基于五参数统一强度理论的刚构桥地震损伤分析
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摘要
混凝土五参数统一强度理论在主应力空间偏平面上的边界线为十二边形,可通过调整中间主应力的影响系数消除角点的奇异性,以单位体积材料当前塑性耗能及其断裂能的比值定义损伤变量,根据相关流动准则推导混凝土的弹塑性损伤本构关系。该模型可同时考虑混凝土材料中间主应力的影响、高应力状态下的静水应力效应、拉压异性和随动强化效应等,不考虑循环荷载下的刚度折减。由图形回归法给出应力更新的数值方法,编写了相应的Fortran语言程序,并将其用于大跨度连续刚构桥地震损伤的模拟,计算结果验证了所用模型的预测能力。
Trace of five-parameter unified-strength theory in the deviatoric plane becomes dodecagon in the Haigh-Westgaard coordinate system.The singularity at the corners is eliminated by adjusting the coefficient of medium principal stresses.Damage variable is supplied by the ratio of plastic dissipation energy and the fracture energy in unit volume of the concrete.Elastoplastic damage constitutive formulations are deduced based on the associated flow rule.This model enables to consider systematically the effect of intermediate principal stress,quadratic meridian in high confined stress space,different behavior in tension and compression as well as kinematic hardening response corresponding to the post yielding ignoring the stiffness degradation caused by cyclic loading.The stress update with mapping return method is presented and the corresponding program is coded to simulate the nonlinear damage evolution of the structure during earthquake.
Trace of five-parameter unified-strength theory in the deviatoric plane becomes dodecagon in the Haigh-Westgaard coordinate system.The singularity at the corners is eliminated by adjusting the coefficient of medium principal stresses.Damage variable is supplied by the ratio of plastic dissipation energy and the fracture energy in unit volume of the concrete.Elastoplastic damage constitutive formulations are deduced based on the associated flow rule.This model enables to consider systematically the effect of intermediate principal stress,quadratic meridian in high confined stress space,different behavior in tension and compression as well as kinematic hardening response corresponding to the post yielding ignoring the stiffness degradation caused by cyclic loading.The stress update with mapping return method is presented and the corresponding program is coded to simulate the nonlinear damage evolution of the structure during earthquake.
引文
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[2]俞茂宏,曾文兵.工程结构分析新理论及其应用[J].工程力学,1994,11(1):9-20.
[3]俞茂宏.混凝土强度理论及其应用[M].北京:高等教育出版社,2002:7-8.
[4]俞茂宏.强度理论的发展和展望[J].工程力学,2004,21(6):1-20.
[5]俞茂宏.强度理论百年总结[J].力学进展,2004,34(4):529-560.
[6]俞茂宏,赵坚等.岩石、混凝土强度理论:历史、现状、发展[J].自然科学进展,1997,7(6):653-660.
[7]Yu Maomong.Unified elasto-plastic associated and non-associ-ated constitutive model and its engineering applications[J].Computers and Structures,1999,71:627-636.
[8]Yu Maohong et al.A unified strength criterion for rock materi-al[J].International Journal of Rock Mechanics&Mining Sci-ences,2002,39:975-989.
[9]Wang Yanbin,Yu Maohong et al.Dynamic plastic response ofa circular plate based on unifiedstrength theory[J].Interna-tional Journal of Impact Engineering,2005,31:25-40.
[10]王延斌,愈茂宏.拉压异性的简支圆板在线性分布荷载作用下的塑性极限分析[J].土木工程学报,2003,36(8):31-36.
[11]徐栓强,愈茂宏.统一强度准则下厚壁圆筒的弹脆性承载能力分析[J].力学季刊,2004,25(4):490-495.
[12]赵均海,等.用统一强度理论求厚壁圆筒和厚壁球壳的极限解[J].应用力学学报,2000,17(1):157-162.
[13]陈惠发,萨里普.混凝土和土的本构方程[M].余天庆,等译.北京:中国建筑工业出版社,2004:33-38.
[14]Lemaitre J.损伤力学教程[M].北京:倪金刚,等译.科学出版社,1996:16-25.
[15]Lubliner J,Oliver J,Oller S,et al.A Plastic damage Model forConcrete[J].Int.J Solids Structures,1989,25(3):299-326.
[16]Jeeho Lee,Gregory L Fenves.Plastic-damage Model for CyclicLoading of Concrete Structures[J].Earthquake Engineeringand Structural Dynamics,1998,27:937-956.
[17]Jeeho Lee,Gregory L Fenves.A Plastic-Damage ConcreteModel for Earthquake Analysis of Dams[J].Earthquake Engi-neering and Structural Dynamics,1998,125:892-890.
[18]郑颖人,沈珠江,龚晓南.广义塑性力学-岩土塑性力学原理[M].北京:中国建筑工业出版社,2004:89-93.
[19]陈惠发.土木工程材料的本构方程[M].余天庆,等译.武汉:华中科技大学出版社,2001:78-108
[20]陈惠发,萨里普.弹性与塑性力学[M].余天庆,等译.北京:中国建筑工业出版社,2004:179-186.
[21]Ted Belytschko,et al.连续体和结构的非线性有限元[M].庄茁译.北京:清华大学出版社,2002:241-255.
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