基于GPU并行计算的地下结构非线性动力分析软件平台开发
|
摘要
为解决地下结构隐式非线性动力分析收敛性差和计算效率低的技术瓶颈,该文建立了基于GPU并行计算的地下结构显式动力分析软件平台。在此平台中提出并实现了一种混凝土弥散开裂模型;给出并实现了一种钢筋纤维与实体单元的耦合方法;基于等参元思想,提出了人工边界节点的单元从属面积的计算方法;为实现节点不协调情况下的土与结构相互作用分析,开发实现了一种实体单元间的两节点接触单元。利用该文开发的软件对日本大开地铁站进行了重力场分析、线性和非线性动力分析。将重力场和线性动力分析结果与ABAQUS分析结果进行了对比,结果表明该文软件计算结果与ABAQUS计算结果一致,且计算效率约为ABAQUS计算效率的5.68倍,验证了软件各模块的正确性和效率。另外,通过将非线性计算结果与灾害调查结果进行对比分析,验证了软件非线性分析的稳定性和合理性。
The implicit nonlinear dynamic analysis of underground structures is of poor convergence and low computational efficiency. Based on GPU parallel computing, a software platform for the explicit dynamic analysis of underground structures was established, which can solve the technical bottleneck of the implicit method. In this platform, a smeared crack model for concrete was proposed and implemented. A coupling method for rebar fibers and solid elements was developed and implemented. Based on the isoparametric element idea, a method for calculating the element area of artificial boundary nodes was proposed. A two-node interface element for solid elements was proposed to perform the interaction analysis between soil and structure with uncoordinated nodes. The gravity field analysis, linear and nonlinear dynamic analysis of Daikai subway station in Japan were performed by the software. The results of gravity field analysis and linear dynamic analysis were compared with the results of ABAQUS. The results of the software were in an agreement with the results of ABAQUS, and the computational efficiency was about 5.68 times the efficiency of ABAQUS. Thusly, the accuracy and efficiency of the software modules were verified. Besides, the stability and rationality of the software nonlinear analysis were verified by comparing the results of nonlinear analysis with the disaster investigation.
The implicit nonlinear dynamic analysis of underground structures is of poor convergence and low computational efficiency. Based on GPU parallel computing, a software platform for the explicit dynamic analysis of underground structures was established, which can solve the technical bottleneck of the implicit method. In this platform, a smeared crack model for concrete was proposed and implemented. A coupling method for rebar fibers and solid elements was developed and implemented. Based on the isoparametric element idea, a method for calculating the element area of artificial boundary nodes was proposed. A two-node interface element for solid elements was proposed to perform the interaction analysis between soil and structure with uncoordinated nodes. The gravity field analysis, linear and nonlinear dynamic analysis of Daikai subway station in Japan were performed by the software. The results of gravity field analysis and linear dynamic analysis were compared with the results of ABAQUS. The results of the software were in an agreement with the results of ABAQUS, and the computational efficiency was about 5.68 times the efficiency of ABAQUS. Thusly, the accuracy and efficiency of the software modules were verified. Besides, the stability and rationality of the software nonlinear analysis were verified by comparing the results of nonlinear analysis with the disaster investigation.
引文
[1]Ma C,Lu D C,Du X L,et al.Effect of buried depth on seismic response of rectangular underground structures considering the influence of ground loss[J].Soil Dynamics&Earthquake Engineering,2018,106:278―297.
[2]路德春,罗磊,王欣,等.土与结构接触面土体软/硬化本构模型及数值实现[J].工程力学,2017,34(7):41―50.Lu Dechun,Luo Lei,Wang Xin,et al.Softening/hardening constitutive model for soil-structure interface and numerical implementation[J].Engineering Mechanics,2017,34(7):41―50.(in Chinese)
[3]杜修力,李洋,赵密,等.下卧刚性基岩条件下场地土-结构体系地震反应分析方法研究[J].工程力学,2017,34(5):52―59.Du Xiuli,Li Yang,Zhao Mi,et al.Seismic response analysis method for soil-structure interaction system of underlying rigid rock base soil condition[J].Engineering Mechanics,2017,34(5):52―59.(in Chinese)
[4]Nakamura S,Yoshida N,Iwatate T.Damage to Daikai subway station during the 1995 Hyogoken-Nanbu earthquake and its investigation[J].Japan Society of Civil Engineers,Committee of Earthquake Engineering,1996:287―295.
[5]An X,Shawky A A,Maekawa K.The collapse mechanism of a subway station during the Great Hanshin Earthquake[J].Cement and Concrete Composites,1997,19(3):241―257.
[6]Maekawa K,Shawky A.Computational approach to path-dependent nonlinear RC/soil interactions[J].Concrete Library International,1996,30(532):197―207.
[7]曹炳政,罗奇峰,马硕,等.神户大开地铁车站的地震反应分析[J].地震工程与工程振动,2002,22(4):102―107.Cao Bingzheng,Luo Qifeng,Ma Shuo,et al.Seismic response analysis of Daikai subway station in Hyogoken-Nanbu earthquake[J].Earthquake Engineering and Engineering Vibration,2002,22(4):102―107.(in Chinese)
[8]Liu J B,Liu X Q.Pushover analysis of Daikai subway station during the Osaka-Kobe earthquake in 1995[C].Proceedings of the 14th World Conference on Earthquake Engineering.Beijing China,2008:No.14-0099.
[9]庄海洋,程绍革,陈国兴.阪神地震中大开地铁车站震害机制数值仿真分析[J].岩土力学,2008,29(1):245―250.Zhuang Haiyang,Cheng Shaoge,Chen Guoxing.Numerical simulation and analysis of earthquake damages of Daikai metro station caused by Kobe earthquake[J].Rock and Soil Mechanics,2008,29(1):245―250.(in Chinese)
[10]杜修力,马超,路德春,等.大开地铁车站地震破坏模拟与机理分析[J].土木工程学报,2017,50(1):53―62.Du Xiuli,Ma Chao,Lu Dechun,et al.Collapse simulation and failure mechanism analysis of the Daikai subway station under seismic loads[J].China Civil Engineering Journal,2017,50(1):53―62.(in Chinese)
[11]Flanagan D,Belytschko T.A uniform strain hexahedron and quadrilateral with orthogonal hourglass control[J].International Journal for Numerical Methods in Engineering,1981,17(5):679―706.
[12]Duncan J M,Chang C Y.Nonlinear analysis of stress and strain in soils[J].Soil Mechanics&Foundation Division Journal,1970,96(5):1629―1653.
[13]Simo J C,Hughes T J R.Computational inelasticity[M].USA:Springer,2008:91―92.
[14]Rots J G,Blaauwendraad J.Crack models for concrete,discrete or smeared?fixed,multi-directional or rotating?[J].Heron,1989,34(1):1―59.
[15]Vecchio F J,Collins M P.The modified compressionfield theory for reinforced concrete elements subjected to shear[J].ACI Journal,1986,83(2):219―231.
[16]杜修力,王国盛,路德春.混凝土材料非线性多轴动态强度准则[J].中国科学:技术科学,2014,44(12):1319―1332.Du Xiuli,Wang Guosheng,Lu Dechun.Nonlinear multiaxial dynamic strength criterion for concrete material[J].Scientia Sinica Technologica,2014,44(12):1319―1332.(in Chinese)
[17]李杰,吴建营.混凝土弹塑性损伤本构模型研究I:基本公式[J].土木工程学报,2006,38(9):14―20.Li Jie,Wu Jianying.Elastoplastic damage constitutive model for concrete based on damage energy release rates,part I:basic formulations[J].China Civil Engineering Journal,2006,38(9):14―20.(in Chinese)
[18]Lubliner J,Oliver J,Oller S,et al.A plastic-damage model for concrete[J].International Journal of Solids and Structures,1989,25(3):299―326.
[19]Lee J,Fenves G L.Plastic-damage model for cyclic loading of concrete structures[J].Journal of Engineering Mechanics,1998,124(8):892―900.
[20]陈惠发,余天庆.混凝土和土的本构方程[M].北京:中国建筑工业出版社,2004:20―22.Chen Huifa,Yu Tianqing.Constitutive equations for materials of concrete and soil[M].Beijing:China Architecture&Building Press.2004:20―22.(in Chinese)
[21]过镇海.混凝土的强度和变形:试验基础和本构关系[M].北京:清华大学出版社,1997:13―15.Guo Zhenhai.Strength and deformation of concrete:experimental basis and constitutive relation[M].Beijing:Tsinghua University Press,1997:13―15.(in Chinese)
[22]GB 50010-2010,混凝土结构设计规范[S].北京:中国建筑工业出版社,2011:209―211.GB 50010-2010,Code for design of concrete structures[S].Beijing:China Architecture&Building Press,2011:209―211.(in Chinese)
[23]Ba?ant Z P,Oh B H.Crack band theory for fracture of concrete[J].Materials and Structures,1983,16(3):155―177.
[24]Suidan M,Schnobrich W C.Finite element analysis of reinforced concrete[J].Journal of the Structural Division,1973,99(10):2109―2122.
[25]费康,张建伟.ABAQUS在岩土工程中的应用[M].北京:中国水利水电出版社,2013:146―152.Fei Kang,Zhang Jianwei.Application of ABAQUS in geotechnical engineering[M].Beijing:China Water Power Press,2013:146―152.(in Chinese)
[26]Belytschko T,Bindeman L P.Assumed strain stabilization of the eight node hexahedral element[J].Computer Methods in Applied Mechanics and Engineering,1993,105(2):225―260.
[27]江见鲸.钢筋混凝土结构非线性有限元分析[M].西安:陕西科学技术出版社,1994:91―116.Jiang Jianjing.Nonlinear finite element analysis of reinforced concrete structures[M].Xi’an:Shaanxi Science and Technology Press,1994:91―116.(in Chinese)
[28]Spacone E,Filippou F C,Taucer F F.Fiber beam-column model for nonlinear analysis of R/C frames[J].Earthquake Engineering&Structural Dynamics,1996,25(7):711―725.
[29]Polak M A.Nonlinear analysis of reinforced-concrete shells[J].Journal of Structural Engineering,1993,119(12):3439―3462.
[30]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49―56.Du Xiuli,Zhao Mi,Wang Jinting.A stress artificial boundary in FEA for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49―56.(in Chinese)
[31]Goodman R E,Taylor R L,Brekke T L.A model for the mechanics of jointed rock[J].Journal of Soil Mechanics and Foundations Division,1968,94(3):637―660.
[32]钱向东,任青文,赵引.一种高效的等参有限元逆变换算法[J].计算力学学报,1998,15(4):437―441.Qian Xiangdong,Ren Qingwen,Zhao Yin.An efficient inverse transformation method of isoparametric finite element method[J].Chinese Journal of Computational Mechanics,1998,15(4):437―441.(in Chinese)
[33]王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109―112.Wang Jinting,Du Xiuli.An explicit difference method for dynamic analysis of a structure system with damping[J].Engineering Mechanics,2002,19(3):109―112.(in Chinese)
[34]何昌荣,杨桂芳.邓肯-张模型参数变化对计算结果的影响[J].岩土工程学报,2002,24(2):170―174.He Changrong,Yang Guifang.Effects of parameters of Duncan-Chang model on calculated results[J].Chinese Journal of Geotechnical Engineering,2002,24(2):170―174.(in Chinese)
[35]蒋录珍,陈隽,李杰.1995年阪神地震中大开车站破坏机理分析[J].世界地震工程,2015,31(3):236―242.Jiang Luzhen,Chen Juan,Li Jie.Damage mechanism analysis of Daikai subway station caused by Kobe earthquake in 1995[J].World Earthquake Engineering,2015,31(3):236―242.(in Chinese)
[36]杜修力.工程波动理论与方法[M].北京:科学出版社,2009:370―374.Du Xiuli.Theories and methods of wave motion for engineering[M].Beijing:Science Press,2009:370―374.(in Chinese)
[2]路德春,罗磊,王欣,等.土与结构接触面土体软/硬化本构模型及数值实现[J].工程力学,2017,34(7):41―50.Lu Dechun,Luo Lei,Wang Xin,et al.Softening/hardening constitutive model for soil-structure interface and numerical implementation[J].Engineering Mechanics,2017,34(7):41―50.(in Chinese)
[3]杜修力,李洋,赵密,等.下卧刚性基岩条件下场地土-结构体系地震反应分析方法研究[J].工程力学,2017,34(5):52―59.Du Xiuli,Li Yang,Zhao Mi,et al.Seismic response analysis method for soil-structure interaction system of underlying rigid rock base soil condition[J].Engineering Mechanics,2017,34(5):52―59.(in Chinese)
[4]Nakamura S,Yoshida N,Iwatate T.Damage to Daikai subway station during the 1995 Hyogoken-Nanbu earthquake and its investigation[J].Japan Society of Civil Engineers,Committee of Earthquake Engineering,1996:287―295.
[5]An X,Shawky A A,Maekawa K.The collapse mechanism of a subway station during the Great Hanshin Earthquake[J].Cement and Concrete Composites,1997,19(3):241―257.
[6]Maekawa K,Shawky A.Computational approach to path-dependent nonlinear RC/soil interactions[J].Concrete Library International,1996,30(532):197―207.
[7]曹炳政,罗奇峰,马硕,等.神户大开地铁车站的地震反应分析[J].地震工程与工程振动,2002,22(4):102―107.Cao Bingzheng,Luo Qifeng,Ma Shuo,et al.Seismic response analysis of Daikai subway station in Hyogoken-Nanbu earthquake[J].Earthquake Engineering and Engineering Vibration,2002,22(4):102―107.(in Chinese)
[8]Liu J B,Liu X Q.Pushover analysis of Daikai subway station during the Osaka-Kobe earthquake in 1995[C].Proceedings of the 14th World Conference on Earthquake Engineering.Beijing China,2008:No.14-0099.
[9]庄海洋,程绍革,陈国兴.阪神地震中大开地铁车站震害机制数值仿真分析[J].岩土力学,2008,29(1):245―250.Zhuang Haiyang,Cheng Shaoge,Chen Guoxing.Numerical simulation and analysis of earthquake damages of Daikai metro station caused by Kobe earthquake[J].Rock and Soil Mechanics,2008,29(1):245―250.(in Chinese)
[10]杜修力,马超,路德春,等.大开地铁车站地震破坏模拟与机理分析[J].土木工程学报,2017,50(1):53―62.Du Xiuli,Ma Chao,Lu Dechun,et al.Collapse simulation and failure mechanism analysis of the Daikai subway station under seismic loads[J].China Civil Engineering Journal,2017,50(1):53―62.(in Chinese)
[11]Flanagan D,Belytschko T.A uniform strain hexahedron and quadrilateral with orthogonal hourglass control[J].International Journal for Numerical Methods in Engineering,1981,17(5):679―706.
[12]Duncan J M,Chang C Y.Nonlinear analysis of stress and strain in soils[J].Soil Mechanics&Foundation Division Journal,1970,96(5):1629―1653.
[13]Simo J C,Hughes T J R.Computational inelasticity[M].USA:Springer,2008:91―92.
[14]Rots J G,Blaauwendraad J.Crack models for concrete,discrete or smeared?fixed,multi-directional or rotating?[J].Heron,1989,34(1):1―59.
[15]Vecchio F J,Collins M P.The modified compressionfield theory for reinforced concrete elements subjected to shear[J].ACI Journal,1986,83(2):219―231.
[16]杜修力,王国盛,路德春.混凝土材料非线性多轴动态强度准则[J].中国科学:技术科学,2014,44(12):1319―1332.Du Xiuli,Wang Guosheng,Lu Dechun.Nonlinear multiaxial dynamic strength criterion for concrete material[J].Scientia Sinica Technologica,2014,44(12):1319―1332.(in Chinese)
[17]李杰,吴建营.混凝土弹塑性损伤本构模型研究I:基本公式[J].土木工程学报,2006,38(9):14―20.Li Jie,Wu Jianying.Elastoplastic damage constitutive model for concrete based on damage energy release rates,part I:basic formulations[J].China Civil Engineering Journal,2006,38(9):14―20.(in Chinese)
[18]Lubliner J,Oliver J,Oller S,et al.A plastic-damage model for concrete[J].International Journal of Solids and Structures,1989,25(3):299―326.
[19]Lee J,Fenves G L.Plastic-damage model for cyclic loading of concrete structures[J].Journal of Engineering Mechanics,1998,124(8):892―900.
[20]陈惠发,余天庆.混凝土和土的本构方程[M].北京:中国建筑工业出版社,2004:20―22.Chen Huifa,Yu Tianqing.Constitutive equations for materials of concrete and soil[M].Beijing:China Architecture&Building Press.2004:20―22.(in Chinese)
[21]过镇海.混凝土的强度和变形:试验基础和本构关系[M].北京:清华大学出版社,1997:13―15.Guo Zhenhai.Strength and deformation of concrete:experimental basis and constitutive relation[M].Beijing:Tsinghua University Press,1997:13―15.(in Chinese)
[22]GB 50010-2010,混凝土结构设计规范[S].北京:中国建筑工业出版社,2011:209―211.GB 50010-2010,Code for design of concrete structures[S].Beijing:China Architecture&Building Press,2011:209―211.(in Chinese)
[23]Ba?ant Z P,Oh B H.Crack band theory for fracture of concrete[J].Materials and Structures,1983,16(3):155―177.
[24]Suidan M,Schnobrich W C.Finite element analysis of reinforced concrete[J].Journal of the Structural Division,1973,99(10):2109―2122.
[25]费康,张建伟.ABAQUS在岩土工程中的应用[M].北京:中国水利水电出版社,2013:146―152.Fei Kang,Zhang Jianwei.Application of ABAQUS in geotechnical engineering[M].Beijing:China Water Power Press,2013:146―152.(in Chinese)
[26]Belytschko T,Bindeman L P.Assumed strain stabilization of the eight node hexahedral element[J].Computer Methods in Applied Mechanics and Engineering,1993,105(2):225―260.
[27]江见鲸.钢筋混凝土结构非线性有限元分析[M].西安:陕西科学技术出版社,1994:91―116.Jiang Jianjing.Nonlinear finite element analysis of reinforced concrete structures[M].Xi’an:Shaanxi Science and Technology Press,1994:91―116.(in Chinese)
[28]Spacone E,Filippou F C,Taucer F F.Fiber beam-column model for nonlinear analysis of R/C frames[J].Earthquake Engineering&Structural Dynamics,1996,25(7):711―725.
[29]Polak M A.Nonlinear analysis of reinforced-concrete shells[J].Journal of Structural Engineering,1993,119(12):3439―3462.
[30]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49―56.Du Xiuli,Zhao Mi,Wang Jinting.A stress artificial boundary in FEA for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49―56.(in Chinese)
[31]Goodman R E,Taylor R L,Brekke T L.A model for the mechanics of jointed rock[J].Journal of Soil Mechanics and Foundations Division,1968,94(3):637―660.
[32]钱向东,任青文,赵引.一种高效的等参有限元逆变换算法[J].计算力学学报,1998,15(4):437―441.Qian Xiangdong,Ren Qingwen,Zhao Yin.An efficient inverse transformation method of isoparametric finite element method[J].Chinese Journal of Computational Mechanics,1998,15(4):437―441.(in Chinese)
[33]王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109―112.Wang Jinting,Du Xiuli.An explicit difference method for dynamic analysis of a structure system with damping[J].Engineering Mechanics,2002,19(3):109―112.(in Chinese)
[34]何昌荣,杨桂芳.邓肯-张模型参数变化对计算结果的影响[J].岩土工程学报,2002,24(2):170―174.He Changrong,Yang Guifang.Effects of parameters of Duncan-Chang model on calculated results[J].Chinese Journal of Geotechnical Engineering,2002,24(2):170―174.(in Chinese)
[35]蒋录珍,陈隽,李杰.1995年阪神地震中大开车站破坏机理分析[J].世界地震工程,2015,31(3):236―242.Jiang Luzhen,Chen Juan,Li Jie.Damage mechanism analysis of Daikai subway station caused by Kobe earthquake in 1995[J].World Earthquake Engineering,2015,31(3):236―242.(in Chinese)
[36]杜修力.工程波动理论与方法[M].北京:科学出版社,2009:370―374.Du Xiuli.Theories and methods of wave motion for engineering[M].Beijing:Science Press,2009:370―374.(in Chinese)