【摘要】 将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明:尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算"小震"作用下结构的承载能力可靠度和"大震"作用下结构的变形能力可靠度是不够的,还需要验算在"中震"和"大震"作用下结构的极限承载能力可靠度。更多还原

【Abstract】 The reliability analysis of large-scale complex structures with implicit performance functions can be realized by combining the finite element response and its sensitivity analysis with the approximate analytical methods in structural reliability theory.In this companion paper,the finite element methods and computational reliability methods including FORM and SORM are efficiently integrated by mechanical transformation,probability transformation and response sensitivity analysis based on the theory of nonlinear displacement fiber beam-column element and direct differential response sensitivity formulations.According to the current seismic design code,the seismic limit state functions of strength and displacement are built up for typical members and storey levels of steel frames.Based on the equivalent static model of the random seismic action,the seismic reliability and its sensitivities of a practical engineering structure is analyzed by the nonlinear finite element reliability method.The results show that although the reliability index for storey-level displacement is high under the action of severe earthquakes,the strength reliability index is very low.This reveals that the structure is still at the high risk of failure.Therefore,it is not sufficient to check the load-carrying capacity reliability under minor earthquakes and deformation reliability under major earthquakes.It is necessary to verify the ultimate load-carrying capacity reliability under both moderate and major earthquakes.更多还原