基于无路径依赖性方法研究工程结构失效模式与体系可靠度

The safety of engineering structures largely depends on their potential failure modes. The traditional methods for identification of the structural failure model and analysis of system reliability are essential path-dependent, which need to simulate the loading history step by step and the elasto-plastic state of elements piece by piece. It is obvious that above methods are very sensitive to the subjective selection of computing model parameters and often achieve unstable results with time-consuming computation. Furthermore, above methods often cannot be adopted in the large complex building structures, since there may be lots of potential failure paths. Hence, in this proposal the redistribution of inner forces will be simulated by reducing the elastic moduli of highly stressed elements ultilizing the iterative linear elastic finite element analysis, based on both the elastic modulus reduction method (EMRM) and the stochastic response analysis method. Then the structural capacity and stiffness distribution in the plastic limit state will be obtained. The dominant failure models and system reliability will be investigated by determining the potential failure elements in the critical state and the diversion of failure models evolution, by taking into account the distribution type of random parameters and correlation of sectional capacities. It is obvious that the proposed method may overcome the limitations of path-dependent traditional methods. Finally, both the element and integral safety factor and reliability index will be computed based on the results of the first and last iterative steps of the EMRM. Adjust strategies of both highly and lowly stressed elements will be established and the two level optimization methods of engineering structures will be proposed.

工程结构的安全性与其潜在失效模式密切相关。传统的结构失效模式和体系可靠度分析方法具有路径依赖性，需要分段模拟加载历史、分区选取本构方程，容易受到模型参数主观选择的影响，且潜在失效路径众多，导致计算效率低、结果不稳定，难以应用于大型复杂建筑结构。鉴于此，本项目利用弹性模量缩减法和随机响应分析方法，通过线弹性迭代并有策略地缩减高承载单元的弹性模量来模拟结构的内力重分布，确定结构进入塑性极限状态时的承载力和刚度分布状态。综合考虑随机参数分布类型和截面强度相关性，分析结构的损伤演化，确定结构进入临界状态时的潜在失效元，据此研究结构主要失效模式和体系可靠度，克服传统方法的路径依赖性及其缺陷。进一步地，根据弹性模量缩减法首步和末步迭代计算结果，计算结构在构件和整体两个层面上的安全系数和可靠度，分别建立高承载和低承载构件的截面强度调整方法，满足结构两层面承载安全性，并达到优化设计目标。

工程结构的安全性与其潜在失效模式密切相关。传统的结构失效模式和体系可靠度分析方法具有路径依赖性，需要分段模拟加载历史、分区选取本构方程，容易受到模型参数主观选择的影响，且潜在失效路径众多，导致计算效率低、结果不稳定，难以应用于大型复杂建筑结构。鉴于此，本项目结合弹性模量缩减法，利用齐次广义屈服函数建立单元承载比，建立自适应动态弹性模量调整策略，进而通过线弹性迭代并有策略地缩减高承载单元的弹性模量来模拟结构的刚度损伤及内力重分布，当结构达到塑性极限状态时根据高承载单元的弹性模量缩减幅度批量识别失效元，并利用塑性铰标识潜在失效元，由此确定结构的失效模式，提出了结构损伤演化模拟、失效元及失效模式识别的高效无路径依赖性方法。同时，对工程结构体系可靠度的高效分析方法进行了研究，建立了工程结构多目标可靠度问题分析的高效向量型响应面法和随机结构失效演化和体系可靠度分析的自适应动态β约界法。结合随机响应面法和弹性模量缩减法，研究建立了工程结构体系可靠度分析的无路径依赖性方法，避免了传统体系可靠度分析中的主要失效模式难以识别和多失效模式联合失效概率计算繁琐两大难点。进一步地，根据弹性模量缩减法首步和末步迭代计算结果，计算结构在构件和整体两个层面上的安全系数和可靠度，分别建立高承载和低承载构件的截面强度调整方法，进而建立工程构件和整体两个层面承载安全性分析理论、和相应的设计方法，据此满足结构两层面承载安全性，并达到优化设计目标。