单层网壳结构弹塑性屈曲分析的离散单元法研究
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摘要
该文提出离散元塑性区法,即将任意2个球元的接触截面划分成若干小面积,通过各小面积的应力状态描述整个截面的塑性发展过程,较离散元塑性铰法更精确。该文推导了杆系离散元截面应变增量计算公式,建立了截面在三维应力-应变状态下的结构弹塑性本构方程、加卸载准则、截面内力积分公式以及计算分析流程。离散元弹塑性屈曲分析的追踪策略与弹性屈曲分析完全相同,即仍采用离散元力控制法或位移控制法。采用Fortran语言自编程序对若干单层网壳结构算例进行弹塑性屈曲分析,验证了离散元塑性区法的正确性和适用性,拓宽了离散单元法在工程领域的应用范围,为结构分析提供了新路径。
This paper presents a discrete element plastic zone method which could be recognized as an exact solution compared with the discrete element plastic hinge method. In the method, the contact cross section between two arbitrary adjacent particles is divided into a finite number of monitored subsections, while the spread of plasticity over the cross section is captured by tracing the stress state of each subsection. The incremental section strain formula in the member Discrete Element Method(DEM) is derived first, then the space elastoplastic constitutive equation, the loading and unloading criterion as well as the integral formula of section internal force are established in turn. Either discrete element force control method or the displacement control method for tracing elastic buckling behavior can be employed directly in elastoplastic buckling analysis. Finally, the calculation flowchart of elastoplastic buckling analysis process in DEM is obtained and an object-oriented computer program is compiled by Fortran Language. The computer program is used to investigate the elastoplastic buckling behaviors of several single-layer reticulated shells. The comparisons made have verified the correctness and applicability of the proposed discrete element plastic zone method. Additionally, the application range of DEM in structural engineering is extended and a novel approach for structural analysis is provided.
This paper presents a discrete element plastic zone method which could be recognized as an exact solution compared with the discrete element plastic hinge method. In the method, the contact cross section between two arbitrary adjacent particles is divided into a finite number of monitored subsections, while the spread of plasticity over the cross section is captured by tracing the stress state of each subsection. The incremental section strain formula in the member Discrete Element Method(DEM) is derived first, then the space elastoplastic constitutive equation, the loading and unloading criterion as well as the integral formula of section internal force are established in turn. Either discrete element force control method or the displacement control method for tracing elastic buckling behavior can be employed directly in elastoplastic buckling analysis. Finally, the calculation flowchart of elastoplastic buckling analysis process in DEM is obtained and an object-oriented computer program is compiled by Fortran Language. The computer program is used to investigate the elastoplastic buckling behaviors of several single-layer reticulated shells. The comparisons made have verified the correctness and applicability of the proposed discrete element plastic zone method. Additionally, the application range of DEM in structural engineering is extended and a novel approach for structural analysis is provided.
引文
[1]Yong Lin Pi,Trahair N S.Nonlinear inelastic analysis of steel beam-columns:I.Theory[J].Journal of Structural Engineering-ASCE,1994,120(7):2041―2061.
[2]Chan S L.Non-linear behavior and design of steel structures[J].Journal of Constructional Steel Research,2001,57(12):1217―1231.
[3]叶康生,吴可伟.空间杆系结构的弹塑性大位移分析[J].工程力学,2013,30(11):1―8.Ye Kangsheng,Wu Kewei.Elasto-plastic large displacement analysis of spatial skeletal structures[J].Engineering Mechanics,2013,30(11):1―8.(in Chinese)
[4]Gebbeken N.A refined numerical approach for the ultimate-load analysis of 3-D steel rod structures[J].Engineering Computers,1998,15(3):312―344.
[5]Larissa Driemeier,Sergio P.Baroncini Proenc,Marcilio Alves.A contribution to the numerical nonlinear analysis of three-dimensional truss systems damage and plasticity[J].Communications in Nonlinear Science,2005,10(5):515―535.
[6]凌道盛,徐兴.非线性有限元及程序[M].浙江:浙江大学出版社,2004:157―162.Ling Daosheng,Xu Xing.Nonlinear finite element and program[M].Zhejiang:Zhejiang University Press,2004:157―162.(in Chinese)
[7]James G.Orbison,William McGuire,John F.Abel.Yield surface applications in nonlinear steel frame analysis[J].Computer Methods in Applied Mechanics and Engineering,1982,33(1/2/3):557―573.
[8]Yang Yeong Bin,Shue Ming Chern,Hung Taw Fan.Yield surfaces for I-sections with bimoments[J].Journal of Structural Engineering-ASCE,1989,115(5):3044―3058.
[9]Afsin Saritas.Modeling of inelastic behavior of curved members with a mixed formulation beam element[J].Finite Elements in Analysis and Design,2009,45(5):357―368.
[10]李灿明,兰亮云,宋红宇,等.GM屈服准则求解I型裂尖塑性区[J].工程力学,2012,29(增刊I):20―28.Li Canming,Lan Liangyun,Song Hongyu,et al.Analysis of plastic zone of mode i crack tip by GM yield[J].Engineering Mechanics,2012,29(Suppl I):20―28.(in Chinese)
[11]Lorig L J,Cundall P A.Modeling of reinforced concrete using the distinct element method[C].New York:Fracture of Concrete and Rock,Springer,1989:276―287.
[12]Dimitri R,De Lorenzis L,Zavarise G.Numerical study on the dynamic behavior of masonry columns and arches on buttresses with the discrete element method[J].Engineering Structures,2011,33(12):3172―3188.
[13]顾祥林,黄庆华,汪小林,等.地震中钢筋混凝土框架结构倒塌反应的试验研究与数值仿真[J].土木工程学报,2012,45(9):36―44.Gu Xianglin,Huang Qinghua,Wang Xiaolin,et al.Spatial collapse responses of reinforced concrete frame structures under earthquake-test study and numerical simulation[J].China Civil Engineering Journal,2012,45(9):36―44.(in Chinese)
[14]顾祥林,付武荣,汪小林,等.混凝土材料与结构破坏过程模拟分析[J].工程力学,2015,32(11):9―17.Gu Xianglin,Fu Wurong,Wang Xiaolin,et al.Numerical investigation on damage processes of concrete materials and structures[J].Engineering Mechanics,2015,32(11):9―17.(in Chinese)
[15]金伟良,方韬.钢筋混凝土框架结构破坏性能的离散单元法模拟[J].工程力学,2005,22(4):67―73.Jin Weiliang,Fang Tao.Numerical Simulation of failure behavior of reinforced concrete frame structures by discrete element method[J].Engineering Mechanics,2005,22(4):67―73.(in Chinese)
[16]张伟.基于离散单元法的群楼拆除爆破仿真模拟[J].工程爆破,2016,22(6):8―12.Zhang Wei.Analogue simulation of buildings demolition blasting based on discrete element method[J].Engineering Blasting,2016,22(6):8―12.(in Chinese)
[17]齐念.DEM/FEM耦合计算方法研究及其在网壳倒塌破坏模拟中的应用[D].南京:东南大学,2016:38―55.Qi Nian.Coupled DEM/FEM method and its application in collapse simulation of reticulated shells[D].Nanjing:Southeast University,2016:38―55.(in Chinese)
[18]齐念,叶继红.基于离散元法的杆系结构几何非线性大变形分析[J].东南大学学报,2013,43(5):917―922.Qi Nian,Ye Jihong.Geometric nonlinear analysis with large deformation of member structures by discrete element method[J].Journal of Southeast University,2013,43(5):917―922.(in Chinese)
[19]Qi N,Ye J H.Nonlinear dynamic analysis of space frame structures by discrete element method[J].Applied Mechanics and Materials,2014,638/639/640:1716―1719.
[20]许玲玲,叶继红,薛素铎.大质量法在基于离散元法多点激励分析中的应用和误差修正[J].土木工程学报,2016,49(增刊1):32―36.Xu Lingling,Ye Jihong,Xue Suduo.Application and error improvement of large mass method used in DEM-based multi-support excitation analysis[J].China Civil Engineering Journal,2016,49(Suppl 1):32―36.(in Chinese)
[21]Ye J H,Qi N.Progressive collapse simulation based on DEM for single-layer reticulated domes[J].Journal of Constructional Steel Research,2017,128:721―731.
[22]叶继红,齐念.基于离散元法与有限元法耦合模型的网壳结构倒塌过程分析[J].建筑结构学报,2017,38(1):52―61.Ye Jihong,Qi Nian.Collapse process simulation of reticulated shells based on coupled DEM/FEM mode[J].Journal of Building Structures,2017,38(1):52―61.(in Chinese)
[23]Ivo C,Massimo M,Bartolomeo P.A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings[J].Engineering Structures,2012,40(7):327―338.
[24]舒兴平,沈蒲生.空间钢框架结构的非线性全过程分析[J].工程力学,1997,14(3):36―45.Shu Xingping,Shen Pusheng.A full range nonlinear analysis for space steel frames[J].Engineering Mechanics,1997,14(3):36―45.(in Chinese)
[25]Simo J C,Hughes T J R.Computational inelasticity[M].New York:Springer,1998:1―370.
[26]张梅.基于离散单元法的单层网壳结构屈曲行为研究[D].南京:东南大学,2017:55―82.Zhang Mei.Buckling analysis of single-layer reticulated shells based on discrete element method[M].Nanjing:Southeast University,2017:55―82.(in Chinese)
[27]沈世钊,陈昕.网壳结构稳定性[M].北京:科学出版社,1999:60―77.Shen Shizhao,Chen Xin.Reticulated shell structure stability[M].Beijing:Science Press,1999:60―77.(in Chinese)
[28]吴可伟.空间杆系结构的弹塑性大位移分析[D].北京:[[清华大学,2012:6―76.Wu Kewei.Elasto-plastic large displacement analysis of spatial skeletal structures[D].Beijing:Tsinghua University,2012:6―76.(in Chinese)
[29]陆华臣.单层球壳多点输入振动台倒塌试验研究[D].南京:东南大学,2015:8―80.Lu Huachen.Shaking table experimental research on collapse processing of domes under multi-support excitations[D].Nanjing:Southeast University,2015:8―80.(in Chinese)
[30]叶继红,李柯燃.多点输入下基于响应敏感性的单层球面网壳冗余特性研究[J].土木工程学报,2016,49(9):20―29.Ye Jihong,Li Keran.Redundancy evaluation of domes under multi-support excitations based on response sensitivity[J].China Civil Engineering Journal,2016,49(9):20―29.(in Chinese)
[2]Chan S L.Non-linear behavior and design of steel structures[J].Journal of Constructional Steel Research,2001,57(12):1217―1231.
[3]叶康生,吴可伟.空间杆系结构的弹塑性大位移分析[J].工程力学,2013,30(11):1―8.Ye Kangsheng,Wu Kewei.Elasto-plastic large displacement analysis of spatial skeletal structures[J].Engineering Mechanics,2013,30(11):1―8.(in Chinese)
[4]Gebbeken N.A refined numerical approach for the ultimate-load analysis of 3-D steel rod structures[J].Engineering Computers,1998,15(3):312―344.
[5]Larissa Driemeier,Sergio P.Baroncini Proenc,Marcilio Alves.A contribution to the numerical nonlinear analysis of three-dimensional truss systems damage and plasticity[J].Communications in Nonlinear Science,2005,10(5):515―535.
[6]凌道盛,徐兴.非线性有限元及程序[M].浙江:浙江大学出版社,2004:157―162.Ling Daosheng,Xu Xing.Nonlinear finite element and program[M].Zhejiang:Zhejiang University Press,2004:157―162.(in Chinese)
[7]James G.Orbison,William McGuire,John F.Abel.Yield surface applications in nonlinear steel frame analysis[J].Computer Methods in Applied Mechanics and Engineering,1982,33(1/2/3):557―573.
[8]Yang Yeong Bin,Shue Ming Chern,Hung Taw Fan.Yield surfaces for I-sections with bimoments[J].Journal of Structural Engineering-ASCE,1989,115(5):3044―3058.
[9]Afsin Saritas.Modeling of inelastic behavior of curved members with a mixed formulation beam element[J].Finite Elements in Analysis and Design,2009,45(5):357―368.
[10]李灿明,兰亮云,宋红宇,等.GM屈服准则求解I型裂尖塑性区[J].工程力学,2012,29(增刊I):20―28.Li Canming,Lan Liangyun,Song Hongyu,et al.Analysis of plastic zone of mode i crack tip by GM yield[J].Engineering Mechanics,2012,29(Suppl I):20―28.(in Chinese)
[11]Lorig L J,Cundall P A.Modeling of reinforced concrete using the distinct element method[C].New York:Fracture of Concrete and Rock,Springer,1989:276―287.
[12]Dimitri R,De Lorenzis L,Zavarise G.Numerical study on the dynamic behavior of masonry columns and arches on buttresses with the discrete element method[J].Engineering Structures,2011,33(12):3172―3188.
[13]顾祥林,黄庆华,汪小林,等.地震中钢筋混凝土框架结构倒塌反应的试验研究与数值仿真[J].土木工程学报,2012,45(9):36―44.Gu Xianglin,Huang Qinghua,Wang Xiaolin,et al.Spatial collapse responses of reinforced concrete frame structures under earthquake-test study and numerical simulation[J].China Civil Engineering Journal,2012,45(9):36―44.(in Chinese)
[14]顾祥林,付武荣,汪小林,等.混凝土材料与结构破坏过程模拟分析[J].工程力学,2015,32(11):9―17.Gu Xianglin,Fu Wurong,Wang Xiaolin,et al.Numerical investigation on damage processes of concrete materials and structures[J].Engineering Mechanics,2015,32(11):9―17.(in Chinese)
[15]金伟良,方韬.钢筋混凝土框架结构破坏性能的离散单元法模拟[J].工程力学,2005,22(4):67―73.Jin Weiliang,Fang Tao.Numerical Simulation of failure behavior of reinforced concrete frame structures by discrete element method[J].Engineering Mechanics,2005,22(4):67―73.(in Chinese)
[16]张伟.基于离散单元法的群楼拆除爆破仿真模拟[J].工程爆破,2016,22(6):8―12.Zhang Wei.Analogue simulation of buildings demolition blasting based on discrete element method[J].Engineering Blasting,2016,22(6):8―12.(in Chinese)
[17]齐念.DEM/FEM耦合计算方法研究及其在网壳倒塌破坏模拟中的应用[D].南京:东南大学,2016:38―55.Qi Nian.Coupled DEM/FEM method and its application in collapse simulation of reticulated shells[D].Nanjing:Southeast University,2016:38―55.(in Chinese)
[18]齐念,叶继红.基于离散元法的杆系结构几何非线性大变形分析[J].东南大学学报,2013,43(5):917―922.Qi Nian,Ye Jihong.Geometric nonlinear analysis with large deformation of member structures by discrete element method[J].Journal of Southeast University,2013,43(5):917―922.(in Chinese)
[19]Qi N,Ye J H.Nonlinear dynamic analysis of space frame structures by discrete element method[J].Applied Mechanics and Materials,2014,638/639/640:1716―1719.
[20]许玲玲,叶继红,薛素铎.大质量法在基于离散元法多点激励分析中的应用和误差修正[J].土木工程学报,2016,49(增刊1):32―36.Xu Lingling,Ye Jihong,Xue Suduo.Application and error improvement of large mass method used in DEM-based multi-support excitation analysis[J].China Civil Engineering Journal,2016,49(Suppl 1):32―36.(in Chinese)
[21]Ye J H,Qi N.Progressive collapse simulation based on DEM for single-layer reticulated domes[J].Journal of Constructional Steel Research,2017,128:721―731.
[22]叶继红,齐念.基于离散元法与有限元法耦合模型的网壳结构倒塌过程分析[J].建筑结构学报,2017,38(1):52―61.Ye Jihong,Qi Nian.Collapse process simulation of reticulated shells based on coupled DEM/FEM mode[J].Journal of Building Structures,2017,38(1):52―61.(in Chinese)
[23]Ivo C,Massimo M,Bartolomeo P.A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings[J].Engineering Structures,2012,40(7):327―338.
[24]舒兴平,沈蒲生.空间钢框架结构的非线性全过程分析[J].工程力学,1997,14(3):36―45.Shu Xingping,Shen Pusheng.A full range nonlinear analysis for space steel frames[J].Engineering Mechanics,1997,14(3):36―45.(in Chinese)
[25]Simo J C,Hughes T J R.Computational inelasticity[M].New York:Springer,1998:1―370.
[26]张梅.基于离散单元法的单层网壳结构屈曲行为研究[D].南京:东南大学,2017:55―82.Zhang Mei.Buckling analysis of single-layer reticulated shells based on discrete element method[M].Nanjing:Southeast University,2017:55―82.(in Chinese)
[27]沈世钊,陈昕.网壳结构稳定性[M].北京:科学出版社,1999:60―77.Shen Shizhao,Chen Xin.Reticulated shell structure stability[M].Beijing:Science Press,1999:60―77.(in Chinese)
[28]吴可伟.空间杆系结构的弹塑性大位移分析[D].北京:[[清华大学,2012:6―76.Wu Kewei.Elasto-plastic large displacement analysis of spatial skeletal structures[D].Beijing:Tsinghua University,2012:6―76.(in Chinese)
[29]陆华臣.单层球壳多点输入振动台倒塌试验研究[D].南京:东南大学,2015:8―80.Lu Huachen.Shaking table experimental research on collapse processing of domes under multi-support excitations[D].Nanjing:Southeast University,2015:8―80.(in Chinese)
[30]叶继红,李柯燃.多点输入下基于响应敏感性的单层球面网壳冗余特性研究[J].土木工程学报,2016,49(9):20―29.Ye Jihong,Li Keran.Redundancy evaluation of domes under multi-support excitations based on response sensitivity[J].China Civil Engineering Journal,2016,49(9):20―29.(in Chinese)
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