结构可靠度随机有限元--理论及工程应用

.2.5.1form 的误差
2.5.2变量置换函数的非线性特点
2.5.3算例
2.6本章小结
第3章模拟随机向量的随机数产生
3.1latin hypercube抽样基本原理
3.2单变量样本点的生成
3.3样本点排序
3.3.1样本点排序的迭代方法
3.3.2样本点排序算法的收敛性分析
3.4抽样空间的选择问题
3.5算例
3.5.1latin hypercube——直接mc法
3.5.2latin hypercube——scis法
3.6本章小结
第4章二次功能函数可靠度分析方法
4.1概述
4.2功能函数主曲率的计算
4.3传统二次可靠度方法的讨论
4.3.1sorm渐进近似公式
4.3.2其他sorm近似计算公式
4.3.3传统 sorm 法的缺陷分
4.4曲面拟合 sorm 算法
4.4.1曲率拟合法
4.4.2点拟合法
4.5曲面拟合 sorm 算法的优点
4.6本章小结
第5章基于验算点的可靠度算法及灵敏度分析
5.1概述
5.2验算点的迭代算法
5.2.1梯度迭代算法
5.2.2非梯度迭代算法
5.3功能函数hessian矩阵计算及曲面拟合sorm分析
5.4latin hypercube法form精度修正
5.4.1基本原理
5.4.2算法讨论
5.5可靠度的灵敏度分析
5.5.1随机变量的重要性灵敏度指标s（1）i
5.5.2失效概率对随机变量均值、方差的灵敏度指标s（2）i，s（3）i
5.6基于验算点的可靠度算法的分析流程
5.7算例
5.8本章小结
第6章随机场离散的方法
6.1概述
6.2随机场相关模型
6.3karhunen-loeve级数展开法
6.3.1直接karhunen-loeve分解
6.3.2正交级数展开法
6.4线性回归法
6.4.1线性回归原理
6.4.2线性回归原理应用于随机场离散
6.5随机场离散方法的比较
6.6随机场离散的影响规律分析
6.6.1随机场相关模型和离散变量数目的影响
6.6.2随机场相关长度的影响
6.7线弹性随机场梁单元
6.7.1随机场梁单元的刚度、质量矩阵
6.7.2随机场梁单元的自重、均布荷载和温度荷载随机场
6.8本章小结
第7章静力随机有限元反应的梯度计算
7.1可靠度随机有限元分析原理
7.2线弹性静力随机有限元反应梯度的计算
7.2.1直接微分法与附加系统法
7.2.2梯度计算过程
7.3考虑几何非线性的梯度计算
7.3.1梁系单元考虑几何非线性的直接迭代法
7.3.2几何非线性结构反应梯度计算的理论分析
7.3.3梯度计算过程及算例考核
7.4随机有限元第一类稳定分析
7.4.1广义特征值的梯度计算
7.4.2几何刚度矩阵的梯度计算
7.4.3稳定系数梯度计算过程及算例考核
7.5本章小结
第8章退化结构的时变结构可靠度、检修制度优化和剩余承载力评定
8.1概述
8.2抗力和作用效应随机过程
8.2.1抗力随机过程
8.2.2作用效应随机过程
8.3终生不修理的退化结构的时变可靠度计算
8.3.1活载为连续过程时
8.3.2活载为poisson过程时
8.3.3活载为bernoulli过程时
8.4根据抗力先验分布的结构检修制度优化
8.4.1桥梁检查
8.4.2桥梁修理
8.4.3退化桥梁构件的时变可靠度
8.4.4检查/修理制度事件树分析
8.4.5检查/修理的总费用
8.4.6检查/修理制度的优化
8.4.7算例
8.5基于预后验分析的结构检修制度优化
8.5.1预后验决策分析
8.5.2考虑poisson过程活载的退化的桥梁构件时变可靠度
8.5.3桥梁检查的效益
8.5.4用检查结果更新抗力退化模型
8.5.5桥梁检查制度的优化
8.6现有桥梁的剩余承载力评定
8.6.1现状车载模型
8.6.2剩余承载力评定
8.7本章小结
第9章结构系统可靠度
9.1概述
9.2ditlevsen上下界法
9.3特殊相关矩阵法
9.4一次多维正态法
9.5顺序条件重要抽样法
9.6对多极限状态函数的方向重要抽样法
9.6.1方向抽样mc法
9.6.2重要抽样mc法
9.6.3方向重要抽样mc法
9.6.4对多极限状态面的方向重要抽样mc法
9.7β-球面外的截尾正态重要抽样法
9.8多响应面法
9.9本章小结
第10章随机有限元动力反应梯度的计算
10.1动力可靠度分析原理
10.2随机结构的动力时程反应分析
10.2.1弹性单自由度随机系统有阻尼动力反应梯度
10.2.2弹性多自由度随机系统有阻尼动力反应梯度
10.3随机结构动力特性的梯度
10.3.1自振频率的梯度计算
10.3.2振型的梯度计算
10.3.3动力特性梯度算法考核
10.4动力时程分析的反应梯度计算过程及算法考核
10.5本章小结
第11章可靠度随机有限元程序resfep编制及算例分析
11.1概述
11.2resfep 主要功能
11.2.1计算类型
11.2.2随机性和分布类型
11.2.3功能函数
11.3resfep程序的编制原理
11.3.1程序模块组织
11.3.2计算流程
11.4算例分析
11.4.1两端固定随机场梁
11.4.2多层框架结构
11.4.3上承式双曲拱桥静力和面内稳定随机分析
11.4.4多联多跨连续梁桥地震落梁随机分析
11.5本章小结
结论与展望
附录a概率分布计算公式
附录bresfep数据文件输入格式
附录c三维杆单元和三维梁单元考虑几何非线性的切线刚度矩阵..
参考文献
prefaceⅰ
chapter 1introduction1
1.1background1
1.2formulation of reliability stochastic finite elements7
1.3related theory and current state9
1.3.1first order reliability methods9
1.3.2second order reliability methods11
1.3.3descretization of random fields12
1.3.4theory of stochastic finite elements13
1.4software of reliabilitys stochastic finite element analysis15
1.5main contents of the book17
chapter 2probability distributions and transformation of random variables20
2.1outline20
2.2nataf distribution21
2.3transformation of random vectors22
2.3.1transformation between nataf and independent standard normal distributions23
2.3.2jacobian matrix of transformation between nataf and independent standard normal distributions24
2.3.3partial differentials of distribution parameters of independent standard normal variables to original ones25
2.4implementaion of transformation software of random vectors26
2.5effects of additional nonlinearity induced by transformation of random vectors27
2.5.1errors in form results28
2.5.2characteristics of nonlinearity in transforms of random vectors29
2.5.3examples31
2.6summary32
chapter 3generating random numbers to simulate random vectors34
3.1idea behind latin hypercube sampling34
3.2generation of samples of single variable35
3.3sequencing samples37
3.3.1iteration methods for sequencing samples37
3.3.2convergence of methods for sequencing samples39
3.4issues on selection of sampling space40
3.5examples42
3.5.1latin hypercube—direct monte carlo methods43
3.5.2latin hypercube—sequential conditioned importance sampling45
3.6summary47
chapter 4reliability methods for second order performance functions49
4.1outline49
4.2principal curvatures of performance functions50
4.3discussion on traditional sorm methods52
4.3.1sorm assymptotic approximate formulae52
4.3.2other sorm approximate formulae53
4.3.3defects of traditional sorm methods56
4.4surfacefitting sorm methods59
4.4.1curvaturefitting method59
4.4.2pointfitting method62
4.5advantages of surfacefitting sorm methods65
4.6summary66
chapter 5reliability methods based on checkpoint and sensitivity analysis67
5.1outline67
5.2iterative methods for searching checkpoint68
5.2.1gradient iteration methods70
5.2.2nongradient iteration methods71
5.3hessian matrix of performance functions and surfacefitting sorm72
5.4latin hypercube form modification73
5.4.1basic ideas73
5.4.2discussions75
5.5sensitivity analysis of reliability76
5.5.1sensitivity index of importance of random variables s（1）i76
5.5.2sensitivity index of failure probability to means and variances of random variables s（2）i,s（3）i77
5.6flow chart of reliability methods based on checkpoint78
5.7examples79
5.8summary83
chapter 6methods of discretization of random fields85
6.1outline85
6.2correlation models for random fields87
6.3karhunenloeve series expansion88
6.3.1direct karhunenloeve resolution89
6.3.2orthogonal series expansion90
6.4linear regression method93
6.4.1theory of linear regression93
6.4.2application of linear regression to discretization of random fields94
6.5comparison between methods of discretization of random fields94
6.6analysis on effects of parameters of discretization of random fields97
6.6.1effects of correlation models and number of discretized variables97
6.6.2effects of correlation length of random fields100
6.7linear and elastic random field beam element101
6.7.1stiffniss and mass matrices of random field beam element102
6.7.2random fields of weight，distributed load and thermal actions of random field beam element103
6.8summary105
chapter 7gradient calculation of static responses of stochastic finite element106
7.1theory of reliability stochastic finite elements106
7.2gradient calculation of static responses of linear and elastic stochastic finite element107
7.2.1direct differentiation method and additional system method107
7.2.2procedure of gradient calculation109
7.3gradient calculation of geometrically nonlinear structures109
7.3.1direct iteration algrithms of geometrically nonlinear beam elements110
7.3.2gradient calculation of geometrically nonlinear structures115
7.3.3procedure of gradient calculation and example117
7.4bifurcation instability analysis of stochastic finite elements118
7.4.1gradient calculation of generalized eigen values119
7.4.2gradient calculation of geometric stiffness matrix120
7.4.3procedure of gradient calculation of instability factor and example121
7.5summary122
chapter 8reliability of timevarying structures，optimization of inspection/repair strategies and evaluation of remaining loadbearing capacity of existing bridges123
8.1outline123
8.2stochastic processes of resistance and action effect124
8.2.1stochastic processes of resistance124
8.2.2stochastic processes of action effect126
8.3timevarying reliability of deteriorating structures without repair126
8.3.1case for continuous live load processes126
8.3.2case for poisson live load processes130
8.3.3case for bernoulli live load processes131
8.4optimization of inspection/repair strategies based on prior resistance distributions134
8.4.1inspection of bridges134
8.4.2repair of bridges135
8.4.3timevarying reliability of structural components of deteriorating bridges136
8.4.4event tree analysis of inspection/repair strategies136
8.4.5total cost of inspection/repair137
8.4.6optimization of inspection/repair strategies138
8.4.7examples138
8.5optimization of inspection/repair strategies based on preposterior decision analysis142
8.5.1preposterior decision analysis142
8.5.2timevarying reliability of deteriorating bridge structural components under poisson live loads143
8.5.3utility of bridge inspection144
8.5.4updating deterioration models of resistance by using inspection data145
8.5.5optimization of bridge inspection schedules146
8.6evaluation of remaining loadbearing capacity of existing bridges150
8.6.1modeling loads of current vehicles150
8.6.2evaluation of remaining loadbearing capacity156
8.7summary159
chapter 9reliability of structural systems161
9.1outline161
9.2ditlevsens upper and lower bounds162
9.3methods of special correlation matrices163
9.4first order multinormal approach164
9.5sequential conditioned importance sampling approach165
9.6directional simulation importance sampling method for multilimit state functions169
9.6.1directional simulation mc method169
9.6.2importance sampling mc method170
9.6.3directional simulation importance sampling mc method171
9.6.4directional simulation importance sampling mc method for multilimit state functions172
9.7importance sampling methods excluding the βsphere from the sampling domain173
9.8multiple response surface approach175
9.9summary178
chapter 10gradient calculation of dynamic responses for stochastic finite elements179
10.1theory of dynamic reliability179
10.2dynamic time history response analysis of stochastic structures181
10.2.1response gradient of linear elastic damped sdof systems182
10.2.2response gradient of linear elastic damped mdof systems185
10.3gradient calculation of dynamic characteristics of stochastic structures187
10.3.1gradient calculation of natural frequencies187
10.3.2gradient calculation of mode shapes188
10.3.3verification of gradient calculation of dynamic characteristics189
10.4procedure of gradient calculation of dynamic characteristics and examples190
10.5summary191
chapter 11implementation of software resfep of reliability stochastic finite element and examples193
11.1outline193
11.2capability of resfep194
11.2.1analytical capability194
11.2.2stochastic properties and distribution types195
11.2.3performance functions196
11.3implementation of resfep197
11.3.1modular architecture of resfep197
11.3.2flow chart198
11.4examples203
11.4.1random field beam with two ends fixed203
11.4.2multistory frame208
11.4.3static and inplan buckling random analysis of a deck arch bridge211
11.4.4random displacement response analysis of a multispan continuous girder with expansion joints to earthquakes219
11.5summary222
conclusions and prospect223
appendix aexpressions for calculation of probability distributions229
appendix bformation of input data of resfep235
appendix ctangent stiffness matrices of 3d beam elements with geometrical nonlinearity245
references260...