结构的鲁棒性、冗余度和易损性
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摘要
为进一步完善结构的鲁棒性、冗余度和易损性相关分析方法,更加准确地获取土木结构的抗力与外力关系,进而优化补强其薄弱易损部位,以减少结构因抗力不足而引发的损伤甚至是安全事故及其所造成的损失.通过综述结构的鲁棒性、冗余度和易损性分析研究进展,类比不同评价指标的表达形式,从而指出结构的鲁棒性、冗余度和易损性分析的本质含义,提出结构的鲁棒性、冗余度和易损性分析应变能评价指标,并据此对结构的鲁棒性、冗余度和易损性分析之间的关系以及基本影响因素展开研究.结果表明:结构的鲁棒性、冗余度和易损性源于不同时期、不同领域,已有文献大多是基于对其含义的不同程度理解,其评价指标也大多具有主观性、相互关联且计算较为复杂,也尚未提出可广泛接受的分析方法;结构的鲁棒性、冗余度和易损性本质均是反映结构特别是损伤结构抵抗外力作用的能力,其中结构鲁棒性、冗余度侧重结构在外力作用下安全储备或剩余容许能力,结构易损性则更直观反映了结构在外力作用下的破坏程度;结构的鲁棒性、冗余度评价指标具有相似的表达形式,并与易损性呈反比例变化;可通过提高结构构件的材料强度及截面尺寸、增加杆端约束、优化荷载路径等措施增强和提高结构的鲁棒性、冗余度,即降低结构的易损性,进而减少结构损伤甚至是安全事故及其所造成的损失.
To further improve the analysis methods of structural robustness,redundancy,and vulnerability,and to obtain the relationship between structural resistance and external load effect,optimization and reinforcement measures can be implemented for the weak or vulnerable parts of a structure to reduce the loss caused by damage or even safety accident due to the lack of structural resistance. Firstly,by reviewing the research progress of structural robustness,redundancy,and vulnerability and comparing different expressions of the current evaluation indexes,the essence of structural robustness,redundancy,and vulnerability were pointed out,and a new evaluation index based on strain energy was proposed. A further study on the relationship between structural robustness,redundancy,and vulnerability,as well as the basic influencing factors was also performed. Results have shown that structural robustness,redundancy,and vulnerability are from different fields and periods,which can reflect the resistance capacity of a structure,especially that of a damaged structure. The evaluation indexes are mostly subjectively defined by a complicated calculation process based on different levels of understanding. A widely accepted analysis method has not been established so far. Specifically,structural robustness and redundancy share similar evaluation index expression,both of which can represent the safety capacity or the remaining tolerance capacity of a structure. Structural vulnerability can directly reflect the structural failure extent,and it is inversely proportional to structural robustness and redundancy in the physical sense. Moreover,the increase in the material strength,the section size,and the structural restraint,together with the optimization of the load path,can increase structural robustness and redundancy and reduce structural vulnerability. The optimization and reinforcement measures can be implemented for the weak or vulnerable parts,thus structural damage,safety accident,as well as the loss cause by them,can be further reduced.
To further improve the analysis methods of structural robustness,redundancy,and vulnerability,and to obtain the relationship between structural resistance and external load effect,optimization and reinforcement measures can be implemented for the weak or vulnerable parts of a structure to reduce the loss caused by damage or even safety accident due to the lack of structural resistance. Firstly,by reviewing the research progress of structural robustness,redundancy,and vulnerability and comparing different expressions of the current evaluation indexes,the essence of structural robustness,redundancy,and vulnerability were pointed out,and a new evaluation index based on strain energy was proposed. A further study on the relationship between structural robustness,redundancy,and vulnerability,as well as the basic influencing factors was also performed. Results have shown that structural robustness,redundancy,and vulnerability are from different fields and periods,which can reflect the resistance capacity of a structure,especially that of a damaged structure. The evaluation indexes are mostly subjectively defined by a complicated calculation process based on different levels of understanding. A widely accepted analysis method has not been established so far. Specifically,structural robustness and redundancy share similar evaluation index expression,both of which can represent the safety capacity or the remaining tolerance capacity of a structure. Structural vulnerability can directly reflect the structural failure extent,and it is inversely proportional to structural robustness and redundancy in the physical sense. Moreover,the increase in the material strength,the section size,and the structural restraint,together with the optimization of the load path,can increase structural robustness and redundancy and reduce structural vulnerability. The optimization and reinforcement measures can be implemented for the weak or vulnerable parts,thus structural damage,safety accident,as well as the loss cause by them,can be further reduced.
引文
[1]FANG Z X,LI H Q.Energy-based approach to structural robustness[J].Journal of Southwest Jiaotong University,2007,15(4):319
[2]STAROSSEK U,HABERLAND M.Approaches to measures of structural robustness[J].Structure and Infrastructure Engineering,2011,7(8):625
[3]吕大刚,宋鹏彦,崔双双,等.结构鲁棒性及其评价指标[J].建筑结构学报,2011,32(11):44L Dagang,SONG Pengyan,CUI Shuangshuang,et al.Structural robustness and it’s assessment indicators[J].Journal of Building Strctures,2011,32(11):44
[4]FRANGOPOL D M,CURLEY J.Effects of damage and redundancy on structural reliability[J].Journal of Structural Engineering,1987,113(7):1533
[5]LIND N C.Vulnerability of damage accumulating systems[J].Reliability Engineering&System Safety,1996,53(2):217
[6]PINTO J T,BLOKLEY D I,WOODMAN N J.The risk of vulnerable failure[J].Structural Safety,2002,24(2):107
[7]BICKEL P J.On some robust estimates of location[J].The Annals of Mathematical Statistics,1965,36(3):847
[8]OWEN A D.A monte carlo study of the robustness of an identifiability test statistic[J].Economic Analysis and Policy,1975,6(2):64
[9]DAVISON E J,GOLDENBERG A.Robust control of a general servomechanism problem:the servo compensator[J].Automatica,1975,11(5):461
[10]KAMAT M P.Robust penalty method for structural synthesis[J].Journal of Engineering Mechanics,1983,109(4):1023
[11]THANEDAR P B,ARORA J S,LI G Y,et al.Robustness,generality and efficiency of optimization algorithms for practical applications[J].Structural Optimization,1990,2(4):203
[12]MORTON J.Accidental damage robustness and stability[M].Wingfield,Berkshire:Brick Development Association,1985:1
[13]TEMPLETON W,EDGELL G J,DE VEKEY R C.Robustness of the domestic house.part4:accidental damage[J].Masonry,1988,2:127
[14]LOPEZ-ALMANSA F,RODELLAR J.Feasibility and robustness of predictive control of building structures by active cables[J].Earthquake Engineering&Structural Dynamics,1990,19(2):157
[15]BEEBY A W.Safety of structures,and a new approach to robustness[J].Structural Engineer,1999,77(4):16
[16]JEN E.Stable or robust?What's the difference?[J].Complexity,2003,8(3):12
[17]FABER M.Robustness of structures:an introduction[J].Structural Engineering International,2006,16(2):101
[18]BAKER J W,SCHUBERT M,FABER M H.On the assessment of robustness[J].Structural Safety,2008,30(3):253
[19]S?RENSEN J D,RIZZUTO E,NARASIMHAN H,et al.Robustness:theoretical framework[J].Structural Engineering International,2012,22(1):66
[20]BIONDINI F,FRANGOPOL D M,RESTELLI S.On structural robustness redundancy and static indeterminacy[C]//Structures Congress 2008.Vancouver:ASCE,2008:24
[21]GHOSN M,FRANGOPOL D M.Structural redundancy and robustness measures and their use in assessment and design[C]//Proceedings of the Tenth International Conference on Applications of Statistics and Probability in Civil Engineering.London;New York:Taylor and Francis,2007:181
[22]STAROSSEK U.Collapse resistance and robustness of bridges[C]//4th International Conference on Bridge Maintenance,Safety and Management.London:Taylor and Francis,2008:1
[23]ROMINU S,IONITA O,BANCILA R.Robustness-a new concept in structural design[J].Pollack Periodica,2008,3(1):113
[24]BIONDINI F.A measure of lifetime structural robustness[C]//Procceedings of the SEI/ASCE Structures Congress.Austin:ASCE,2009:1749
[25]GHOSN M,MOSES F,FRANGOPOL D M.Redundancy and robustness of highway bridge superstructures and substructures[J].Structure and Infrastructure Engineering,2010,6(1/2):257
[26]BIONDINI F,FRANGOPOL D M.Structural robustness and redundancy of deteriorating concrete bridges[C]//Proceedings of the Fifth International IABMAS Conference.London:Taylor and Francis,2010:2473
[27]BIONDINI F,FRANGOPOL D M.Lifetime structural robustness of concrete bridge piers under corrosion bridge maintenance[C]//Safety,Management,Resilience and Sustainability:Proceedings of the Sixth International IABMAS Conference.London:Taylor and Francis,2012:8
[28]叶列平,林旭川,曲哲,等.基于广义结构刚度的构件重要性评价方法研究[J].建筑科学与工程学报,2010,27(1):1YE Lieping,LIN Xuchuan,QU Zhe,et al.Evaluating method of element importance of structural system[J].Journal of Architecture and Civil Engineering,2010,27(1):1
[29]高扬.结构鲁棒性定量计算中的构件重要性系数[D].上海:上海交通大学,2009GAO Yang.Importance coefficients of components in quantitativeevaluation of structural robustness[D].Shanghai:Shanghai Jiaotong University,2009
[30]COPI I M.The inconsistency or redundancy of principia mathematica[J].Philosophy and Phenomenological Research,1950,11(2):190
[31]OLIVER B M.Reduction of signal redundancy:No.2,681,385[P].1954-06-15
[32]WILDER T W.An analysis of statically indeterminate trusses having members stressed beyond the proportional limit[R].Washington:National Advisory Committee for Aeronautics,1953
[33]FOULKES J.The minimum-weight design of structural frames[J].Proceedings of the Royal Society of London A:Mathema Tical,Physical and Engineering Sciences,1954,223(1155):482
[34]MOSES F.Optimum design,redundancy and reliability of structural system[J].Computers&Structures,1986,24(2):239
[35]FRANGOPOL D M.Sensitivity studies in reliability-based analysis of redundant structures[J].Structural Safety,1985,3(1):13
[36]FRANGOPOL D M,CURLEY J P.Effects of redundancy deterioration on the reliability of truss systems and bridges[C]//Effects of Deterioration on Safety and Reliability of Structures.Seattle:ASCE,1986:30
[37]FRANGOPOL D M,NAKIB R,SHING B P.Bridge redundancy assessment[C]//Second Workshop on Bridge Engineering Research in Progress.Reno:University of Nevada,1990:167
[38]SHEA G H.Recommended lateral force requirements and commentary[M].7th ed.Sacramento:Structural Engineers Association of California,1999:101
[39]CONNOR R J,DEXTER R J,MAHMOUD H.Inspection and management of bridges with fracture-critical details[M].Washington DC:Transportation Research Board,2005:2
[40]于刚.结构易损性分析及其在桥梁健康监测中的应用[D].上海:同济大学,2009YU Gang.Structural vulnerability analysis and its application on bridge health monitoring[D].Shanghai:Tongji Univerity,2009
[41]GHOSN M,MOSES F.Redundancy in highway bridge superstructures[R].Washington DC:Transportation Research Board,National Academy Press,1998
[42]LIU W D,NEUENHOFFER A,GHOSN M,et al.Redundancy in highway bridge substructures[R].Washington DC:Transportation Research Board,National Academy Press,2001
[43]GHOSN M,YANG J,BEAL D,et al.Bridge system safety and redundancy[R].Washington DC:Transportation Research Board,National Academy Press,2014
[44]陈以一,赵宪忠.高冗余度钢结构倒塌控制设计指南[M].上海:同济大学出版社,2007:77CHEN Yiyi,ZHAO Xianzong.Control design guidelines of steel structure collapsed with high redundancy[M].Shanghai:Tongji U-niversity Press,2007:77
[45]MERTZ D.Steel bridge design handbook:redundancy[R].Washington DC:Federal Highway Administration,2012
[46]PANDEY P,BARAI S.Structural sensitivity as a measure of redundancy[J].Journal of Structural Engineering,1997,123(3):360
[47]FABER M H,MAES M A,STRAUB D,et al.On the quantification of robustness of structures[C]//Proceedings of the 25thInternational Conference on Offshore Mechanics and Arctic Engineering(OMAE2006).New York:ASME,2006:1
[48]SCHARRER E.Vascularization and vulnerability of the cornuammonis in the opossum[J].Archives of Neurology&Psychiatry,1940,44(3):483
[49]BIOT M A,ARNOLD L.Study of vulnerability of aircraft to damage induced flutter[R].Maryland:Ballistic Research Laboratories,1950
[50]KORDES E E,OSULLIVAN Jr W J.Structural vulnerability of theBoeing B-29 aircraft wing to damage by warhead fragments[R].Langley Field,Va:Langley Aeronautical Lab,1952
[51]GREENSPON J E.Energy approaches to structural vulnerability application of the new bell stress-strain laws[R].Maryland:Ballistic Research Laboratories Aberdeen Proving Ground,1976
[52]SHAH H C.Glossary of terms for probabilistic seismic-risk and hazard analysis[J].Earthquake Spectra,1984,1(1):33
[53]TASSIOS T P.The vulnerability concept revisited[J].WIT Transactions onthe Built Environment,1995,15(7):343
[54]WU X,BLOCKLEY D I,WOODMAN N J.Vulnerability of structural systems.part 1:rings and clusters,part 2:failure scenarios[J].Civil Engineering Systems,1993,10(4):301
[55]LU Z,YU Y,WOODMAN N J,et al.A theory of structural vulnerability[J].Structural Engineer,1999,77(18):17
[56]AGARWAL J,BLOCKLEY D I,WOODMAN N J.Vulnerability of structural systems[J].Structural Safety,2003,25(3):263
[57]AGARWAL J,BLOCKLEY D I,WOODMAN N J.Vulnerability of systems[J].Civil Engineering&Environmental Systems,2001,18(2):141
[58]HASHIMOTO M.Vulnerability and reliability of structural systems[D].Bristol:University of Bristol,1994
[59]YU Y.Analysis of structural vulnerability[D].Bristol:University of Bristol,1997
[60]LU Z.Structural vulnerability analysis[D].Bristol:University of Bristol,1998
[61]PINTO J T Q S.The risk of a vulnerable scenario[D].Bristol:University of Bristol,2002
[62]FARRELL J J,LIPNER N,CHIU J S,et al.Target vulnerability and hardness uncertainty analysis[R].Redondo Beach,California:Trw Defense Systems Group Redondo Beach,1977
[63]LIND N C.A measure of vulnerability and damage tolerance[J].Reliability Engineering&System Safety,1995,48(1):1
[64]BLOCKLEY D I,AGARWAL J,PINTO J T,et al.Structural vulnerability,reliability and risk[J].Progress in Structural Engineering and Materials,2002,4(2):203
[65]SUN L M,YU G.Vulnerability analysis for design of bridge health monitoring system[C]//SPIE Smart Structures and Materials Nondestructive Evaluation and Health Monitoring.San Digo:SPIE,2010
[66]YAN D,CHANG C C.Vulnerability assessment of single-pylon cable-stayed bridges using plastic limit analysis[J].Engineering Structures,2010,32(8):2049
[67]TORBOL M,GOMEZ H,FENG M.Fragility analysis of highway bridges based on long-term monitoring data[J].Computer Aided Civil and Infrastructure Engineering,2013,28(3):178
[68]CAO B,SARKAR P P.Numerical simulation of dynamic response of a long-span bridge to assess its vulnerability to nonsynoptic wind[J].Engineering Structures,2015,84:67
[69]LONETTI P,PASCUZZO A.Vulnerability and failure analysis of hybrid cable-stayed suspension bridges subjected to damage mechanisms[J].Engineering Failure Analysis,2014,45:470
[70]LIU C M,LIU X L.Structural vulnerability analysis of three dimensional truss[C]//IABSE Symposium on Structures and Extreme E-vents.Zurich:IABSE,2005:1
[2]STAROSSEK U,HABERLAND M.Approaches to measures of structural robustness[J].Structure and Infrastructure Engineering,2011,7(8):625
[3]吕大刚,宋鹏彦,崔双双,等.结构鲁棒性及其评价指标[J].建筑结构学报,2011,32(11):44L Dagang,SONG Pengyan,CUI Shuangshuang,et al.Structural robustness and it’s assessment indicators[J].Journal of Building Strctures,2011,32(11):44
[4]FRANGOPOL D M,CURLEY J.Effects of damage and redundancy on structural reliability[J].Journal of Structural Engineering,1987,113(7):1533
[5]LIND N C.Vulnerability of damage accumulating systems[J].Reliability Engineering&System Safety,1996,53(2):217
[6]PINTO J T,BLOKLEY D I,WOODMAN N J.The risk of vulnerable failure[J].Structural Safety,2002,24(2):107
[7]BICKEL P J.On some robust estimates of location[J].The Annals of Mathematical Statistics,1965,36(3):847
[8]OWEN A D.A monte carlo study of the robustness of an identifiability test statistic[J].Economic Analysis and Policy,1975,6(2):64
[9]DAVISON E J,GOLDENBERG A.Robust control of a general servomechanism problem:the servo compensator[J].Automatica,1975,11(5):461
[10]KAMAT M P.Robust penalty method for structural synthesis[J].Journal of Engineering Mechanics,1983,109(4):1023
[11]THANEDAR P B,ARORA J S,LI G Y,et al.Robustness,generality and efficiency of optimization algorithms for practical applications[J].Structural Optimization,1990,2(4):203
[12]MORTON J.Accidental damage robustness and stability[M].Wingfield,Berkshire:Brick Development Association,1985:1
[13]TEMPLETON W,EDGELL G J,DE VEKEY R C.Robustness of the domestic house.part4:accidental damage[J].Masonry,1988,2:127
[14]LOPEZ-ALMANSA F,RODELLAR J.Feasibility and robustness of predictive control of building structures by active cables[J].Earthquake Engineering&Structural Dynamics,1990,19(2):157
[15]BEEBY A W.Safety of structures,and a new approach to robustness[J].Structural Engineer,1999,77(4):16
[16]JEN E.Stable or robust?What's the difference?[J].Complexity,2003,8(3):12
[17]FABER M.Robustness of structures:an introduction[J].Structural Engineering International,2006,16(2):101
[18]BAKER J W,SCHUBERT M,FABER M H.On the assessment of robustness[J].Structural Safety,2008,30(3):253
[19]S?RENSEN J D,RIZZUTO E,NARASIMHAN H,et al.Robustness:theoretical framework[J].Structural Engineering International,2012,22(1):66
[20]BIONDINI F,FRANGOPOL D M,RESTELLI S.On structural robustness redundancy and static indeterminacy[C]//Structures Congress 2008.Vancouver:ASCE,2008:24
[21]GHOSN M,FRANGOPOL D M.Structural redundancy and robustness measures and their use in assessment and design[C]//Proceedings of the Tenth International Conference on Applications of Statistics and Probability in Civil Engineering.London;New York:Taylor and Francis,2007:181
[22]STAROSSEK U.Collapse resistance and robustness of bridges[C]//4th International Conference on Bridge Maintenance,Safety and Management.London:Taylor and Francis,2008:1
[23]ROMINU S,IONITA O,BANCILA R.Robustness-a new concept in structural design[J].Pollack Periodica,2008,3(1):113
[24]BIONDINI F.A measure of lifetime structural robustness[C]//Procceedings of the SEI/ASCE Structures Congress.Austin:ASCE,2009:1749
[25]GHOSN M,MOSES F,FRANGOPOL D M.Redundancy and robustness of highway bridge superstructures and substructures[J].Structure and Infrastructure Engineering,2010,6(1/2):257
[26]BIONDINI F,FRANGOPOL D M.Structural robustness and redundancy of deteriorating concrete bridges[C]//Proceedings of the Fifth International IABMAS Conference.London:Taylor and Francis,2010:2473
[27]BIONDINI F,FRANGOPOL D M.Lifetime structural robustness of concrete bridge piers under corrosion bridge maintenance[C]//Safety,Management,Resilience and Sustainability:Proceedings of the Sixth International IABMAS Conference.London:Taylor and Francis,2012:8
[28]叶列平,林旭川,曲哲,等.基于广义结构刚度的构件重要性评价方法研究[J].建筑科学与工程学报,2010,27(1):1YE Lieping,LIN Xuchuan,QU Zhe,et al.Evaluating method of element importance of structural system[J].Journal of Architecture and Civil Engineering,2010,27(1):1
[29]高扬.结构鲁棒性定量计算中的构件重要性系数[D].上海:上海交通大学,2009GAO Yang.Importance coefficients of components in quantitativeevaluation of structural robustness[D].Shanghai:Shanghai Jiaotong University,2009
[30]COPI I M.The inconsistency or redundancy of principia mathematica[J].Philosophy and Phenomenological Research,1950,11(2):190
[31]OLIVER B M.Reduction of signal redundancy:No.2,681,385[P].1954-06-15
[32]WILDER T W.An analysis of statically indeterminate trusses having members stressed beyond the proportional limit[R].Washington:National Advisory Committee for Aeronautics,1953
[33]FOULKES J.The minimum-weight design of structural frames[J].Proceedings of the Royal Society of London A:Mathema Tical,Physical and Engineering Sciences,1954,223(1155):482
[34]MOSES F.Optimum design,redundancy and reliability of structural system[J].Computers&Structures,1986,24(2):239
[35]FRANGOPOL D M.Sensitivity studies in reliability-based analysis of redundant structures[J].Structural Safety,1985,3(1):13
[36]FRANGOPOL D M,CURLEY J P.Effects of redundancy deterioration on the reliability of truss systems and bridges[C]//Effects of Deterioration on Safety and Reliability of Structures.Seattle:ASCE,1986:30
[37]FRANGOPOL D M,NAKIB R,SHING B P.Bridge redundancy assessment[C]//Second Workshop on Bridge Engineering Research in Progress.Reno:University of Nevada,1990:167
[38]SHEA G H.Recommended lateral force requirements and commentary[M].7th ed.Sacramento:Structural Engineers Association of California,1999:101
[39]CONNOR R J,DEXTER R J,MAHMOUD H.Inspection and management of bridges with fracture-critical details[M].Washington DC:Transportation Research Board,2005:2
[40]于刚.结构易损性分析及其在桥梁健康监测中的应用[D].上海:同济大学,2009YU Gang.Structural vulnerability analysis and its application on bridge health monitoring[D].Shanghai:Tongji Univerity,2009
[41]GHOSN M,MOSES F.Redundancy in highway bridge superstructures[R].Washington DC:Transportation Research Board,National Academy Press,1998
[42]LIU W D,NEUENHOFFER A,GHOSN M,et al.Redundancy in highway bridge substructures[R].Washington DC:Transportation Research Board,National Academy Press,2001
[43]GHOSN M,YANG J,BEAL D,et al.Bridge system safety and redundancy[R].Washington DC:Transportation Research Board,National Academy Press,2014
[44]陈以一,赵宪忠.高冗余度钢结构倒塌控制设计指南[M].上海:同济大学出版社,2007:77CHEN Yiyi,ZHAO Xianzong.Control design guidelines of steel structure collapsed with high redundancy[M].Shanghai:Tongji U-niversity Press,2007:77
[45]MERTZ D.Steel bridge design handbook:redundancy[R].Washington DC:Federal Highway Administration,2012
[46]PANDEY P,BARAI S.Structural sensitivity as a measure of redundancy[J].Journal of Structural Engineering,1997,123(3):360
[47]FABER M H,MAES M A,STRAUB D,et al.On the quantification of robustness of structures[C]//Proceedings of the 25thInternational Conference on Offshore Mechanics and Arctic Engineering(OMAE2006).New York:ASME,2006:1
[48]SCHARRER E.Vascularization and vulnerability of the cornuammonis in the opossum[J].Archives of Neurology&Psychiatry,1940,44(3):483
[49]BIOT M A,ARNOLD L.Study of vulnerability of aircraft to damage induced flutter[R].Maryland:Ballistic Research Laboratories,1950
[50]KORDES E E,OSULLIVAN Jr W J.Structural vulnerability of theBoeing B-29 aircraft wing to damage by warhead fragments[R].Langley Field,Va:Langley Aeronautical Lab,1952
[51]GREENSPON J E.Energy approaches to structural vulnerability application of the new bell stress-strain laws[R].Maryland:Ballistic Research Laboratories Aberdeen Proving Ground,1976
[52]SHAH H C.Glossary of terms for probabilistic seismic-risk and hazard analysis[J].Earthquake Spectra,1984,1(1):33
[53]TASSIOS T P.The vulnerability concept revisited[J].WIT Transactions onthe Built Environment,1995,15(7):343
[54]WU X,BLOCKLEY D I,WOODMAN N J.Vulnerability of structural systems.part 1:rings and clusters,part 2:failure scenarios[J].Civil Engineering Systems,1993,10(4):301
[55]LU Z,YU Y,WOODMAN N J,et al.A theory of structural vulnerability[J].Structural Engineer,1999,77(18):17
[56]AGARWAL J,BLOCKLEY D I,WOODMAN N J.Vulnerability of structural systems[J].Structural Safety,2003,25(3):263
[57]AGARWAL J,BLOCKLEY D I,WOODMAN N J.Vulnerability of systems[J].Civil Engineering&Environmental Systems,2001,18(2):141
[58]HASHIMOTO M.Vulnerability and reliability of structural systems[D].Bristol:University of Bristol,1994
[59]YU Y.Analysis of structural vulnerability[D].Bristol:University of Bristol,1997
[60]LU Z.Structural vulnerability analysis[D].Bristol:University of Bristol,1998
[61]PINTO J T Q S.The risk of a vulnerable scenario[D].Bristol:University of Bristol,2002
[62]FARRELL J J,LIPNER N,CHIU J S,et al.Target vulnerability and hardness uncertainty analysis[R].Redondo Beach,California:Trw Defense Systems Group Redondo Beach,1977
[63]LIND N C.A measure of vulnerability and damage tolerance[J].Reliability Engineering&System Safety,1995,48(1):1
[64]BLOCKLEY D I,AGARWAL J,PINTO J T,et al.Structural vulnerability,reliability and risk[J].Progress in Structural Engineering and Materials,2002,4(2):203
[65]SUN L M,YU G.Vulnerability analysis for design of bridge health monitoring system[C]//SPIE Smart Structures and Materials Nondestructive Evaluation and Health Monitoring.San Digo:SPIE,2010
[66]YAN D,CHANG C C.Vulnerability assessment of single-pylon cable-stayed bridges using plastic limit analysis[J].Engineering Structures,2010,32(8):2049
[67]TORBOL M,GOMEZ H,FENG M.Fragility analysis of highway bridges based on long-term monitoring data[J].Computer Aided Civil and Infrastructure Engineering,2013,28(3):178
[68]CAO B,SARKAR P P.Numerical simulation of dynamic response of a long-span bridge to assess its vulnerability to nonsynoptic wind[J].Engineering Structures,2015,84:67
[69]LONETTI P,PASCUZZO A.Vulnerability and failure analysis of hybrid cable-stayed suspension bridges subjected to damage mechanisms[J].Engineering Failure Analysis,2014,45:470
[70]LIU C M,LIU X L.Structural vulnerability analysis of three dimensional truss[C]//IABSE Symposium on Structures and Extreme E-vents.Zurich:IABSE,2005:1