钢框架结构的非线性静力抗震可靠性分析:Ⅰ有限元反应及其灵敏度

Nonlinear static seismic reliability analysis of steel frame structures:Ⅰ Finite element response and its sensitivity

作为一种随机有限元方法,有限元可靠度方法通过有限元反应灵敏度分析将结构可靠度分析的近似解析方法与结构确定性分析的有限元方法结合起来,可以有效地处理结构反应是基本随机变量的隐式函数这一难题,因此成为大型复杂结构可靠度分析的有效工具。采用基于位移的非线性纤维梁柱单元对钢框架结构进行有限元建模,推导了单元与截面的基本方程。针对基于位移的纤维梁柱单元,采用逐级递进方式,分别推导了整体级、单元级、截面级和材料级的有限元反应灵敏度直接微分表达式。研究结果可为采用FORM或SORM等近似解析法进行钢框架结构的非线性静力有限元可靠性分析提供算法支持和编程依据。

As a stochastic finite element method, the finite element reliability method （FERM）, which combines the approximate analytical methods of structural reliability analysis with deterministic finite element methods of structural response analysis, can successfully overcome the difficulties in which structural responses are implicit functions of basic random variables; hence, FERM has become an effective tool for large-scale complex structure reliability analysis and risk assessment. In this paper, the finite element model is built up for steel frame structures by using displacement-based nonlinear fiber beam-column elements, and the basic equations for element and section are derived. The direct differential formulations of finite element response sensitivity at the global, element, section and material levels for the displacement-based beam-column elements are given in the manner of a hierarchical structure. The formulations given in this paper can provide an algorithm support and programming basis for the nonlinear static finite element reliability analysis of steel frame structures by using approximate analytical techniques, such as FORM or SORM.