基于极限承载能力和地震延性需求的结构可靠度研究
|
摘要
结构的极限承载能力和地震延性需求是反映工程结构强度和延性的两个重要指标,也是结构安全性和适用性评估以及结构抗震设计的重要参数。本论文基于极限分析理论和广义屈服准则,研究建立了复杂结构极限承载能力分析的弹性模量缩减法；结合随机有限元、极限分析和点可靠度理论,研究建立了复杂结构体系可靠度分析的影响系数法和随机弹性模量缩减法；对经典的单轴Bouc-Wen模型进行改进,分别建立了单、双向地震激励和平扭耦联作用下非弹性体系非线性地震动力响应分析的新型Bouc-Wen模型,结合69条强震记录定量地分析了p-Δ效应、捏拢效应、强度退化、刚度退化等因素对非弹性体系的地震延性需求和Park-Ang地震损伤指标的概率统计特征的影响,并建立了地震延性需求的经验概率分布模型和预测方程。上述研究成果对于工程结构的安全性、适用性评估以及抗震可靠度分析具有重要的理论意义和工程应用价值。本论文的主要研究工作有：
(1)基于极限分析理论和广义屈服准则,定义了单元承载比、承载比均匀度、基准承载比等参数的物理意义和计算表达式,并以单元承载比作为控制参数,结合应变能平衡原理研究建立了复杂结构极限承载能力分析的弹性模量缩减法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于由多种材料和多种单元类型构成的复杂结构的极限承载能力分析。
(2)基于常应变法、圆弧法、应变能守恒和应变能平衡等不同原理研究建立了确定弹性模量缩减因子的四种策略,并结合空间桁架、刚架以及板壳结构对四种策略的计算精度和效率进行讨论,发现基于应变能平衡原理的弹性模量缩减法具有较高的计算效率和计算精度,为弹性模量缩减因子的确定提供了明确的物理意义和科学依据。
(3)针对极限分析的解析法、数学规划法以及传统弹性模量调整法中“比例加载”这一限定,对所建立的弹性模量缩减法作进一步改进,研究提出了一种适用于非比例加载条件下结构极限承载能力分析的新方法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于恒荷载和活荷载共同作用下的复杂工程结构的极限承载能力分析。
(4)考虑P-Δ效应、捏拢效应、强度退化、刚度退化以及应变硬化等因素对非弹性体系地震动力响应的影响,研究建立了单向地震激励作用下非弹性单自由度体系非线性地震动力响应分析的新型单轴Bouc-Wen模型,并结合69条强震记录定量地分析了P-A效应和捏拢效应对非弹性单自由度体系的地震延性需求和Park-Ang地震损伤指标的概率统计特征的影响,进而建立了地震延性需求的经验概率分布模型和预测方程。
(5)提出采用规一化位移作为控制参数,以圆形屈服而来描述双向规一化恢复力之间的耦合效应,研究建立了双向地震激励下非弹性体系非线性地震动力响应分析的新型双轴Bouc-Wen模型,结合69条强震记录定量地分析了双向地震激励和P-A效应对地震延性需求和Park-Ang损伤指标的概率统计特征的影响,并建立了地震延性需求和累积滞回耗能的近似公式。
(6)提出采用圆形屈服面来描述双向规一化抗侧恢复力之间的耦合效应,采用锥体或球体屈服而来描述双向抗侧恢复力和扭矩之问的耦合效应,研究建立了平而不规则结构非弹性地震动力响应分析的平扭耦联Bouc-Wen模型,结合69条强震记录定量地分析了结构的规一化屈服强度、非耦联平动自振周期、规一化刚度偏心距、非耦联扭转平动频率比、屈服后刚度比等参数对平面不规则结构非弹性平扭耦联效应的概率统计特征的影响。
(7)结合极限分析的弹性模量调整策略和点可靠度理论,研究建立了结构体系可靠度分析的影响系数法。该方法利用确定性有限元分析建立外荷载和单元内力之间的关系,以单元可靠指标作为控制参数定义结构的可靠指标均匀度和基准可靠指标,通过系统地调整各单元的弹性模量以模拟结构的可靠指标重分布和失效状态转移,通过一系列线弹性有限元迭代分析确定结构的最终失效模式和体系可靠度。计算结果显示,该方法的计算精度高、收敛速度快,且有效克服了传统体系可靠度分析中失效状态演化过程模拟复杂、主要失效模式难以识别两大难点。
(8)结合随机有限元、极限分析和点可靠度理论,研究建立了空间变异结构体系可靠度分析的随机弹性模量缩减法。该方法考虑结构参数和外荷载的空间变异性,利用数值积分法确定随机场局部平均间的协方差矩阵,采用摄动随机有限元法确定结构的随机响应量和各控制单元的可靠指标,进而以单元可靠指标作为控制参数,结合弹性模量调整策略和随机有限元迭代分析模拟结构的可靠指标重分布和失效状态转移,最终确定结构的整体失效模式和体系可靠度。由于该方法避免通过虚拟塑性铰、虚加外荷载来模拟结构的失效演化历程和破坏模式,所以结构的单元刚度矩阵和荷载列阵计算公式始终保持不变,因此具有计算精度高、收敛速度快、且可以有效考虑结构参数和外荷载的空间变异性等特点。
Ultimate bearing capacity and seismic ductility demand are two important indices representing strength and ductility performance of engineering structures, which are also key parameters for safety and applicability evaluation as well as structural seismic design. In this study, the Elastic Modulus Reduction Method (EMRM) was proposed to evaluate ultimate bearing capacity of complex structures based on the generalized yield criterion and limit analysis theory. Two novel methods including the Influence Coefficient Method (ICM) and Stochastic Elastic Modulus Reduction Method (SEMRM) were developed for system reliability analysis of large complicated structures based on theories of stochastic finite flement, limit analysis and component reliability. Furthermore, three new Bouc-Wen models for nonlinear seismic dynamic analysis of inelastic systems under unidirectional-, bidirectional-, and lateral-torsional coupling excitations were developed by improving the traditional uniaxial model. The influences of P-△and pinching effects as well as strength and stiffness degradations on probabilistic characteristics of seismic ductility demand and Park-Ang damage index of inelastic system were also quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic system with strength and stiffness degradations as well as P-△and pinching effects were also developed. This study provides significative foundation of theory research and guidance of engineering application in safety and applicability evaluation as well as seismic reliability analysis. The main contents of this thesis are as follows:
(1) The element bearing ratio (EBR), degree of uniformity of EBRs, and the reference EBR were defined based on the generalized yield criterion and limit analysis theory. By adopting the EBR as a governing parameter, the Elastic Modulus Reduction Method (EMRM) was developed based on the Strain Energy Equilibrium Principle (SEEP). Numerical examples show that the EMRM is accurate and efficient for limit analysis of complex structures constructed with multi-material and with complicated configuration.
(2) Four strategies including the Fixed Strain Method (FSM), the Circular Arc Method (CAM), the Strain Energy Conservation Law (SECL), and the Strain Energy Equilibrium Principle (SEEP) were proposed to determine the elastic modulus reduction factor. The applications and limitations of above four strategies in limit analysis of spatial frame and truss as well as thin plate and shell structures were investigated. Numerical results show that flexibility and accuracy of the SEEP is most satisfied, which provides a rational way to determine the elastic modulus reduction factor.
(3) A novel method to calculate ultimate bearing capacity of frame structure under combined action of initial constant and proportional loads was developed by modifying the proposed Elastic Modulus Reduction Method (EMRM), which eliminates the assumption of proportional loading existed in various analytical and mathematical programming methods as well as traditional elastic modulus adjustment procedures for limit analysis. Numerical results show that the method is accurate and efficient to evaluate ultimate bearing capacity of frame structure under both dead and live loads.
(4) A new uniaxial Bouc-Wen model for nonlinear seismic dynamic response analysis of inelastic single-degree-of-freedom (SDOF) system under unidirectional ground motion excitation was developed considering P-A effect, pinching effect, strength and stiffness degradations, and strain hardening. The influences of P-A and pinching effects on probabilistic characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic SDOF system were quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic SDOF system with P-A and pinching effects were also developed.
(5) Adopting the normalized displacement as governing parameter, a new biaxial Bouc-Wen model for nonlinear seismic dynamic analysis of inelastic two-degree-of-freedom (2DOF) system under bidirectional ground motion excitations was developed using circular yield surface to describe coupling effect of biaxial normalized restoring forces. The influences of bidirectional excitation and P-A effect on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic 2DOF system were discussed using 69 earthquake records. Approximate prediction equations for seismic ductility demand and cumulative dissipated energy of inelastic 2DOF system under bidirectional excitation and with P-△effect were also developed.
(6) By adopting the circular yield surface to describe the coupling effect between biaxial normalized lateral restoring forces and the pyramidal or spheriform yield surface to describe the coupling effect of normalized biaxial lateral restoring forces and torsion, a new lateral-torsional coupling Bouc-Wen model for nonlinear seismic dynamic analysis of planar asymmetric structure under bidirectional ground motion excitations was developed. The influences of the normalized yield strength, uncoupled translational frequency ratio, normalized stiffness eccentricity, uncoupled lateral-to-torsional frequency ratio, and post-yield stiffness to initial stiffness ratio on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of planar asymmetric structure were also investigated using 69 earthquake records.
(7) The Influence Coefficient Method (ICM) was proposed to evaluate system reliability of frame structure by combining elastic modulus adjustment procedure and component reliability theory. The relationship between internal forces and external loads was determined by determinate linear elastic finite element analysis and the element reliability index was adopted as governing parameter to define the degree of uniformity of reliability indices and reference reliability index. A new procedure for elastic modulus adjustment was proposed to simulate redistribution of element reliability indices and transition of failure modes. The failure probability of complex structural system can be achieved based on iterative linear elastic finite element analyses. Numerical results show that the ICM is accurate and efficient for system reliability analysis of large complicated structures, and overcomes difficulties for simulation of failure transition and identification of dominant failure modes in traditional methods.
(8) The Stochastic Elastic Modulus Reduction Method (SEMRM) for system reliability analysis of spatial variance frame was proposed based on theories of random field, limit analysis and component reliability. The structural parameters and external loads were modeled as random fields to account for their spatial variations and the covariance matrix of local averages of random fields was calculated using the numerical integration method. The stochastic response and reliability index of each element were achieved by the Perturbation Stochastic Finite Element Method (PSFEM). By adopting the element reliability index as governing parameter, a new strategy for elastic modulus adjustment in system reliability analysis was developed. The collapse mechanism and system reliability index of stochastic frame can be determined through iterative stochastic finite element analyses. Comparing with traditional failure mode approaches, the SEMRM is accurate and efficient, which also avoids modification of element stiffness matrix and artificial loading to simulate failure mode transition and accounts for spatial variations of both structural parameters and external loads rationally.
(1)基于极限分析理论和广义屈服准则,定义了单元承载比、承载比均匀度、基准承载比等参数的物理意义和计算表达式,并以单元承载比作为控制参数,结合应变能平衡原理研究建立了复杂结构极限承载能力分析的弹性模量缩减法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于由多种材料和多种单元类型构成的复杂结构的极限承载能力分析。
(2)基于常应变法、圆弧法、应变能守恒和应变能平衡等不同原理研究建立了确定弹性模量缩减因子的四种策略,并结合空间桁架、刚架以及板壳结构对四种策略的计算精度和效率进行讨论,发现基于应变能平衡原理的弹性模量缩减法具有较高的计算效率和计算精度,为弹性模量缩减因子的确定提供了明确的物理意义和科学依据。
(3)针对极限分析的解析法、数学规划法以及传统弹性模量调整法中“比例加载”这一限定,对所建立的弹性模量缩减法作进一步改进,研究提出了一种适用于非比例加载条件下结构极限承载能力分析的新方法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于恒荷载和活荷载共同作用下的复杂工程结构的极限承载能力分析。
(4)考虑P-Δ效应、捏拢效应、强度退化、刚度退化以及应变硬化等因素对非弹性体系地震动力响应的影响,研究建立了单向地震激励作用下非弹性单自由度体系非线性地震动力响应分析的新型单轴Bouc-Wen模型,并结合69条强震记录定量地分析了P-A效应和捏拢效应对非弹性单自由度体系的地震延性需求和Park-Ang地震损伤指标的概率统计特征的影响,进而建立了地震延性需求的经验概率分布模型和预测方程。
(5)提出采用规一化位移作为控制参数,以圆形屈服而来描述双向规一化恢复力之间的耦合效应,研究建立了双向地震激励下非弹性体系非线性地震动力响应分析的新型双轴Bouc-Wen模型,结合69条强震记录定量地分析了双向地震激励和P-A效应对地震延性需求和Park-Ang损伤指标的概率统计特征的影响,并建立了地震延性需求和累积滞回耗能的近似公式。
(6)提出采用圆形屈服面来描述双向规一化抗侧恢复力之间的耦合效应,采用锥体或球体屈服而来描述双向抗侧恢复力和扭矩之问的耦合效应,研究建立了平而不规则结构非弹性地震动力响应分析的平扭耦联Bouc-Wen模型,结合69条强震记录定量地分析了结构的规一化屈服强度、非耦联平动自振周期、规一化刚度偏心距、非耦联扭转平动频率比、屈服后刚度比等参数对平面不规则结构非弹性平扭耦联效应的概率统计特征的影响。
(7)结合极限分析的弹性模量调整策略和点可靠度理论,研究建立了结构体系可靠度分析的影响系数法。该方法利用确定性有限元分析建立外荷载和单元内力之间的关系,以单元可靠指标作为控制参数定义结构的可靠指标均匀度和基准可靠指标,通过系统地调整各单元的弹性模量以模拟结构的可靠指标重分布和失效状态转移,通过一系列线弹性有限元迭代分析确定结构的最终失效模式和体系可靠度。计算结果显示,该方法的计算精度高、收敛速度快,且有效克服了传统体系可靠度分析中失效状态演化过程模拟复杂、主要失效模式难以识别两大难点。
(8)结合随机有限元、极限分析和点可靠度理论,研究建立了空间变异结构体系可靠度分析的随机弹性模量缩减法。该方法考虑结构参数和外荷载的空间变异性,利用数值积分法确定随机场局部平均间的协方差矩阵,采用摄动随机有限元法确定结构的随机响应量和各控制单元的可靠指标,进而以单元可靠指标作为控制参数,结合弹性模量调整策略和随机有限元迭代分析模拟结构的可靠指标重分布和失效状态转移,最终确定结构的整体失效模式和体系可靠度。由于该方法避免通过虚拟塑性铰、虚加外荷载来模拟结构的失效演化历程和破坏模式,所以结构的单元刚度矩阵和荷载列阵计算公式始终保持不变,因此具有计算精度高、收敛速度快、且可以有效考虑结构参数和外荷载的空间变异性等特点。
Ultimate bearing capacity and seismic ductility demand are two important indices representing strength and ductility performance of engineering structures, which are also key parameters for safety and applicability evaluation as well as structural seismic design. In this study, the Elastic Modulus Reduction Method (EMRM) was proposed to evaluate ultimate bearing capacity of complex structures based on the generalized yield criterion and limit analysis theory. Two novel methods including the Influence Coefficient Method (ICM) and Stochastic Elastic Modulus Reduction Method (SEMRM) were developed for system reliability analysis of large complicated structures based on theories of stochastic finite flement, limit analysis and component reliability. Furthermore, three new Bouc-Wen models for nonlinear seismic dynamic analysis of inelastic systems under unidirectional-, bidirectional-, and lateral-torsional coupling excitations were developed by improving the traditional uniaxial model. The influences of P-△and pinching effects as well as strength and stiffness degradations on probabilistic characteristics of seismic ductility demand and Park-Ang damage index of inelastic system were also quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic system with strength and stiffness degradations as well as P-△and pinching effects were also developed. This study provides significative foundation of theory research and guidance of engineering application in safety and applicability evaluation as well as seismic reliability analysis. The main contents of this thesis are as follows:
(1) The element bearing ratio (EBR), degree of uniformity of EBRs, and the reference EBR were defined based on the generalized yield criterion and limit analysis theory. By adopting the EBR as a governing parameter, the Elastic Modulus Reduction Method (EMRM) was developed based on the Strain Energy Equilibrium Principle (SEEP). Numerical examples show that the EMRM is accurate and efficient for limit analysis of complex structures constructed with multi-material and with complicated configuration.
(2) Four strategies including the Fixed Strain Method (FSM), the Circular Arc Method (CAM), the Strain Energy Conservation Law (SECL), and the Strain Energy Equilibrium Principle (SEEP) were proposed to determine the elastic modulus reduction factor. The applications and limitations of above four strategies in limit analysis of spatial frame and truss as well as thin plate and shell structures were investigated. Numerical results show that flexibility and accuracy of the SEEP is most satisfied, which provides a rational way to determine the elastic modulus reduction factor.
(3) A novel method to calculate ultimate bearing capacity of frame structure under combined action of initial constant and proportional loads was developed by modifying the proposed Elastic Modulus Reduction Method (EMRM), which eliminates the assumption of proportional loading existed in various analytical and mathematical programming methods as well as traditional elastic modulus adjustment procedures for limit analysis. Numerical results show that the method is accurate and efficient to evaluate ultimate bearing capacity of frame structure under both dead and live loads.
(4) A new uniaxial Bouc-Wen model for nonlinear seismic dynamic response analysis of inelastic single-degree-of-freedom (SDOF) system under unidirectional ground motion excitation was developed considering P-A effect, pinching effect, strength and stiffness degradations, and strain hardening. The influences of P-A and pinching effects on probabilistic characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic SDOF system were quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic SDOF system with P-A and pinching effects were also developed.
(5) Adopting the normalized displacement as governing parameter, a new biaxial Bouc-Wen model for nonlinear seismic dynamic analysis of inelastic two-degree-of-freedom (2DOF) system under bidirectional ground motion excitations was developed using circular yield surface to describe coupling effect of biaxial normalized restoring forces. The influences of bidirectional excitation and P-A effect on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic 2DOF system were discussed using 69 earthquake records. Approximate prediction equations for seismic ductility demand and cumulative dissipated energy of inelastic 2DOF system under bidirectional excitation and with P-△effect were also developed.
(6) By adopting the circular yield surface to describe the coupling effect between biaxial normalized lateral restoring forces and the pyramidal or spheriform yield surface to describe the coupling effect of normalized biaxial lateral restoring forces and torsion, a new lateral-torsional coupling Bouc-Wen model for nonlinear seismic dynamic analysis of planar asymmetric structure under bidirectional ground motion excitations was developed. The influences of the normalized yield strength, uncoupled translational frequency ratio, normalized stiffness eccentricity, uncoupled lateral-to-torsional frequency ratio, and post-yield stiffness to initial stiffness ratio on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of planar asymmetric structure were also investigated using 69 earthquake records.
(7) The Influence Coefficient Method (ICM) was proposed to evaluate system reliability of frame structure by combining elastic modulus adjustment procedure and component reliability theory. The relationship between internal forces and external loads was determined by determinate linear elastic finite element analysis and the element reliability index was adopted as governing parameter to define the degree of uniformity of reliability indices and reference reliability index. A new procedure for elastic modulus adjustment was proposed to simulate redistribution of element reliability indices and transition of failure modes. The failure probability of complex structural system can be achieved based on iterative linear elastic finite element analyses. Numerical results show that the ICM is accurate and efficient for system reliability analysis of large complicated structures, and overcomes difficulties for simulation of failure transition and identification of dominant failure modes in traditional methods.
(8) The Stochastic Elastic Modulus Reduction Method (SEMRM) for system reliability analysis of spatial variance frame was proposed based on theories of random field, limit analysis and component reliability. The structural parameters and external loads were modeled as random fields to account for their spatial variations and the covariance matrix of local averages of random fields was calculated using the numerical integration method. The stochastic response and reliability index of each element were achieved by the Perturbation Stochastic Finite Element Method (PSFEM). By adopting the element reliability index as governing parameter, a new strategy for elastic modulus adjustment in system reliability analysis was developed. The collapse mechanism and system reliability index of stochastic frame can be determined through iterative stochastic finite element analyses. Comparing with traditional failure mode approaches, the SEMRM is accurate and efficient, which also avoids modification of element stiffness matrix and artificial loading to simulate failure mode transition and accounts for spatial variations of both structural parameters and external loads rationally.
引文
[1]韩建平,吕西林,李慧.基于性能的地震工程研究的新进展及对结构非线性分析的要求[J].地震工程与工程振动,2007,27(4)：15-23.
[2]易伟建,张海燕.结构随机延性需求谱的理论研究[J].工程力学,2006,23(5)：14-19.
[3]张海燕,易伟建.结构随机延性需求谱的应用研究[J].工程力学,2006,23(6)：11-16.
[4]张海燕,易伟建.基于位移的概率极限状态设计[J].地震工程与工程振动,2009,29(1)：83-88.
[5]Mackenzie, D., Boyle, J.T. and Hamilton, R. The elastic compensation method for limit and shakedown analysis:A review [J]. Journal of Strain Analysis for Engineering Design,2000,35(3):171-188.
[6]Marin-Artieda, C.C. and Dargush, G.F. Approximate limit load evaluation of structural frames using linear elastic analysis [J]. Engineering Structures,2007,29(3):296-304.
[7]Dhalla, A.K. and Jones, G.L. ASME code classification of pipe stresses:A simplified elastic procedure [J]. International Journal of Pressure Vessels and Piping,1986,26(2):145-166.
[8]Seshadri, R. Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis [J]. Nuclear Engineering and Design,1995,153(2-3):287-303.
[9]Mackenzie, D., Shi, J. and Boyle, J.T. Finite element modelling for limit analysis by the elastic compensation method [J]. Computers & Structures,1994,51(4):403-410.
[10]Yang, P., Liu, Y., Ohtake, Y, Yuan, H., and Cen, Z. Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions [J]. International Journal of Pressure Vessels and Piping,2005,82(10):770-776.
[11]Chen, L.J., Liu, Y.H., Yang, P. and Cen, Z.Z. Limit analysis of structures containing flaws based on a modified elastic compensation method [J]. European Journal of Mechanics-A/Solids,2008,27(2): 195-209.
[12]Yang, L.F., Yu, B. and Qiao, Y.P. Elastic modulus reduction method for limit load evaluation of frame structures [J]. Acta Mechanica Solida Sinica,2009,22(2):109-115.
[13]Adibi-Asl, R. and Seshadri, R. Local limit load analysis using m-beta method [J]. Journal of Pressure Vessel Technology,2007,129:296-305.
[14]Adibi-Asl, R., Fanous, I.F.Z. and Seshadri, R. Elastic modulus adjustment procedures--Improved convergence schemes [J]. International Journal of Pressure Vessels and Piping,2006,83(2):154-160.
[15]Yu, B. and Yang, L.F. Elastic modulus reduction method for limit analysis of thin plate and shell structures [J]. Thin-Walled Structures,2010,48:291-298.
[16]Mackenzie, D., Nadarajah, G, Shi, J. and Boyle, J.T. Simple bounds on limit loads by elastic finite element analysis [J]. Journal of Pressure Vessel Technology,1993,115:27-32.
[17]谢礼立,马玉宏,翟长海.基于性态的抗震设防与设计地震动[M].北京：科学出版社,2009.
[18]Chopra, A.K. and Chintanapakdee, C. Inelastic deformation ratios for design and evaluation of structures: Single-degree-of-freedom bilinear systems [J]. Journal of Structural Engineering-ASCE,2004,130(9): 1309-1319.
[19]翟长海,谢礼立,张敏政.工程结构等强度位移比潜研究[J].哈尔滨工业大学学报,2005,37(1)：45-49.
[20]翟长海,龚茂盛,谢礼立,张敏政.工程结构等强度位移比谱影响因素分析[J].哈尔滨工业大学学报,2005,37(4)：455-458.
[21]Hong, H.P. and Hong, P. Assessment of ductility demand and reliability of bilinear single-degree-of-freedom systems under earthquake loading [J]. Canadian Journal of Civil Engineering,2007,34(12): 1606-1615.
[22]Rupakhety, R. and Sigbjornsson, R. Ground Motion Prediction Equations (GMPEs) for inelastic displacement and ductility demands of constant-strength SDOF systems [J]. Bulletin of Earthquake Engineering,2009,7(3):661-679.
[23]张凯,刘洪兵,王巍峰,刘玮.竖向不规则结构的抗震性能评估[J].振动与冲击,2009,28(7)：175-179.
[24]翟长海,公茂盛,张茂花,谢礼立,张敏政.工程结构等延性地震抗力谱研究[J].地震工程与工程振动,2004,24(1)：22-29.
[25]公茂盛,翟长海,谢礼立.非弹性反应谱衰减规律研究[J].哈尔滨工业大学学报,2006,38(5)：763-766.
[26]翟长海,谢礼立,张茂花.阻尼对工程结构等延性地震抗力谱的影响分析[J].哈尔滨工业大学学报,2006,38(10)：1705-1709.
[27]翟长海,李爽,谢礼立,孙亚民.近场脉冲型地震动位移比谱特征研究[J].土木工程学报,2008,41(10)：1-6.
[28]Foliente, G.C. Hysteresis modeling of wood joints and structural systems [J]. Journal of Structural Engineering-ASCE,1995,121(6):1013-1022.
[29]Ma, F., Zhang, H., Bockstedte, A., Foliente, G.C. and Paevere, P. Parameter analysis of the differential model of hysteresis [J]. Journal of Applied Mechanics-Transactions of the ASME,2004,71(3):342-349.
[30]Ayoub, A. and Chenouda, M. Response spectra of degrading structural systems [J]. Engineering Structures,2009,31(7):1393-1402.
[31]Wen, Y.K. Methods of random vibration for inelastic structures [J]. Applied Mechanics Reviews,1989, 42(2):39-52.
[32]Foliente, G.C., Singh, M.P. and Noori, M.N. Equivalent linearization of generally pinching hysteretic, degrading systems [J]. Earthquake Engineering & Structural Dynamics,1996,25(6):611-629.
[33]Ma, F., Ng, C.H. and Ajavakom, N. On system identification and response prediction of degrading structures [J]. Structural Control & Health Monitoring,2006,13(1):347-364.
[34]Goda, K., Hong, H.P. and Lee, C.S. Probabilistic characteristics of seismic ductility demand of SDOF systems with Bouc-Wen hysteretic behavior [J]. Journal of Earthquake Engineering,2009,13(5): 600-622.
[35]Park, Y.J., Wen, Y.K. and Ang, A.H.S. Random vibration of hysteretic systems under bidirectional ground motions [J]. Earthquake Engineering & Structural Dynamics,1986,14:543-557.
[36]Park, Y.J. Equivalent linearization for seismic responses I:formulation and error analysis [J]. Journal of Engineering Mechanics-ASCE,1992,118(11):2207-2226.
[37]Dobsona, S., Nooria, M., Houa, Z., Dimentberga, M. and Baberb, T. Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis [J]. International Journal of Non-Linear Mechanics, 1997,32(4):669-680.
[38]Marano, G.C. and Greco, R. Damage and ductility demand spectra assessment of hysteretic degrading systems subject to stochastic seismic loads [J]. Journal of Earthquake Engineering,2006,10(5):615-640.
[39]Marano, G.C. and Sgobba, S. Stochastic energy analysis of seismic isolated bridges [J]. Soil Dynamics and Earthquake Engineering,2007,27(8):759-773.
[40]Goda, K. and Atkinson, G.M. Seismic demand estimation of inelastic SDOF systems for earthquakes in Japan [J]. Bulletin of the Seismological Society of America,2009,99:3284-3299.
[41]Goda, K. and Atkinson, G.M. Non-iterative equivalent linearization of inelastic SDOF systems for earthquakes in Japan and California [J]. Earthquake Engineering & Structural Dynamics,2010,39(11): 1219-1238.
[42]Yi, W.J., Zhang, H.Y. and Kunnath, S.K. Probabilistic constant-strength ductility demand spectra [J]. Journal of Structural Engineering-ASCE,2007,133(4):567-575.
[43]Kalkan, E. and Graizer, V. Coupled tilt and translational ground motion response spectra [J]. Journal of Structural Engineering-ASCE,2007,133(5):605-619.
[44]Wang, C.H. and Chang, S.Y. Development and validation of a generalized biaxial hysteresis model. Journal of Engineering Mechanics-ASCE,2007,133(2):141-152.
[45]Takizawa, H. and Aoyama, H. Biaxial effects in modelling earthquake response of R/C structures [J]. Earthquake Engineering & Structural Dynamics,1976,4(6):523-552.
[46]Chowdhury, R., Rao, B.N., and Prasad, A.M. Hysteresis model for RC structural element accounting bi-directional lateral load interaction [C]. In Proceedings of the ASME Pressure Vessels and Piping Conference, Denver, Colorado,2005,5:229-236.
[47]Magliulo, G. and Ramasco, R. Seismic response of three-dimensional RC multi-storey frame building under uni- and bi-directional input ground motion [J]. Earthquake Engineering & Structural Dynamics, 2007,36(12):1641-1657.
[48]Wen, Y.K. and Eliopoulos, D. Method for nonstationary random vibration of inelastic structures [J]. Probabilistic Engineering Mechanics,1994,9(1-2):115-123.
[49]Wang, C.H. and Wen, Y.K. Evaluation of pre-Northridge low-rise steel buildings Ⅰ:Modeling [J]. Journal of Structural Engineering-ASCE,2000,126(10):1160-1168.
[50]Wang, C.H. and Foliente, G.C. Seismic reliability of low-rise nonsymmetric woodframe buildings [J]. Journal of Structural Engineering-ASCE,2006,132(5):733-744.
[51]Stefano, M.D. and Faella, G. An evaluation of the inelastic response of systems under biaxial seismic excitations [J]. Engineering Structures,1996,18(9):724-731.
[52]下东升,李宏男,王国.双向地震动作用弹塑性反应谱研究[J].大连理工大学学报,2005,45(2)：248-253.
[53]Perus, L. and Fajfar, P. On the inelastic torsional response of single-storey structures under bi-axial excitation [J]. Earthquake Engineering & Structural Dynamics,2005,34(8):931-941.
[54]Lin, J.L. and Tsai, K.C. Seismic analysis of two-way asymmetric building systems under bi-directional seismic ground motions [J]. Earthquake Engineering & Structural Dynamics,2008,37(2):305-328.
[55]Chao, S.H. and Loh, C.H. A biaxial hysteretic model for a structural system incorporating strength deterioration and pinching phenomena [J]. International Journal of Non-Linear Mechanics,2009,44(7): 745-756.
[56]Lee, C.S. and Hong, H.P. Statistics of inelastic responses of hysteretic systems under bidirectional seismic excitations [J]. Engineering Structures,2010,32(8):2074-2086.
[57]Lucchini, A., Monti, G. and Kunnath, S. Seismic behavior of single-story asymmetric-plan buildings under uniaxial excitation [J]. Earthquake Engineering & Structural Dynamics,2009,38(9):1053-1070.
[58]De Stefano, M. and Pintucchi, B. A review of research on seismic behaviour of irregular building structures since 2002 [J]. Bulletin of Earthquake Engineering,2008,6(2):285-308.
[59]Syamal, P.K. and Pekau, O.A. Dynamic response of bilinear asymmetric structures [J]. Earthquake Engineering & Structural Dynamics,1985,13(4):527-541.
[60]Ryan, K.L. and Chopra, A.K. Estimation of seismic demands on isolators based on nonlinear analysis [J]. Journal of Structural Engineering,2004,130(3):392-402.
[61]Goel, R.K. and Chopra, A.K. Inelastic seismic response of one-story, asymmetric-plan systems-Effects of stiffness and strength distribution [J]. Earthquake Engineering & Structural Dynamics,1990,19(7): 949-970.
[62]Goel, R.K. and Chopra, A.K. Inelastic seismic response of one-storey, asymmetric-plan systems:Effects of system parameters and yielding [J]. Earthquake Engineering & Structural Dynamics,1991,20(3): 201-222.
[63]Goel, R.K. and Chopra, A.K. Effects of plan asymmetry in inelastic seismic response of one-story systems [J]. Journal of Structural Engineering-ASCE,1991,117(5):1492-1513.
[64]Jangid, R.S. and Datta, T.K. Nonlinear response of torsionally coupled base isolated structure [J]. Journal of Structural Engineering,1994,120(1):1-22.
[65]Ozaki, M., Azuhata, T. Takahashi, T. and Shaomei, M. Inelastic deformation of one-story asymmetric-plan systems subjected to srong earthquake ground motions [J]. Earthquake Spectra,1994, 10(4):777-790.
[66]de la Llera, J.C. and Chopra, A.K. Understanding the inelastic seismic behaviour of asymmetric-plan buildings [J]. Earthquake Engineering & Structural Dynamics,1995,24(4):549-572.
[67]de la Llera, J.C., Vasquez, J., Chopra, A.K., and Almazan, J.L. A macro-element model for inelastic building analysis [J]. Earthquake Engineering & Structural Dynamics,2000,29(12):1725-1757.
[68]Dutta, S.C. Effect of strength deterioration on inelastic seismic torsional behaviour of asymmetric RC buildings [J]. Building and Environment,2001,36(10):1109-1118.
[69]Ryan, K.L. and Chopra, A.K. Estimation of seismic demands on isolators in asymmetric buildings using non-linear analysis [J]. Earthquake Engineering & Structural Dynamics,2004,33(3):395-418.
[70]Ryan, K.L. and Chopra, A.K. Estimating the seismic displacement of friction pendulum isolators based on non-linear response history analysis [J]. Earthquake Engineering & Structural Dynamics,2004,33(3): 359-373.
[71]Koliopulos, P.K. and Chandler, A.M. Stochastic linearization of inelastic seismic torsional response-Formulation and case studies. Engineering Structures,1995,17(7):494-504.
[72]De-la-Colina, J. Effects of torsion factors on simple non-linear systems using fully-bidirectional analyses [J]. Earthquake Engineering & Structural Dynamics,1999,28(7):691-706.
[73]Riddell, R. and Santa-Maria, H. Inelastic response of one-storey asymmetric plan systems subjected to bidirectional earthquake motions [J]. Earthquake Engineering & Structural Dynamics,1999,28(3): 273-285.
[74]Marusic, D. and Fajfar, P. On the inelastic seismic response of asymmetric buildings under bi-axial excitation [J]. Earthquake Engineering & Structural Dynamics,2005,34(8):943-963.
[75]Humar, J., Mahgoub, M. and Ghorbanie-Asl, M. Effect of second-order forces on seismic responses [J]. Canadian Journal of Civil Engineering,2006,33:692-706.
[76]MacRae, G.A. P-Delta effects on single-degree-of-freedom structures in earthquakes [J]. Earthquake Spectra,1994,10(3):359-568.
[77]Tremblay, R., Cote, B. and Leger, P. An evaluation of P-delta amplification factors in multistorey steel moment resisting frames [J]. Canadian Journal of Civil Engineering,1999,26(5):535-548.
[78]Gupta, A. and Krawinkler, H. Dynamic P-delta effects for flexible inelastic steel structures [J]. Journal of Structural Engineering-ASCE,2000,126(1):145-154.
[79]Williamson, E.B. Evaluation of damage and P-delta effects for system under earthquake excitation [J]. Journal of Structural Engineering-ASCE,2003,129(8):1036-1046.
[80]Bernal, D. P-delta effects in the inelastic response of mutistorey buildings [C]. In Proceedings of Pacific Conference on Earthquake Engineering, Wairakei, New Zealand,1987,2:221-230.
[81]翟长海,孙亚民,谢礼立.考虑P-delta效应的等延性位移比谱[J].哈尔滨工业大学学报,2007,39(10)：1513-1517.
[82]童根树,赵永峰.动力P-Delta效应对地震力调整系数的影响[J].浙江大学学报(工学版),2007,41(1)：120-126.
[83]Stefanou, G. The stochastic finite element method:Past, present and future [J]. Computer Methods in Applied Mechanics and Engineering,2009,198(9-12):1031-1051.
[84]Koduru, S.D. and Haukaas, T. Feasibility of FORM in finite element reliability analysis [J]. Structural Safety,2010,32(2):145-153.
[85]Der Kiureghian, A. and De Stefano, M. Efficient algorithm for second-order reliability analysis [J]. Journal of Engineering Mechanics-ASCE,1991,117(12):2904-2923.
[86]Cardoso, J.B., de Almeida, J.R., Dias, J.M. Structural reliability analysis using Monte Carlo simulation and neural networks [J]. Advances in Engineering Software,2008,39(6):505-513.
[87]Allaix, D.L. and Carbone, V.I. Discretization of 2D random fields:A genetic algorithm approach [J]. Engineering Structures,2009,31(5):1111-1119.
[88]Der Kiureghian, A. and Ke, J.B. The stochastic finite element method in structural reliability [J]. Probabilistic Engineering Mechanics,1988,3(2):83-91.
[89]Liu, W.K., Belytschko, T. and Mani, A. Probabilistic finite elements for nonlinear structural dynamics [J]. Computer Methods in Applied Mechanics and Engineering,1986,56(1):61-81.
[90]Liu, W. K., Belytschko, T. and Mani, A. Random field finite elements [J]. International Journal for Numerical Methods in Engineering,1986,23(10):1831-1845.
[91]Li, C.C. and Der Kiureghian, A. Optimal discretization of random fields [J]. Journal of Engineering Mechanics-ASCE,1993,119(6):1136-1154.
[92]Vanmarcke, E., Shinozuka, M., Nakagiri, S. Schueller, G.I. and Grigoriu, M. Random fields and stochastic finite elements [J]. Structural Safety,1986,3(3-4):143-166.
[93]Zhu, W.Q. and Wu, W.Q. A stochastic finite element method for real eigenvalue problems [J]. Probabilistic Engineering Mechanics,1991,6(3-4):228-232.
[94]Knabe, W., Przewloki,V and Roynski, G. Spatial averages for linear elements for two-parameter random field [J]. Probabilistic Engineering Mechanics,1998,13(3):147-167.
[95]Chakraborty, S. and Bhattacharyya, B. An efficient 3D stochastic finite element method [J]. International Journal of Solids and Structures,2002,39(9):2465-2475.
[96]Chakraborty, S. and Dey, S.S. Stochastic finite element simulation of random structure on uncertain foundation under random loading [J]. International Journal of Mechanical Sciences,1996,38(11): 1209-1218.
[97]Chakraborty, S. and Sarkar, S.K. Analysis of a curved beam on uncertain elastic foundation [J]. Finite Elements in Analysis and Design,2000,36:73-82.
[98]Deodatis, G. Weighted Integral Method Ⅰ:Stochastic stiffness matrix [J]. Journal of Engineering Mechanics-ASCE,1991,117(8):1851-1864.
[99]Deodatis, G. and Shinozuka, M. Weighted integral method Ⅱ:Response variability and reliability [J]. Journal of Engineering Mechanics-ASCE,1991,117(8):1865-1877.
[100]Sudret, B. and Der Kiureghian, A. Stochastic finite element methods and reliability:A state-of-the-art report [R]. Universty of California, Berkeley,2000, UCB/SEMM-2000/08
[101]秦权.随机有限元及其进展Ⅰ.随机场的离散和反应矩的计算[J].工程力学,1994,11(4)：1-10.
[102]Spanos, P.D. and Ghanem, R. Stochastic finite element expansion for random media [J]. Journal of Engineering Mechanics-ASCE,1989,115(5):1035-1053
[103]Shinozuka, M. and Astill, C.J. Random eigenvalue problems in structural analysis [J]. American Institute of Aeronautics and Astronautics (AIAA) Journal,1972,10(4):456-462.
[104]Cambou, B. Application of first-order uncertainty analysis in the finite element method in linear elasticity. Proceedings of the Second International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Aachen, Germany,1975,67-87.
[105]Handa, K., Anderson, K. Application of finite element methods in statistical analysis of structures [C]. In Proceedings of 3rd International Conference on Structural Safety and Reliability, Trondheim, Norway, 1981,409-417.
[106]Hisada, T. and Nakagiri, S. Role of the stochastic finite element method in structural safety and reliability [C], In Proceedings of the 4th International Conference on Structural Safety and Reliability, Kobe, Japan, 1985,213-219.
[107]朱位秋,任永坚.随机场的局部平均与随机有限元法[J].航空学报,1986,7(6)：604-611.
[108]朱位秋,任永坚.基于随机场局部平均的随机有限元法[J].固体力学学报,1988,9(4)：281-293.
[109]刘宁,卓家寿.三维弹塑性随机有限元的迭代计算方法研究[J].河海大学学报,1996,24(1)：1-8.
[110]刘宁.三维可分向量随机场局部平均的三维随机有限元及可靠度计算[J].水利学报,1995,6：75-82.
[111]张汝清,高行山.随机变量的变分原理及有限元法[J].应用数学和力学,1992,13(5)：383-388.
[112]高行山,张汝清.有限变形弹性理论随机变量变分原理及有限元法[J].应用数学和力学,1994,15(10)：855-862.
[113]杨绿峰,高兑现,李桂青.随机结构在随机激励下的二阶摄动随机势能泛函及其应用[J].应用力学学报,1999,16(4)：35-39.
[114]Yang, L.F., Leung, A.Y.T., Yan, L.B. and Wong, C.W.Y. Stochastic spline Ritz method based on stochastic variational principle [J]. Engineering Structures,2005,27(3):455-462.
[115]Ghanem, R.G. and Spanos, P. Stochastic Finite Elements:A Spectral Approach [M]. New York: Springer-Verlag,1991.
[116]Zhao, Y.G. and Ono, T. System relibility evaluation of ductile frame structures [J]. Journal of Structural Engineering-ASCE,1998,124(6):678-685.
[117]Zhao, Y.G, Zhong, W.Q. and Ang, A.H.S. Estimating joint failure probability of series structural systems [J]. Journal of Engineering Mechanics-ASCE,2007,133:588-596.
[118]Moses, F. System reliability developments in structural engineering [J]. Structural Safety,1982,1(1): 3-13.
[119]Feng, Y.S. Enumerating significant failure modes of a structural system by using criterion methods [J]. Computers & Structures,1988,30(5):1153-1157.
[120]冯元生,董聪.枚举结构主要失效模式的一种方法[J].航空学报,1991,12(9)：537-541.
[121]冯元生,董聪.枚举结构主要失效模式的一种新方法[J].西北工业大学学报,1991,9(3)：284-289.
[122]Cornell, C.A. Bounds on the reliability of structural systems [J]. Journal of Structural Division-ASCE, 1967,93(1):171-200.
[123]Ditlevsen, O. Narrow reliability bounds for structural systems [J]. Mechanics Based Design of Structures and Machines,1979,7(4):453-472.
[124]Thoft-Christensen, P. and Murotsu, Y. Application of structural systems reliability theory [M]. New York: Springer-Verlag,1986.
[125]Feng, Y.S. A Method of computing structural system reliability with high accuracy [J]. Computers and Structures,1989,3(1):1-5.
[126]董聪,夏人伟.现代结构系统可靠性评估理论研究进展[J].力学进展,1995,25(4)：537-548.
[127]Zhang, Y.C. High-order reliability bounds for series systems and application to structural systems [J]. Computers & Structures,1993,46(2):381-386.
[128]Greig, G.L. An assessment of high-order bounds for structural reliability [J]. Structural Safety,1992, 11(3-4):213-225.
[129]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4)：1-9.
[130]郭书祥.结构体系失效概率计算的一种快速有效方法[J].计算力学学报,2007,24(1)：107-110.
[131]Ang, A.H.S. and Ma, H.F. On the reliability of structural systems [J], In Proceedings of the 3rd ICOSSAR, Trondheim, Norway,1981,295-314.
[132]Ditlevsen, O. System reliability bounding by conditioning [J]. Journal of the Engineering Mechanics Division,1982,108(5):708-716.
[133]Thoft-Christensen, P. and Dalsgard S(?)rensen, J. Reliability of structural systems with correlated elements [J]. Applied Mathematical Modelling,1982,6(3):171-178.
[134]杨绿峰,余波,乔永平.弹性模量缩减法分析刚架结构的极限承载力[J].防灾减灾工程学报,2009,29(3)：306-312.
[135]Yu, B. and Yang, L.F. Elastic modulus reduction method for limit analysis considering initial constant and proportional loadings [J]. Finite Elements in Analysis and Design,2010,46(12):1086-1092.
[136]杨绿峰,余波,张伟.弹性模量缩减法分析杆系和板壳结构的极限承载力[J].工程力学,2009,26(12)：64-70.
[137]余波,杨绿峰,乔永平.基于承载比的弹性补偿有限元法分析杆系结构的极限承载力[J].结构工程师,2008,24(6)：67-71.
[138]杨绿峰,乔永平,余波.基于弹性补偿有限元法的拱桥极限分析[J].长沙交通学院院报,2008,24(1)：1-5.
[139]乔永平,杨绿峰,余波.弹性补偿有限元法研究斜板桥的塑性极限承载力[J].中外公路,2008,28(4)：134-138.
[140]张伟,杨绿峰,韩晓风.基于弹性模量缩减法的钢岔管安全评价[J].水力发电学报,2010,29(1)：171-179.
[141]张伟,杨绿峰,韩晓风.基于弹性补偿有限元法的无梁岔管安全评价[J].水利学报,2010,40(10)：1175-1183.
[142]杨绿峰,余波,莫远昌.基于弹性模量缩减法研究结构体系可靠度[J].广西大学学报(自然科学版),2008,33(4)：349-357.
[143]Shi, J., Boyle, J.T., Mackenzie, D., Hamilton, R. Approximate limit design of frames using elastic analysis [J]. Computers & Structures,1996,61(3):495-501.
[144]Hamilton, R. and Boyle, J.T. Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria [J]. Thin-Walled Structures,2002,40(6):503-522.
[145]Tran, T.N., Kreiiig, R., Vu, D.K and Staat, M. Upper bound limit and shakedown analysis of shells using the exact Ilyushin yield surface [J]. Computers & Structures,2008,86(17-18):1683-1695.
[146]Hamilton, R., Mackenzie, D., Shi, J., Boyle, J.T. Simplified lower bound limit analysis of pressurised cylinder/cylinder intersections using generalised yield criteria [J]. International Journal of Pressure Vessels and Piping,1996,67(2):219-226.
[147]Seshadri, R. and Mangalaramanan, S.P. Lower bound limit loads using variational concepts:the m-alpha method [J]. International Journal of Pressure Vessels and Piping,1997,71(2):93-106.
[148]王飞,陈钢,刘应华,岑章志.极限分析的弹性补偿法及其应用[J].应用力学学报,2004,21(4)：147-150.
[149]陈立杰,刘应华,杨璞,徐秉业.复杂结构塑性极限分析的修正弹性补偿法[J].机械工程学报,2007,43(5)：187-193.
[150]Shi, J., Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅲ--Torispherical heads under internal pressure [J]. International Journal of Pressure Vessels and Piping, 1992,53(1):121-142.
[151]Nadarajah, C., Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅱ-Nozzle sphere intersections with internal pressure and radial load [J]. International Journal of Pressure Vessels and Piping,1992,53(1):97-119.
[152]Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅰ--Simple examples [J]. International Journal of Pressure Vessels and Piping,1992,53(1):77-95.
[153]Seshadri, R. and Indermohan, H. Lower bound limit load determination:The m-beta multiplier method [J]. Journal of Pressure Vessel Technology,2004,126:237-240.
[154]Fanous, I.F.Z. and Seshadri, R. Limit load analysis using the reference volume concept [J]. International Journal of Pressure Vessels and Piping,2009,86(5):291-295.
[155]Jahed, H., Sethuraman, R. and Dubey, R.N. A variable material property approach for solving elastic-plastic problems [J]. International Journal of Pressure Vessels and Piping,1997,71(3):285-291.
[156]Famiyesin, O.O.R., Hossain, K.M.A., Chia, Y.H. and Slade, P.A. Numerical and analytical predictions of the limit load of rectangular two way slabs [J]. Computers & Structures,2001,79(1):43-52.
[157]张伟,杨绿峰,韩晓凤.考虑恒荷载作用效应的弹性补偿有限元法[J].工业建筑,2010,40(3)：52-59.
[158]Zhang, Y.G., Zhang, P. and Xue, W.M. Limit analysis considering initial constant loadings and proportional loadings [J].1994,14(3):229-234.
[159]Goda, K. and Hong, H.P. Estimation of seismic loss for spatially distributed buildings [J]. Earthquake Spectra,2008,24(4):889-910.
[160]Ajavakom, N., Ng, C.H. and Ma, F. Performance of nonlinear degrading structures:Identification, validation, and prediction [J]. Computers & Structures,2008,86(7-8):652-662.
[161]Chopra, A.K. Dynamics of Structures:Theory and Applications to Earthquake Engineering (3rd edition) [M]. Upper Saddle River, New Jersey:Pearson Prentice Hall,2007.
[162]Shampine, L.F. and Reichelt, M.W. The MATLAB ODE suite [J]. SIAM Journal of Scientific Computing, 1997,18(1):1-22.
[163]Park, Y.J. and Ang, A.H.S. Mechanistic seismic damage model for reinforced concrete [J]. Journal of Structural Engineering-ASCE,1985,111(4):722-739.
[164]Chung, S.T. and Loh, C.H. Identification and verification of seismic demand from different hysteretic models [J]. Journal of Earthquake Engineering,2002,6(3):31-355.
[165]Pacific Earthquake Engineering Research (PEER) Center. Next generation attenuation database [DB]. http://peer.berkeley.edu/nga/index.html. (last accessed May 1st,2010).
[166]Hong, H.P. and Goda, K. Orientation-dependent ground-motion measure for seismic-hazard assessment [J]. Bulletin of the Seismological Society of America,2007,97:1525-1538.
[167]杨伟,欧进萍.基于能量原理的Park & Ang损伤模型简化计算方法[J].地震工程与工程振动,2009,29(2)：159-165.
[168]Akkar, S.D. and Miranda, E. Statistical evaluation of approximate methods for estimating maximum deformation demands on existing structures [J]. Journal of Structural Engineering-ASCE,2005,131(1): 160-172.
[169]Riddell, R., Garcia, J.E. and Garces, E. Inelastic deformation response of SDOF systems subjected to earthquakes [J]. Earthquake Engineering & Structural Dynamics,2002,31(3):515-538.
[170]Miranda, E. Estimation of inelastic deformation demands of SDOF systems [J]. Journal of Structural Engineering-ASCE,2001,127(9):1005-1012.
[171]Wen, Y.K. Method for random vibration of hysteretic systems [J]. Journal of the Engineering Mechanics Division,1976,102(2):249-263.
[172]Baber, T.T. and Wen, Y.K. Random vibration hysteretic, degrading systems [J]. Journal of the Engineering Mechanics Division,1981,107(6):1069-1087.
[173]Baber, T.T. and Noori, M.N. Random vibration of degrading, pinching systems [J]. Journal of Engineering Mechanics-ASCE,1985,111(8):101-1026.
[174]李英民,杨洁,赖明.双向水平地震动峰值特性的相关性研究[J].重庆建筑大学学报,1999,21(2)：5-12.
[175]李英民,赖明,白绍良.基于三参数模型的双向水平地震动相关设计反应谱研究[J].世界地震工程,2002,18(4)：5-10.
[176]Ghayamghamian, M.R., Nouri, G.R., Igel, H. and Tobita, T. The effect of torsional ground motion on structural response:code recommendation for accidental eccentricity [J]. Bulletin of the Seismological Society of America,2009,99:1261-1270.
[177]Myslimaj, B. and Tso, W.K. Desirable strength distribution for asymmetric structures with strength-stiffness dependent elements [J]. Journal of Earthquake Engineering,2004,8(2):231-248.
[178]Tso, W.K. and Myslimaj, B. A yield displacement distribution-based approach for strength assignment to lateral force-resisting elements having strength dependent stiffness [J]. Earthquake Engineering & Structural Dynamics,2003,32(15):2319-2351.
[179]Atkinson, G.M. and Goda, K. Inelastic seismic demand of real versus simulated ground-motion records for cascadia subduction earthquakes [J]. Bulletin of the Seismological Society of America,2010,100: 102-115.
[180]何晓宇,李宏男.偏心形式对偏心结构扭转耦联地震响应的影响[J].世界地震工程,2008,24(3)：36-44.
[181]Park, S., Choi, S., Sikorsky, C., Stubbs, N. Efficient method for calculation of system reliability of a complex structure [J]. International Journal of Solids and Structures,2004,41(18-19):5035-5050.
[182]欧进萍,侯钢领.建筑结构设计可靠度的影响因素与比较研究[J].建筑科学,1999,15(5)：51-55.
[183]Chen, J.B. and Li, J. Development-process-of-nonlinearity-based reliability evaluation of structures [J]. Probabilistic Engineering Mechanics,2007,22(3):267-275.
[184]Haukaas, T. and Kiureghian, A.D. Strategies for finding the design point in non-linear finite element reliability analysis [J]. Probabilistic Engineering Mechanics,2006,21(2):133-147.
[185]Der Kiureghian, A., Haukaas, T. and Fujimura, K. Structural reliability software at the University of California, Berkeley [J]. Structural Safety,2006,28(1-2):44-67.
[186]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5)：79-87.
[187]Haukaas, T. and Der Kiureghian, A. Finite element reliability and sensitivity methods for performance-based engineering [R]. Pacific Earthquake Engineering Research Center,2003, PEER 2003/14.
[188]Ditlevsen, O. and Madsen, H.O. Structural reliability methods [M]. Internet edition 2.3.7,2007, http://www.web.mek.dtu.dk/staff/od/books.htm (First edition published by John Wiley & Sons Ltd, Chichester,1996, ISBN 0 471 96086 1).
[189]Der Kiureghian, A. and Liu, P.L. Structural reliability under incomplete probability information [J]. Journal of Engineering Mechanics-ASCE,1986,112(1):85-104.
[190]Hasofer, A.M. and Lind, N.C. Exact and invariant second-moment code format [J]. Journal of the Engineering Mechanics Division,1974,100(1):111-121.
[191]Rackwitz, R. and Fiessler, B. Structural reliability under combined load sequence [J]. Computer & Structures,1978,114(12):2195-2199.
[192]Zhang, Y. and Der Kiureghian, A. Two improved algorithms for reliability analysis [C]. In Proceedings of the 6th IFIP WG7.5 Working Conference on Reliability and Optimization of Stuctural Systems, Assisi, Italy,1994,297-304.
[193]Zhang, Y. and Der Kiureghian, A. Finite element reliability methods for inelastic structures [R]. University of California, Berkeley,1997, UCB/SEMM-97/05.
[194]Der Kiureghian, A., Lin, H.Z. and Hwang, S.J. Second-order reliability approximations [J]. Journal of Engineering Mechanics-ASCE,1987,113(8):1208-1225.
[195]Nadarajah, S. On the approximations for multinormal integration [J]. Computers & Industrial Engineering, 2008,54(3):705-708.
[2]易伟建,张海燕.结构随机延性需求谱的理论研究[J].工程力学,2006,23(5)：14-19.
[3]张海燕,易伟建.结构随机延性需求谱的应用研究[J].工程力学,2006,23(6)：11-16.
[4]张海燕,易伟建.基于位移的概率极限状态设计[J].地震工程与工程振动,2009,29(1)：83-88.
[5]Mackenzie, D., Boyle, J.T. and Hamilton, R. The elastic compensation method for limit and shakedown analysis:A review [J]. Journal of Strain Analysis for Engineering Design,2000,35(3):171-188.
[6]Marin-Artieda, C.C. and Dargush, G.F. Approximate limit load evaluation of structural frames using linear elastic analysis [J]. Engineering Structures,2007,29(3):296-304.
[7]Dhalla, A.K. and Jones, G.L. ASME code classification of pipe stresses:A simplified elastic procedure [J]. International Journal of Pressure Vessels and Piping,1986,26(2):145-166.
[8]Seshadri, R. Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis [J]. Nuclear Engineering and Design,1995,153(2-3):287-303.
[9]Mackenzie, D., Shi, J. and Boyle, J.T. Finite element modelling for limit analysis by the elastic compensation method [J]. Computers & Structures,1994,51(4):403-410.
[10]Yang, P., Liu, Y., Ohtake, Y, Yuan, H., and Cen, Z. Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions [J]. International Journal of Pressure Vessels and Piping,2005,82(10):770-776.
[11]Chen, L.J., Liu, Y.H., Yang, P. and Cen, Z.Z. Limit analysis of structures containing flaws based on a modified elastic compensation method [J]. European Journal of Mechanics-A/Solids,2008,27(2): 195-209.
[12]Yang, L.F., Yu, B. and Qiao, Y.P. Elastic modulus reduction method for limit load evaluation of frame structures [J]. Acta Mechanica Solida Sinica,2009,22(2):109-115.
[13]Adibi-Asl, R. and Seshadri, R. Local limit load analysis using m-beta method [J]. Journal of Pressure Vessel Technology,2007,129:296-305.
[14]Adibi-Asl, R., Fanous, I.F.Z. and Seshadri, R. Elastic modulus adjustment procedures--Improved convergence schemes [J]. International Journal of Pressure Vessels and Piping,2006,83(2):154-160.
[15]Yu, B. and Yang, L.F. Elastic modulus reduction method for limit analysis of thin plate and shell structures [J]. Thin-Walled Structures,2010,48:291-298.
[16]Mackenzie, D., Nadarajah, G, Shi, J. and Boyle, J.T. Simple bounds on limit loads by elastic finite element analysis [J]. Journal of Pressure Vessel Technology,1993,115:27-32.
[17]谢礼立,马玉宏,翟长海.基于性态的抗震设防与设计地震动[M].北京：科学出版社,2009.
[18]Chopra, A.K. and Chintanapakdee, C. Inelastic deformation ratios for design and evaluation of structures: Single-degree-of-freedom bilinear systems [J]. Journal of Structural Engineering-ASCE,2004,130(9): 1309-1319.
[19]翟长海,谢礼立,张敏政.工程结构等强度位移比潜研究[J].哈尔滨工业大学学报,2005,37(1)：45-49.
[20]翟长海,龚茂盛,谢礼立,张敏政.工程结构等强度位移比谱影响因素分析[J].哈尔滨工业大学学报,2005,37(4)：455-458.
[21]Hong, H.P. and Hong, P. Assessment of ductility demand and reliability of bilinear single-degree-of-freedom systems under earthquake loading [J]. Canadian Journal of Civil Engineering,2007,34(12): 1606-1615.
[22]Rupakhety, R. and Sigbjornsson, R. Ground Motion Prediction Equations (GMPEs) for inelastic displacement and ductility demands of constant-strength SDOF systems [J]. Bulletin of Earthquake Engineering,2009,7(3):661-679.
[23]张凯,刘洪兵,王巍峰,刘玮.竖向不规则结构的抗震性能评估[J].振动与冲击,2009,28(7)：175-179.
[24]翟长海,公茂盛,张茂花,谢礼立,张敏政.工程结构等延性地震抗力谱研究[J].地震工程与工程振动,2004,24(1)：22-29.
[25]公茂盛,翟长海,谢礼立.非弹性反应谱衰减规律研究[J].哈尔滨工业大学学报,2006,38(5)：763-766.
[26]翟长海,谢礼立,张茂花.阻尼对工程结构等延性地震抗力谱的影响分析[J].哈尔滨工业大学学报,2006,38(10)：1705-1709.
[27]翟长海,李爽,谢礼立,孙亚民.近场脉冲型地震动位移比谱特征研究[J].土木工程学报,2008,41(10)：1-6.
[28]Foliente, G.C. Hysteresis modeling of wood joints and structural systems [J]. Journal of Structural Engineering-ASCE,1995,121(6):1013-1022.
[29]Ma, F., Zhang, H., Bockstedte, A., Foliente, G.C. and Paevere, P. Parameter analysis of the differential model of hysteresis [J]. Journal of Applied Mechanics-Transactions of the ASME,2004,71(3):342-349.
[30]Ayoub, A. and Chenouda, M. Response spectra of degrading structural systems [J]. Engineering Structures,2009,31(7):1393-1402.
[31]Wen, Y.K. Methods of random vibration for inelastic structures [J]. Applied Mechanics Reviews,1989, 42(2):39-52.
[32]Foliente, G.C., Singh, M.P. and Noori, M.N. Equivalent linearization of generally pinching hysteretic, degrading systems [J]. Earthquake Engineering & Structural Dynamics,1996,25(6):611-629.
[33]Ma, F., Ng, C.H. and Ajavakom, N. On system identification and response prediction of degrading structures [J]. Structural Control & Health Monitoring,2006,13(1):347-364.
[34]Goda, K., Hong, H.P. and Lee, C.S. Probabilistic characteristics of seismic ductility demand of SDOF systems with Bouc-Wen hysteretic behavior [J]. Journal of Earthquake Engineering,2009,13(5): 600-622.
[35]Park, Y.J., Wen, Y.K. and Ang, A.H.S. Random vibration of hysteretic systems under bidirectional ground motions [J]. Earthquake Engineering & Structural Dynamics,1986,14:543-557.
[36]Park, Y.J. Equivalent linearization for seismic responses I:formulation and error analysis [J]. Journal of Engineering Mechanics-ASCE,1992,118(11):2207-2226.
[37]Dobsona, S., Nooria, M., Houa, Z., Dimentberga, M. and Baberb, T. Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis [J]. International Journal of Non-Linear Mechanics, 1997,32(4):669-680.
[38]Marano, G.C. and Greco, R. Damage and ductility demand spectra assessment of hysteretic degrading systems subject to stochastic seismic loads [J]. Journal of Earthquake Engineering,2006,10(5):615-640.
[39]Marano, G.C. and Sgobba, S. Stochastic energy analysis of seismic isolated bridges [J]. Soil Dynamics and Earthquake Engineering,2007,27(8):759-773.
[40]Goda, K. and Atkinson, G.M. Seismic demand estimation of inelastic SDOF systems for earthquakes in Japan [J]. Bulletin of the Seismological Society of America,2009,99:3284-3299.
[41]Goda, K. and Atkinson, G.M. Non-iterative equivalent linearization of inelastic SDOF systems for earthquakes in Japan and California [J]. Earthquake Engineering & Structural Dynamics,2010,39(11): 1219-1238.
[42]Yi, W.J., Zhang, H.Y. and Kunnath, S.K. Probabilistic constant-strength ductility demand spectra [J]. Journal of Structural Engineering-ASCE,2007,133(4):567-575.
[43]Kalkan, E. and Graizer, V. Coupled tilt and translational ground motion response spectra [J]. Journal of Structural Engineering-ASCE,2007,133(5):605-619.
[44]Wang, C.H. and Chang, S.Y. Development and validation of a generalized biaxial hysteresis model. Journal of Engineering Mechanics-ASCE,2007,133(2):141-152.
[45]Takizawa, H. and Aoyama, H. Biaxial effects in modelling earthquake response of R/C structures [J]. Earthquake Engineering & Structural Dynamics,1976,4(6):523-552.
[46]Chowdhury, R., Rao, B.N., and Prasad, A.M. Hysteresis model for RC structural element accounting bi-directional lateral load interaction [C]. In Proceedings of the ASME Pressure Vessels and Piping Conference, Denver, Colorado,2005,5:229-236.
[47]Magliulo, G. and Ramasco, R. Seismic response of three-dimensional RC multi-storey frame building under uni- and bi-directional input ground motion [J]. Earthquake Engineering & Structural Dynamics, 2007,36(12):1641-1657.
[48]Wen, Y.K. and Eliopoulos, D. Method for nonstationary random vibration of inelastic structures [J]. Probabilistic Engineering Mechanics,1994,9(1-2):115-123.
[49]Wang, C.H. and Wen, Y.K. Evaluation of pre-Northridge low-rise steel buildings Ⅰ:Modeling [J]. Journal of Structural Engineering-ASCE,2000,126(10):1160-1168.
[50]Wang, C.H. and Foliente, G.C. Seismic reliability of low-rise nonsymmetric woodframe buildings [J]. Journal of Structural Engineering-ASCE,2006,132(5):733-744.
[51]Stefano, M.D. and Faella, G. An evaluation of the inelastic response of systems under biaxial seismic excitations [J]. Engineering Structures,1996,18(9):724-731.
[52]下东升,李宏男,王国.双向地震动作用弹塑性反应谱研究[J].大连理工大学学报,2005,45(2)：248-253.
[53]Perus, L. and Fajfar, P. On the inelastic torsional response of single-storey structures under bi-axial excitation [J]. Earthquake Engineering & Structural Dynamics,2005,34(8):931-941.
[54]Lin, J.L. and Tsai, K.C. Seismic analysis of two-way asymmetric building systems under bi-directional seismic ground motions [J]. Earthquake Engineering & Structural Dynamics,2008,37(2):305-328.
[55]Chao, S.H. and Loh, C.H. A biaxial hysteretic model for a structural system incorporating strength deterioration and pinching phenomena [J]. International Journal of Non-Linear Mechanics,2009,44(7): 745-756.
[56]Lee, C.S. and Hong, H.P. Statistics of inelastic responses of hysteretic systems under bidirectional seismic excitations [J]. Engineering Structures,2010,32(8):2074-2086.
[57]Lucchini, A., Monti, G. and Kunnath, S. Seismic behavior of single-story asymmetric-plan buildings under uniaxial excitation [J]. Earthquake Engineering & Structural Dynamics,2009,38(9):1053-1070.
[58]De Stefano, M. and Pintucchi, B. A review of research on seismic behaviour of irregular building structures since 2002 [J]. Bulletin of Earthquake Engineering,2008,6(2):285-308.
[59]Syamal, P.K. and Pekau, O.A. Dynamic response of bilinear asymmetric structures [J]. Earthquake Engineering & Structural Dynamics,1985,13(4):527-541.
[60]Ryan, K.L. and Chopra, A.K. Estimation of seismic demands on isolators based on nonlinear analysis [J]. Journal of Structural Engineering,2004,130(3):392-402.
[61]Goel, R.K. and Chopra, A.K. Inelastic seismic response of one-story, asymmetric-plan systems-Effects of stiffness and strength distribution [J]. Earthquake Engineering & Structural Dynamics,1990,19(7): 949-970.
[62]Goel, R.K. and Chopra, A.K. Inelastic seismic response of one-storey, asymmetric-plan systems:Effects of system parameters and yielding [J]. Earthquake Engineering & Structural Dynamics,1991,20(3): 201-222.
[63]Goel, R.K. and Chopra, A.K. Effects of plan asymmetry in inelastic seismic response of one-story systems [J]. Journal of Structural Engineering-ASCE,1991,117(5):1492-1513.
[64]Jangid, R.S. and Datta, T.K. Nonlinear response of torsionally coupled base isolated structure [J]. Journal of Structural Engineering,1994,120(1):1-22.
[65]Ozaki, M., Azuhata, T. Takahashi, T. and Shaomei, M. Inelastic deformation of one-story asymmetric-plan systems subjected to srong earthquake ground motions [J]. Earthquake Spectra,1994, 10(4):777-790.
[66]de la Llera, J.C. and Chopra, A.K. Understanding the inelastic seismic behaviour of asymmetric-plan buildings [J]. Earthquake Engineering & Structural Dynamics,1995,24(4):549-572.
[67]de la Llera, J.C., Vasquez, J., Chopra, A.K., and Almazan, J.L. A macro-element model for inelastic building analysis [J]. Earthquake Engineering & Structural Dynamics,2000,29(12):1725-1757.
[68]Dutta, S.C. Effect of strength deterioration on inelastic seismic torsional behaviour of asymmetric RC buildings [J]. Building and Environment,2001,36(10):1109-1118.
[69]Ryan, K.L. and Chopra, A.K. Estimation of seismic demands on isolators in asymmetric buildings using non-linear analysis [J]. Earthquake Engineering & Structural Dynamics,2004,33(3):395-418.
[70]Ryan, K.L. and Chopra, A.K. Estimating the seismic displacement of friction pendulum isolators based on non-linear response history analysis [J]. Earthquake Engineering & Structural Dynamics,2004,33(3): 359-373.
[71]Koliopulos, P.K. and Chandler, A.M. Stochastic linearization of inelastic seismic torsional response-Formulation and case studies. Engineering Structures,1995,17(7):494-504.
[72]De-la-Colina, J. Effects of torsion factors on simple non-linear systems using fully-bidirectional analyses [J]. Earthquake Engineering & Structural Dynamics,1999,28(7):691-706.
[73]Riddell, R. and Santa-Maria, H. Inelastic response of one-storey asymmetric plan systems subjected to bidirectional earthquake motions [J]. Earthquake Engineering & Structural Dynamics,1999,28(3): 273-285.
[74]Marusic, D. and Fajfar, P. On the inelastic seismic response of asymmetric buildings under bi-axial excitation [J]. Earthquake Engineering & Structural Dynamics,2005,34(8):943-963.
[75]Humar, J., Mahgoub, M. and Ghorbanie-Asl, M. Effect of second-order forces on seismic responses [J]. Canadian Journal of Civil Engineering,2006,33:692-706.
[76]MacRae, G.A. P-Delta effects on single-degree-of-freedom structures in earthquakes [J]. Earthquake Spectra,1994,10(3):359-568.
[77]Tremblay, R., Cote, B. and Leger, P. An evaluation of P-delta amplification factors in multistorey steel moment resisting frames [J]. Canadian Journal of Civil Engineering,1999,26(5):535-548.
[78]Gupta, A. and Krawinkler, H. Dynamic P-delta effects for flexible inelastic steel structures [J]. Journal of Structural Engineering-ASCE,2000,126(1):145-154.
[79]Williamson, E.B. Evaluation of damage and P-delta effects for system under earthquake excitation [J]. Journal of Structural Engineering-ASCE,2003,129(8):1036-1046.
[80]Bernal, D. P-delta effects in the inelastic response of mutistorey buildings [C]. In Proceedings of Pacific Conference on Earthquake Engineering, Wairakei, New Zealand,1987,2:221-230.
[81]翟长海,孙亚民,谢礼立.考虑P-delta效应的等延性位移比谱[J].哈尔滨工业大学学报,2007,39(10)：1513-1517.
[82]童根树,赵永峰.动力P-Delta效应对地震力调整系数的影响[J].浙江大学学报(工学版),2007,41(1)：120-126.
[83]Stefanou, G. The stochastic finite element method:Past, present and future [J]. Computer Methods in Applied Mechanics and Engineering,2009,198(9-12):1031-1051.
[84]Koduru, S.D. and Haukaas, T. Feasibility of FORM in finite element reliability analysis [J]. Structural Safety,2010,32(2):145-153.
[85]Der Kiureghian, A. and De Stefano, M. Efficient algorithm for second-order reliability analysis [J]. Journal of Engineering Mechanics-ASCE,1991,117(12):2904-2923.
[86]Cardoso, J.B., de Almeida, J.R., Dias, J.M. Structural reliability analysis using Monte Carlo simulation and neural networks [J]. Advances in Engineering Software,2008,39(6):505-513.
[87]Allaix, D.L. and Carbone, V.I. Discretization of 2D random fields:A genetic algorithm approach [J]. Engineering Structures,2009,31(5):1111-1119.
[88]Der Kiureghian, A. and Ke, J.B. The stochastic finite element method in structural reliability [J]. Probabilistic Engineering Mechanics,1988,3(2):83-91.
[89]Liu, W.K., Belytschko, T. and Mani, A. Probabilistic finite elements for nonlinear structural dynamics [J]. Computer Methods in Applied Mechanics and Engineering,1986,56(1):61-81.
[90]Liu, W. K., Belytschko, T. and Mani, A. Random field finite elements [J]. International Journal for Numerical Methods in Engineering,1986,23(10):1831-1845.
[91]Li, C.C. and Der Kiureghian, A. Optimal discretization of random fields [J]. Journal of Engineering Mechanics-ASCE,1993,119(6):1136-1154.
[92]Vanmarcke, E., Shinozuka, M., Nakagiri, S. Schueller, G.I. and Grigoriu, M. Random fields and stochastic finite elements [J]. Structural Safety,1986,3(3-4):143-166.
[93]Zhu, W.Q. and Wu, W.Q. A stochastic finite element method for real eigenvalue problems [J]. Probabilistic Engineering Mechanics,1991,6(3-4):228-232.
[94]Knabe, W., Przewloki,V and Roynski, G. Spatial averages for linear elements for two-parameter random field [J]. Probabilistic Engineering Mechanics,1998,13(3):147-167.
[95]Chakraborty, S. and Bhattacharyya, B. An efficient 3D stochastic finite element method [J]. International Journal of Solids and Structures,2002,39(9):2465-2475.
[96]Chakraborty, S. and Dey, S.S. Stochastic finite element simulation of random structure on uncertain foundation under random loading [J]. International Journal of Mechanical Sciences,1996,38(11): 1209-1218.
[97]Chakraborty, S. and Sarkar, S.K. Analysis of a curved beam on uncertain elastic foundation [J]. Finite Elements in Analysis and Design,2000,36:73-82.
[98]Deodatis, G. Weighted Integral Method Ⅰ:Stochastic stiffness matrix [J]. Journal of Engineering Mechanics-ASCE,1991,117(8):1851-1864.
[99]Deodatis, G. and Shinozuka, M. Weighted integral method Ⅱ:Response variability and reliability [J]. Journal of Engineering Mechanics-ASCE,1991,117(8):1865-1877.
[100]Sudret, B. and Der Kiureghian, A. Stochastic finite element methods and reliability:A state-of-the-art report [R]. Universty of California, Berkeley,2000, UCB/SEMM-2000/08
[101]秦权.随机有限元及其进展Ⅰ.随机场的离散和反应矩的计算[J].工程力学,1994,11(4)：1-10.
[102]Spanos, P.D. and Ghanem, R. Stochastic finite element expansion for random media [J]. Journal of Engineering Mechanics-ASCE,1989,115(5):1035-1053
[103]Shinozuka, M. and Astill, C.J. Random eigenvalue problems in structural analysis [J]. American Institute of Aeronautics and Astronautics (AIAA) Journal,1972,10(4):456-462.
[104]Cambou, B. Application of first-order uncertainty analysis in the finite element method in linear elasticity. Proceedings of the Second International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Aachen, Germany,1975,67-87.
[105]Handa, K., Anderson, K. Application of finite element methods in statistical analysis of structures [C]. In Proceedings of 3rd International Conference on Structural Safety and Reliability, Trondheim, Norway, 1981,409-417.
[106]Hisada, T. and Nakagiri, S. Role of the stochastic finite element method in structural safety and reliability [C], In Proceedings of the 4th International Conference on Structural Safety and Reliability, Kobe, Japan, 1985,213-219.
[107]朱位秋,任永坚.随机场的局部平均与随机有限元法[J].航空学报,1986,7(6)：604-611.
[108]朱位秋,任永坚.基于随机场局部平均的随机有限元法[J].固体力学学报,1988,9(4)：281-293.
[109]刘宁,卓家寿.三维弹塑性随机有限元的迭代计算方法研究[J].河海大学学报,1996,24(1)：1-8.
[110]刘宁.三维可分向量随机场局部平均的三维随机有限元及可靠度计算[J].水利学报,1995,6：75-82.
[111]张汝清,高行山.随机变量的变分原理及有限元法[J].应用数学和力学,1992,13(5)：383-388.
[112]高行山,张汝清.有限变形弹性理论随机变量变分原理及有限元法[J].应用数学和力学,1994,15(10)：855-862.
[113]杨绿峰,高兑现,李桂青.随机结构在随机激励下的二阶摄动随机势能泛函及其应用[J].应用力学学报,1999,16(4)：35-39.
[114]Yang, L.F., Leung, A.Y.T., Yan, L.B. and Wong, C.W.Y. Stochastic spline Ritz method based on stochastic variational principle [J]. Engineering Structures,2005,27(3):455-462.
[115]Ghanem, R.G. and Spanos, P. Stochastic Finite Elements:A Spectral Approach [M]. New York: Springer-Verlag,1991.
[116]Zhao, Y.G. and Ono, T. System relibility evaluation of ductile frame structures [J]. Journal of Structural Engineering-ASCE,1998,124(6):678-685.
[117]Zhao, Y.G, Zhong, W.Q. and Ang, A.H.S. Estimating joint failure probability of series structural systems [J]. Journal of Engineering Mechanics-ASCE,2007,133:588-596.
[118]Moses, F. System reliability developments in structural engineering [J]. Structural Safety,1982,1(1): 3-13.
[119]Feng, Y.S. Enumerating significant failure modes of a structural system by using criterion methods [J]. Computers & Structures,1988,30(5):1153-1157.
[120]冯元生,董聪.枚举结构主要失效模式的一种方法[J].航空学报,1991,12(9)：537-541.
[121]冯元生,董聪.枚举结构主要失效模式的一种新方法[J].西北工业大学学报,1991,9(3)：284-289.
[122]Cornell, C.A. Bounds on the reliability of structural systems [J]. Journal of Structural Division-ASCE, 1967,93(1):171-200.
[123]Ditlevsen, O. Narrow reliability bounds for structural systems [J]. Mechanics Based Design of Structures and Machines,1979,7(4):453-472.
[124]Thoft-Christensen, P. and Murotsu, Y. Application of structural systems reliability theory [M]. New York: Springer-Verlag,1986.
[125]Feng, Y.S. A Method of computing structural system reliability with high accuracy [J]. Computers and Structures,1989,3(1):1-5.
[126]董聪,夏人伟.现代结构系统可靠性评估理论研究进展[J].力学进展,1995,25(4)：537-548.
[127]Zhang, Y.C. High-order reliability bounds for series systems and application to structural systems [J]. Computers & Structures,1993,46(2):381-386.
[128]Greig, G.L. An assessment of high-order bounds for structural reliability [J]. Structural Safety,1992, 11(3-4):213-225.
[129]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4)：1-9.
[130]郭书祥.结构体系失效概率计算的一种快速有效方法[J].计算力学学报,2007,24(1)：107-110.
[131]Ang, A.H.S. and Ma, H.F. On the reliability of structural systems [J], In Proceedings of the 3rd ICOSSAR, Trondheim, Norway,1981,295-314.
[132]Ditlevsen, O. System reliability bounding by conditioning [J]. Journal of the Engineering Mechanics Division,1982,108(5):708-716.
[133]Thoft-Christensen, P. and Dalsgard S(?)rensen, J. Reliability of structural systems with correlated elements [J]. Applied Mathematical Modelling,1982,6(3):171-178.
[134]杨绿峰,余波,乔永平.弹性模量缩减法分析刚架结构的极限承载力[J].防灾减灾工程学报,2009,29(3)：306-312.
[135]Yu, B. and Yang, L.F. Elastic modulus reduction method for limit analysis considering initial constant and proportional loadings [J]. Finite Elements in Analysis and Design,2010,46(12):1086-1092.
[136]杨绿峰,余波,张伟.弹性模量缩减法分析杆系和板壳结构的极限承载力[J].工程力学,2009,26(12)：64-70.
[137]余波,杨绿峰,乔永平.基于承载比的弹性补偿有限元法分析杆系结构的极限承载力[J].结构工程师,2008,24(6)：67-71.
[138]杨绿峰,乔永平,余波.基于弹性补偿有限元法的拱桥极限分析[J].长沙交通学院院报,2008,24(1)：1-5.
[139]乔永平,杨绿峰,余波.弹性补偿有限元法研究斜板桥的塑性极限承载力[J].中外公路,2008,28(4)：134-138.
[140]张伟,杨绿峰,韩晓风.基于弹性模量缩减法的钢岔管安全评价[J].水力发电学报,2010,29(1)：171-179.
[141]张伟,杨绿峰,韩晓风.基于弹性补偿有限元法的无梁岔管安全评价[J].水利学报,2010,40(10)：1175-1183.
[142]杨绿峰,余波,莫远昌.基于弹性模量缩减法研究结构体系可靠度[J].广西大学学报(自然科学版),2008,33(4)：349-357.
[143]Shi, J., Boyle, J.T., Mackenzie, D., Hamilton, R. Approximate limit design of frames using elastic analysis [J]. Computers & Structures,1996,61(3):495-501.
[144]Hamilton, R. and Boyle, J.T. Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria [J]. Thin-Walled Structures,2002,40(6):503-522.
[145]Tran, T.N., Kreiiig, R., Vu, D.K and Staat, M. Upper bound limit and shakedown analysis of shells using the exact Ilyushin yield surface [J]. Computers & Structures,2008,86(17-18):1683-1695.
[146]Hamilton, R., Mackenzie, D., Shi, J., Boyle, J.T. Simplified lower bound limit analysis of pressurised cylinder/cylinder intersections using generalised yield criteria [J]. International Journal of Pressure Vessels and Piping,1996,67(2):219-226.
[147]Seshadri, R. and Mangalaramanan, S.P. Lower bound limit loads using variational concepts:the m-alpha method [J]. International Journal of Pressure Vessels and Piping,1997,71(2):93-106.
[148]王飞,陈钢,刘应华,岑章志.极限分析的弹性补偿法及其应用[J].应用力学学报,2004,21(4)：147-150.
[149]陈立杰,刘应华,杨璞,徐秉业.复杂结构塑性极限分析的修正弹性补偿法[J].机械工程学报,2007,43(5)：187-193.
[150]Shi, J., Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅲ--Torispherical heads under internal pressure [J]. International Journal of Pressure Vessels and Piping, 1992,53(1):121-142.
[151]Nadarajah, C., Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅱ-Nozzle sphere intersections with internal pressure and radial load [J]. International Journal of Pressure Vessels and Piping,1992,53(1):97-119.
[152]Mackenzie, D. and Boyle, J.T. A method of estimating limit loads by iterative elastic analysis Ⅰ--Simple examples [J]. International Journal of Pressure Vessels and Piping,1992,53(1):77-95.
[153]Seshadri, R. and Indermohan, H. Lower bound limit load determination:The m-beta multiplier method [J]. Journal of Pressure Vessel Technology,2004,126:237-240.
[154]Fanous, I.F.Z. and Seshadri, R. Limit load analysis using the reference volume concept [J]. International Journal of Pressure Vessels and Piping,2009,86(5):291-295.
[155]Jahed, H., Sethuraman, R. and Dubey, R.N. A variable material property approach for solving elastic-plastic problems [J]. International Journal of Pressure Vessels and Piping,1997,71(3):285-291.
[156]Famiyesin, O.O.R., Hossain, K.M.A., Chia, Y.H. and Slade, P.A. Numerical and analytical predictions of the limit load of rectangular two way slabs [J]. Computers & Structures,2001,79(1):43-52.
[157]张伟,杨绿峰,韩晓凤.考虑恒荷载作用效应的弹性补偿有限元法[J].工业建筑,2010,40(3)：52-59.
[158]Zhang, Y.G., Zhang, P. and Xue, W.M. Limit analysis considering initial constant loadings and proportional loadings [J].1994,14(3):229-234.
[159]Goda, K. and Hong, H.P. Estimation of seismic loss for spatially distributed buildings [J]. Earthquake Spectra,2008,24(4):889-910.
[160]Ajavakom, N., Ng, C.H. and Ma, F. Performance of nonlinear degrading structures:Identification, validation, and prediction [J]. Computers & Structures,2008,86(7-8):652-662.
[161]Chopra, A.K. Dynamics of Structures:Theory and Applications to Earthquake Engineering (3rd edition) [M]. Upper Saddle River, New Jersey:Pearson Prentice Hall,2007.
[162]Shampine, L.F. and Reichelt, M.W. The MATLAB ODE suite [J]. SIAM Journal of Scientific Computing, 1997,18(1):1-22.
[163]Park, Y.J. and Ang, A.H.S. Mechanistic seismic damage model for reinforced concrete [J]. Journal of Structural Engineering-ASCE,1985,111(4):722-739.
[164]Chung, S.T. and Loh, C.H. Identification and verification of seismic demand from different hysteretic models [J]. Journal of Earthquake Engineering,2002,6(3):31-355.
[165]Pacific Earthquake Engineering Research (PEER) Center. Next generation attenuation database [DB]. http://peer.berkeley.edu/nga/index.html. (last accessed May 1st,2010).
[166]Hong, H.P. and Goda, K. Orientation-dependent ground-motion measure for seismic-hazard assessment [J]. Bulletin of the Seismological Society of America,2007,97:1525-1538.
[167]杨伟,欧进萍.基于能量原理的Park & Ang损伤模型简化计算方法[J].地震工程与工程振动,2009,29(2)：159-165.
[168]Akkar, S.D. and Miranda, E. Statistical evaluation of approximate methods for estimating maximum deformation demands on existing structures [J]. Journal of Structural Engineering-ASCE,2005,131(1): 160-172.
[169]Riddell, R., Garcia, J.E. and Garces, E. Inelastic deformation response of SDOF systems subjected to earthquakes [J]. Earthquake Engineering & Structural Dynamics,2002,31(3):515-538.
[170]Miranda, E. Estimation of inelastic deformation demands of SDOF systems [J]. Journal of Structural Engineering-ASCE,2001,127(9):1005-1012.
[171]Wen, Y.K. Method for random vibration of hysteretic systems [J]. Journal of the Engineering Mechanics Division,1976,102(2):249-263.
[172]Baber, T.T. and Wen, Y.K. Random vibration hysteretic, degrading systems [J]. Journal of the Engineering Mechanics Division,1981,107(6):1069-1087.
[173]Baber, T.T. and Noori, M.N. Random vibration of degrading, pinching systems [J]. Journal of Engineering Mechanics-ASCE,1985,111(8):101-1026.
[174]李英民,杨洁,赖明.双向水平地震动峰值特性的相关性研究[J].重庆建筑大学学报,1999,21(2)：5-12.
[175]李英民,赖明,白绍良.基于三参数模型的双向水平地震动相关设计反应谱研究[J].世界地震工程,2002,18(4)：5-10.
[176]Ghayamghamian, M.R., Nouri, G.R., Igel, H. and Tobita, T. The effect of torsional ground motion on structural response:code recommendation for accidental eccentricity [J]. Bulletin of the Seismological Society of America,2009,99:1261-1270.
[177]Myslimaj, B. and Tso, W.K. Desirable strength distribution for asymmetric structures with strength-stiffness dependent elements [J]. Journal of Earthquake Engineering,2004,8(2):231-248.
[178]Tso, W.K. and Myslimaj, B. A yield displacement distribution-based approach for strength assignment to lateral force-resisting elements having strength dependent stiffness [J]. Earthquake Engineering & Structural Dynamics,2003,32(15):2319-2351.
[179]Atkinson, G.M. and Goda, K. Inelastic seismic demand of real versus simulated ground-motion records for cascadia subduction earthquakes [J]. Bulletin of the Seismological Society of America,2010,100: 102-115.
[180]何晓宇,李宏男.偏心形式对偏心结构扭转耦联地震响应的影响[J].世界地震工程,2008,24(3)：36-44.
[181]Park, S., Choi, S., Sikorsky, C., Stubbs, N. Efficient method for calculation of system reliability of a complex structure [J]. International Journal of Solids and Structures,2004,41(18-19):5035-5050.
[182]欧进萍,侯钢领.建筑结构设计可靠度的影响因素与比较研究[J].建筑科学,1999,15(5)：51-55.
[183]Chen, J.B. and Li, J. Development-process-of-nonlinearity-based reliability evaluation of structures [J]. Probabilistic Engineering Mechanics,2007,22(3):267-275.
[184]Haukaas, T. and Kiureghian, A.D. Strategies for finding the design point in non-linear finite element reliability analysis [J]. Probabilistic Engineering Mechanics,2006,21(2):133-147.
[185]Der Kiureghian, A., Haukaas, T. and Fujimura, K. Structural reliability software at the University of California, Berkeley [J]. Structural Safety,2006,28(1-2):44-67.
[186]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5)：79-87.
[187]Haukaas, T. and Der Kiureghian, A. Finite element reliability and sensitivity methods for performance-based engineering [R]. Pacific Earthquake Engineering Research Center,2003, PEER 2003/14.
[188]Ditlevsen, O. and Madsen, H.O. Structural reliability methods [M]. Internet edition 2.3.7,2007, http://www.web.mek.dtu.dk/staff/od/books.htm (First edition published by John Wiley & Sons Ltd, Chichester,1996, ISBN 0 471 96086 1).
[189]Der Kiureghian, A. and Liu, P.L. Structural reliability under incomplete probability information [J]. Journal of Engineering Mechanics-ASCE,1986,112(1):85-104.
[190]Hasofer, A.M. and Lind, N.C. Exact and invariant second-moment code format [J]. Journal of the Engineering Mechanics Division,1974,100(1):111-121.
[191]Rackwitz, R. and Fiessler, B. Structural reliability under combined load sequence [J]. Computer & Structures,1978,114(12):2195-2199.
[192]Zhang, Y. and Der Kiureghian, A. Two improved algorithms for reliability analysis [C]. In Proceedings of the 6th IFIP WG7.5 Working Conference on Reliability and Optimization of Stuctural Systems, Assisi, Italy,1994,297-304.
[193]Zhang, Y. and Der Kiureghian, A. Finite element reliability methods for inelastic structures [R]. University of California, Berkeley,1997, UCB/SEMM-97/05.
[194]Der Kiureghian, A., Lin, H.Z. and Hwang, S.J. Second-order reliability approximations [J]. Journal of Engineering Mechanics-ASCE,1987,113(8):1208-1225.
[195]Nadarajah, S. On the approximations for multinormal integration [J]. Computers & Industrial Engineering, 2008,54(3):705-708.