有限元等效应力法在高拱坝应力分析中的适用性研究
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摘要
有限单元法进行拱坝分析具有诸多方面的优点,但存在较大的应力集中,而经等效应力法处理可在一定程度上削除这种应力集中的影响。目前,有限元等效应力法应用于高拱坝分析设计可行性还不确定。有限元等效应力法应用于拱坝分析还处于起步阶段,其可行性有待进一步的深入研究,特别是在高拱坝分析设计中的应用更应慎重考虑。随着我国高拱坝工程的不断发展,有必要对有限元等效应力法在高拱坝分析中的适用性作进一步的研究。本文首先介绍了拱坝等效应力和非线性开裂分析方法,并提出利用非线性分析结果作为参照对等效应力法及其应力控制标准进行检验研究究。坝体分析采用ANSYS有限元软件。运用ANSYS自带APDL语言和结果文件数据,可比较方便地计算拱坝上下游面的等效应力;运用ANSYS中的Concrete65单元和混凝土材料开裂模型可模拟拱坝受荷后的非线性开裂。通过非线性开裂解和有限元等效应力解的对比研究有限元等效应力法进行高拱坝应力分析及规范提出的1.5MPa应力控制标准应用于高拱坝分析时的适用性。
从分析结果可以看出,有限元等效应力法计算结果相对于单纯利用有限元法所计算的应力值大大降低,因此等效应力法可以有效削除应力集中的影响。而与非线性开裂分析结果比较后可知,等效应力值与非线性开裂应力值大体接近,并且两者总体的应力分布规律比较相似,因此可以说明等效应力法可以应用于高拱坝的坝体应力分析。其次,由非线性开裂分析结果可知,坝体只在坝基面上游侧产生最大不超过0.3坝厚范围的局部裂缝,裂缝仍处于稳定状态,对大坝正常运行影响不大。而温降和温升工况最大等效主拉应力值均在1.5MPa以内,因此《规范》关于等效应力法最大拉应力控制值1.5MPa的规定在高拱坝的应用中仍能适用。
The finite element method has a lot of advantages, but the stress results by this method are always involved with great stress convergence. Fortunately in some degree this kind of stress convergence can be eliminated or reduced to a lower level processed with the finite element equivalent stress method. At present it is doubtable to analyze high arch dam stress with the FEM equivalent stress method. Now the FEM equivalent stress method is being used for arch dam analysis at its initial stage, and its feasibility should be studied about more deeply, especially for high arch dams. So it's necessary to study the validity of the FEM equivalent stress method further for the analysis of high arch dam stress. Firstly this paper introduces the FEM equivalent stress method and the nonlinear cracking FEM, and intends to study the applicability of the FEM equivalent stress method as well as its tensile stress criterion contained in the design specification by comparison with the results gained by both of the above methods. The arch dam stress is analyzed with the ANSYS FEM software. Meanwhile it is easy to calculate the equivalent stress of arch dam by running an APDL program on the basis of the ANSYS result data; and it is feasible to analyze nonlinear cracking stress of arch dam using the concrete65 element and concrete cracking principle. Through comparison with two kinds of stress results and crack development the validity of the FEM equivalent stress method and the 1.5MPa of the equivalent tensile stress limit will be researched for the stress analysis of high arch dam.
After comparing two sets of results referred above, it is clear that the FEM equivalent stress method can cut down the stress result calculated straight by FEM and eliminate the stress convergence. The stress values gained by both methods are basically close as well as the stress distribution about the dam height. So the equivalent FEM can be used to analyze the stress of high arch dam. On the other hand, from the nonlinear cracking analysis results, cracks only happen at some local positions, and they are all in a steady-going state. It's clear that these cracks have not any important impact on the arch dam's working order. Meanwhile the greatest equivalent principle tensile stress is less than 1.5MPa.So the 1.5MPa of equivalent tensile stress limits by the current design specification is also feasible.
从分析结果可以看出,有限元等效应力法计算结果相对于单纯利用有限元法所计算的应力值大大降低,因此等效应力法可以有效削除应力集中的影响。而与非线性开裂分析结果比较后可知,等效应力值与非线性开裂应力值大体接近,并且两者总体的应力分布规律比较相似,因此可以说明等效应力法可以应用于高拱坝的坝体应力分析。其次,由非线性开裂分析结果可知,坝体只在坝基面上游侧产生最大不超过0.3坝厚范围的局部裂缝,裂缝仍处于稳定状态,对大坝正常运行影响不大。而温降和温升工况最大等效主拉应力值均在1.5MPa以内,因此《规范》关于等效应力法最大拉应力控制值1.5MPa的规定在高拱坝的应用中仍能适用。
The finite element method has a lot of advantages, but the stress results by this method are always involved with great stress convergence. Fortunately in some degree this kind of stress convergence can be eliminated or reduced to a lower level processed with the finite element equivalent stress method. At present it is doubtable to analyze high arch dam stress with the FEM equivalent stress method. Now the FEM equivalent stress method is being used for arch dam analysis at its initial stage, and its feasibility should be studied about more deeply, especially for high arch dams. So it's necessary to study the validity of the FEM equivalent stress method further for the analysis of high arch dam stress. Firstly this paper introduces the FEM equivalent stress method and the nonlinear cracking FEM, and intends to study the applicability of the FEM equivalent stress method as well as its tensile stress criterion contained in the design specification by comparison with the results gained by both of the above methods. The arch dam stress is analyzed with the ANSYS FEM software. Meanwhile it is easy to calculate the equivalent stress of arch dam by running an APDL program on the basis of the ANSYS result data; and it is feasible to analyze nonlinear cracking stress of arch dam using the concrete65 element and concrete cracking principle. Through comparison with two kinds of stress results and crack development the validity of the FEM equivalent stress method and the 1.5MPa of the equivalent tensile stress limit will be researched for the stress analysis of high arch dam.
After comparing two sets of results referred above, it is clear that the FEM equivalent stress method can cut down the stress result calculated straight by FEM and eliminate the stress convergence. The stress values gained by both methods are basically close as well as the stress distribution about the dam height. So the equivalent FEM can be used to analyze the stress of high arch dam. On the other hand, from the nonlinear cracking analysis results, cracks only happen at some local positions, and they are all in a steady-going state. It's clear that these cracks have not any important impact on the arch dam's working order. Meanwhile the greatest equivalent principle tensile stress is less than 1.5MPa.So the 1.5MPa of equivalent tensile stress limits by the current design specification is also feasible.
引文
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[2] Wllam KJ,Warnke EP.Constitutive Models for the Triaxial Behavior of Concrete. IABSE Proceeding,1975,19:1-30
[3]Ottosen NS.A Failure Criterion for Concrete.ASCE,1977,103(EM4):527-535
[4] Darwin D,Pecknold D A.Nonlinear Biaxial Stress-Strain Law for Concrete. ASCE, 1977,103(EM2):229-241
[5] Sargin M.Stress-Strain Curves of Normal and Lightweight Concrete in Compression. Journal of ACI,1978,51(11)
[6] Elwi A A,Murray D W.A 3D Hypoelastic Concrete Constitutive Relationship.ASCE, 1979,105(EM4):623-641
[7] Ottosen N S.Constitutive Model for Short-Time Loading of Concrete.ASCE,1979,105 (EMD :127-141
[8] Kotsovos MD.A mathematical description of the strength properties of concrete under generalized stress.Magazine of Concrete Research,1979,31(128):151-158
[9] Kotsovos M D. A mathematical model of the deformational behavior of concrete under generalised stress based on fundamental materials properties. Materials and Structrues,1980,13(76):289-298
[10]Gerstle KH.Simple Formulation of Biaixial Concrete Behavior.ACI, 1982, 78(1): 62—68
[11] Gerstle KH.Simple Formulation of Triaxial Concrete Behavior. ACI, 1982, 78(5): 382- 387
[12] Chen WF.Plasticity in Reinforced Concrete.McGraw-Hill Book Company.New York, 1982
[13] Comite Euro-International du Beton.Bulletin D'information No.l56.Concrete under Multiaxial States of Stress Constitutive Equantions for Practical Design, Paris,1983
[14] Stankowski T,Gerstle KH. Simple Formulation of Concrete Behavior Under Multiaxial Load Histories ACI,1985,82(2):213-221
[15]朱伯芳.国际拱坝学术讨论会专题综述.混凝土坝技术.水利发电,1987,2,1988,8,49-52
[16]傅作新,钱向东.有限单元法在拱坝设计中的应用.河海大学学报(自然科学学版),1991年,第2期,8-15
[17]DL/T 5057-1996水工混凝土结构设计规范.北京:中国电力出版社,1997
[18]朱伯芳.大体积混凝土温度应力与温度控制.北京:中国电力出版社,1999
[19]李瓒,陈兴华,郑建波,王光伦.混凝土拱坝设计.北京:中国电力出版社,2000
[20]徐芝纶.弹性力学简明教程(第三版).高等教育出版社,2002,8,146-149
[21]GB 50010-2002混凝土结构设计规范.北京:中国建筑工业出版社,2002
[22]朱伯芳,高季章,陈祖,厉易生.拱坝设计与研究.北京:中国水利水电出版社,2002
[23]钱向东.基于有限元等效应力法的拱坝强度设计准则探讨.河海大学学报(自然科学学版),2003年,第31卷,第3期,318-320
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[25]The ANSYS Parametric Design Language Guide.ANSYS Inc,2007
[26]博弈创作室.APDL参数化有限元分析技术及其应用实例.北京:中国水利水电出版社,2004
[27]The Elements Reference.ANSYS Inc,2007
[28]The Theory Reference for ANSYS and ANSYS Workbench.ANSYS Inc,2007
[29]陈晓霞主编.ANSYS 7.0高级分析.北京:机械工业出版社,2004
[30]韦未,李同春,牛志伟.拱坝拉应力控制指标的探讨.西北水力发电,2007年,第23卷,第2期,19-21
[31]李同春,章杭惠.改进的拱坝等效应力分析方法.河海大学学报(自然科学学版),2004年,第32卷,第1期,104-107
[32]章杭惠,李同春,温召旺.有限元内力法求解拱坝等效应力.水电站设计,2003年,第19卷,第2期,23-26
[33]武亮,叶文明,何仕华.基于ANSYS的拱坝等效应力分析.水利水电技术,2006年,第37卷,第9期,27-29
[34]张义,张燎军.有限元等效应力基于ANSYS的计算.水利科技与经济,2006年,第12卷,第4期,266-267
[35]傅作新.拱坝设计计算的几个问题.水电站设计,2002年,第18卷,第2期,7-11
[36]江见鲸,陆新征,叶列平.混凝土结构有限元分析.北京:清华大学出版社,2005
[37]黄文雄,许庆春,王德信.拱坝的非线性开裂有限元分析.河海大学学报,1994年,第22卷,第5期,100-103
[38]田斌,夏颂佑.高拱坝坝踵开裂非线性有限元分析.人民长江,1997年,第28卷,第5期,32-34
[39]孙林松,王德信,孙雯俊,高健.小湾拱坝开裂约束下体型优化设计研究.云南水力发电,1998年,第14卷,第3期,6-8
[40]陆新征,江见鲸.利用ANSYS Solid65单元分析复杂应力条件下的混凝土结构.
[41]SL 282-2003混凝土拱坝设计规范.北京:中国水利水电出版社,2003
[42]朱伯芳,董福品.高拱坝应力控制标准研究.水力发电,2001年,第8期,57-59
[43]李同春,陈会芳,章杭惠,王仁坤.网格尺寸对拱坝等效应力分析的影响.水利学报,2004年,第9期,83-87
[44]周岑,孙利民.钢筋混凝土结构弹塑性分析在ANSYS中的实现.
[45]董哲仁.钢筋混凝土非线性分析研究进展.水利水电技术,1998年,第29卷,第10期,10-13
[46]司炳君,孙治国,艾庆华.Solid65单元在混凝土结构有限元分析中的应用.
[47]Structures with Material Nonlinearities.ANSYS Inc,2007
[48]汪冬生,吴铁军.ANSYS中的钢筋混凝土单元.武汉理工大学学报,2004年,第28卷,第4期,526-529
[49]刘杰,王龙海,李向国,陈建国.基于薄层裂缝单元的钢筋混凝土结构非线性有限元分析.石家庄铁道学院学报,2007年,第20卷,第1期,19-23
[50]朱伯芳.拱坝的有限元等效应力及复杂应力下的强度储备.水利水电技术,2005年,第36卷,第1期,43-47
[51]王富耻,张朝晖.ANSYS 10.0有限元分析理论与工程应用.电子工业出版社,2006
[52]舒士霖主编.钢筋混凝土结构(第二版).杭州:浙江大学出版社,1996
[2] Wllam KJ,Warnke EP.Constitutive Models for the Triaxial Behavior of Concrete. IABSE Proceeding,1975,19:1-30
[3]Ottosen NS.A Failure Criterion for Concrete.ASCE,1977,103(EM4):527-535
[4] Darwin D,Pecknold D A.Nonlinear Biaxial Stress-Strain Law for Concrete. ASCE, 1977,103(EM2):229-241
[5] Sargin M.Stress-Strain Curves of Normal and Lightweight Concrete in Compression. Journal of ACI,1978,51(11)
[6] Elwi A A,Murray D W.A 3D Hypoelastic Concrete Constitutive Relationship.ASCE, 1979,105(EM4):623-641
[7] Ottosen N S.Constitutive Model for Short-Time Loading of Concrete.ASCE,1979,105 (EMD :127-141
[8] Kotsovos MD.A mathematical description of the strength properties of concrete under generalized stress.Magazine of Concrete Research,1979,31(128):151-158
[9] Kotsovos M D. A mathematical model of the deformational behavior of concrete under generalised stress based on fundamental materials properties. Materials and Structrues,1980,13(76):289-298
[10]Gerstle KH.Simple Formulation of Biaixial Concrete Behavior.ACI, 1982, 78(1): 62—68
[11] Gerstle KH.Simple Formulation of Triaxial Concrete Behavior. ACI, 1982, 78(5): 382- 387
[12] Chen WF.Plasticity in Reinforced Concrete.McGraw-Hill Book Company.New York, 1982
[13] Comite Euro-International du Beton.Bulletin D'information No.l56.Concrete under Multiaxial States of Stress Constitutive Equantions for Practical Design, Paris,1983
[14] Stankowski T,Gerstle KH. Simple Formulation of Concrete Behavior Under Multiaxial Load Histories ACI,1985,82(2):213-221
[15]朱伯芳.国际拱坝学术讨论会专题综述.混凝土坝技术.水利发电,1987,2,1988,8,49-52
[16]傅作新,钱向东.有限单元法在拱坝设计中的应用.河海大学学报(自然科学学版),1991年,第2期,8-15
[17]DL/T 5057-1996水工混凝土结构设计规范.北京:中国电力出版社,1997
[18]朱伯芳.大体积混凝土温度应力与温度控制.北京:中国电力出版社,1999
[19]李瓒,陈兴华,郑建波,王光伦.混凝土拱坝设计.北京:中国电力出版社,2000
[20]徐芝纶.弹性力学简明教程(第三版).高等教育出版社,2002,8,146-149
[21]GB 50010-2002混凝土结构设计规范.北京:中国建筑工业出版社,2002
[22]朱伯芳,高季章,陈祖,厉易生.拱坝设计与研究.北京:中国水利水电出版社,2002
[23]钱向东.基于有限元等效应力法的拱坝强度设计准则探讨.河海大学学报(自然科学学版),2003年,第31卷,第3期,318-320
[24]DL/T 5346-2006混凝土拱坝设计规范.北京:中国电力出版社,2006
[25]The ANSYS Parametric Design Language Guide.ANSYS Inc,2007
[26]博弈创作室.APDL参数化有限元分析技术及其应用实例.北京:中国水利水电出版社,2004
[27]The Elements Reference.ANSYS Inc,2007
[28]The Theory Reference for ANSYS and ANSYS Workbench.ANSYS Inc,2007
[29]陈晓霞主编.ANSYS 7.0高级分析.北京:机械工业出版社,2004
[30]韦未,李同春,牛志伟.拱坝拉应力控制指标的探讨.西北水力发电,2007年,第23卷,第2期,19-21
[31]李同春,章杭惠.改进的拱坝等效应力分析方法.河海大学学报(自然科学学版),2004年,第32卷,第1期,104-107
[32]章杭惠,李同春,温召旺.有限元内力法求解拱坝等效应力.水电站设计,2003年,第19卷,第2期,23-26
[33]武亮,叶文明,何仕华.基于ANSYS的拱坝等效应力分析.水利水电技术,2006年,第37卷,第9期,27-29
[34]张义,张燎军.有限元等效应力基于ANSYS的计算.水利科技与经济,2006年,第12卷,第4期,266-267
[35]傅作新.拱坝设计计算的几个问题.水电站设计,2002年,第18卷,第2期,7-11
[36]江见鲸,陆新征,叶列平.混凝土结构有限元分析.北京:清华大学出版社,2005
[37]黄文雄,许庆春,王德信.拱坝的非线性开裂有限元分析.河海大学学报,1994年,第22卷,第5期,100-103
[38]田斌,夏颂佑.高拱坝坝踵开裂非线性有限元分析.人民长江,1997年,第28卷,第5期,32-34
[39]孙林松,王德信,孙雯俊,高健.小湾拱坝开裂约束下体型优化设计研究.云南水力发电,1998年,第14卷,第3期,6-8
[40]陆新征,江见鲸.利用ANSYS Solid65单元分析复杂应力条件下的混凝土结构.
[41]SL 282-2003混凝土拱坝设计规范.北京:中国水利水电出版社,2003
[42]朱伯芳,董福品.高拱坝应力控制标准研究.水力发电,2001年,第8期,57-59
[43]李同春,陈会芳,章杭惠,王仁坤.网格尺寸对拱坝等效应力分析的影响.水利学报,2004年,第9期,83-87
[44]周岑,孙利民.钢筋混凝土结构弹塑性分析在ANSYS中的实现.
[45]董哲仁.钢筋混凝土非线性分析研究进展.水利水电技术,1998年,第29卷,第10期,10-13
[46]司炳君,孙治国,艾庆华.Solid65单元在混凝土结构有限元分析中的应用.
[47]Structures with Material Nonlinearities.ANSYS Inc,2007
[48]汪冬生,吴铁军.ANSYS中的钢筋混凝土单元.武汉理工大学学报,2004年,第28卷,第4期,526-529
[49]刘杰,王龙海,李向国,陈建国.基于薄层裂缝单元的钢筋混凝土结构非线性有限元分析.石家庄铁道学院学报,2007年,第20卷,第1期,19-23
[50]朱伯芳.拱坝的有限元等效应力及复杂应力下的强度储备.水利水电技术,2005年,第36卷,第1期,43-47
[51]王富耻,张朝晖.ANSYS 10.0有限元分析理论与工程应用.电子工业出版社,2006
[52]舒士霖主编.钢筋混凝土结构(第二版).杭州:浙江大学出版社,1996