because the dome may still can bear loads and the failure is attributed to members' losing strength after dynamic instability. Therefore, it is of paramount importance and significance to evaluate the safety of such dome via failure probability considering both stable behaviors and after-instability behaviors.

The present paper deals with failure probability assessment of a single-layer dome under stochastic ground motion where dynamic instability can't be ignored. The double orthogonal decomposition of stochastic process is adopted to model the stochastic ground motion. Probability density method (PDEM) is employed to carry out the stochastic analysis. Two physical paths are concerned in such stochastic dynamic system, say the stable path and unstable path. To finally obtain the global failure probability of the dome, failure probability of each physical path should be studied independently.

An energetic criterion for identification of dynamic instability is incorporated into PDEM to study the unstable probability by imposing an absorbing boundary. Actually, unstable probability is identical to failure probability of unstable path if dynamic instability indicates structural failure. However, if failure after dynamic instability is concerned , inverse absorbing strategy is firstly implemented to get the probabilistic information of response after dynamic instability which is probability unpreserved. Then complementary stochastic process within the safety domain is proposed to make up the probability unpreserved system to be probability preserved. After that, the failure probability of unstable path can be evaluated by imposing absorbing boundary on the basis of the modified probability preserved system. On the other hand, the probabilistic information of stable path can also be calculated by inversely absorbing the unstable probabilistic information in the stochastic system and evolves independently. Likewise, the failure probability of stable path can be determined accordingly. Then the global failure probability of the single-layer reticulated dome is the summation of the failure probabilities of both paths.