含缺陷的电热体温度场的Green函数法分析
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摘要
大型水坝、桥梁、核电站安全壳等重大混凝土工程的安全可靠性、耐久性问题是涉及国家经济发展与国家安全的重大问题。而已有的混凝土大型结构和基础设施的损伤积累和灾变行为日趋突出。因此,对重大混凝土工程结构进行损伤监测与分析己成为重要研究课题之一。
本文以混凝土工程结构的损伤监测与分析为背景,通过建立碳纤维混凝土缺陷体的电热理论模型,运用Green(格林)函数法对相应模型内部温度场进行求解,研究与编程分析,得出了预期结果。并围绕该问题进行了相关的探索性的理论分析与研究。这将对混凝土中的损伤进行红外热成像无损检测技术提供一定的理论依据。主要成果与创新之处如下:
1、建立了含有内热源的热传导温度分析模型;
2、对含有椭圆形缺陷的电热体通过稳恒电场分析得到了焦耳热源的函数解析表达;
3、通过对含有椭圆形缺陷的电热体模型做近似处理,构造格林函数,并分析求解得到温度场的解析解;
4、对材料不同物性参数(主要是电阻率与导热系数)、缺陷几何尺寸的变化及通电时间的变化对温度造成的影响进行了分析研究,得出了相应的结论,这将对红外检测具有一定的指导意义。
本文研究涉及到力学、电学、混凝土材料学、传热学等多学科,其成果对提高混凝土红外无损检测的效率和精度,增进红外在混凝土结构无损检测中的应用具有重要的现实意义,而且对碳纤维混凝土在关键土木结构中应用,并实现损伤实时监测具有一定的指导意义。
This paper's research subject originates from the State Natural Sciences Foundation project—carbon fiber intelligence level many coupling mechanism and the field territory diagnosis (the project number: 10672128).
The safety , reliability and durability of large concrete porject, including large dam,bridge,containment vessel of nuclear power station and etc., are momentous problems relating to national economic development and national safety.However,the problems of accumulation damages and catastrophic behavior of the in being larger concrete structures and national infrastructure become very prominent. Therefore, study on monitoring and analyzing the damage of momentous concrete structures is one of the important research subjects in civil engineering.
This article take concrete structure's damage monitor and the analysis as the background, Through establishment carbon fiber concretes flaw body's electric heating theoretical model carries on the solution to the model interior temperature field, the research and the analysis with the green function method and drawn the corresponding conclusion, And revolved this question to carry on the related exploring theoretical analysis and the research.
The main achievement and the innovation place of are as follows:
(1) The heat conduction temperature anatomic model with internal heat source were established.
(2) Obtained the Joule heat generation's analytic expression of electric heating object with ellipse flaw through analysis steady permanent electric field theory.
(3) Adopting approximate processing, this paper presents an approximate method of obtaining the temperature field by Green's function, and gives the solution of electric heating object with ellipse flaw.
(4) Through analytical study different material natural parameter(mainly is the electronic resistivity and the thermal conductivity ) and different flaw size which have had the influence to the temperature change , and drawn the corresponding conclusion, which has the guiding sense to the infrared detection .
This article studies involves to mechanics, the electricity, the concretes material study, heat transfer theory and so on multi-disciplinary, its achievement to enhances the conventional concretes infrared non-destructive inspection the efficiency and the precision, promotes the infrared thermal imagery to have certain practical significance in the concrete structure non-destructive inspection application, moreover applies to the carbon fiber concretes in the essential construction structure, and realizes the damage real-time monitor to have the instruction function.)
本文以混凝土工程结构的损伤监测与分析为背景,通过建立碳纤维混凝土缺陷体的电热理论模型,运用Green(格林)函数法对相应模型内部温度场进行求解,研究与编程分析,得出了预期结果。并围绕该问题进行了相关的探索性的理论分析与研究。这将对混凝土中的损伤进行红外热成像无损检测技术提供一定的理论依据。主要成果与创新之处如下:
1、建立了含有内热源的热传导温度分析模型;
2、对含有椭圆形缺陷的电热体通过稳恒电场分析得到了焦耳热源的函数解析表达;
3、通过对含有椭圆形缺陷的电热体模型做近似处理,构造格林函数,并分析求解得到温度场的解析解;
4、对材料不同物性参数(主要是电阻率与导热系数)、缺陷几何尺寸的变化及通电时间的变化对温度造成的影响进行了分析研究,得出了相应的结论,这将对红外检测具有一定的指导意义。
本文研究涉及到力学、电学、混凝土材料学、传热学等多学科,其成果对提高混凝土红外无损检测的效率和精度,增进红外在混凝土结构无损检测中的应用具有重要的现实意义,而且对碳纤维混凝土在关键土木结构中应用,并实现损伤实时监测具有一定的指导意义。
This paper's research subject originates from the State Natural Sciences Foundation project—carbon fiber intelligence level many coupling mechanism and the field territory diagnosis (the project number: 10672128).
The safety , reliability and durability of large concrete porject, including large dam,bridge,containment vessel of nuclear power station and etc., are momentous problems relating to national economic development and national safety.However,the problems of accumulation damages and catastrophic behavior of the in being larger concrete structures and national infrastructure become very prominent. Therefore, study on monitoring and analyzing the damage of momentous concrete structures is one of the important research subjects in civil engineering.
This article take concrete structure's damage monitor and the analysis as the background, Through establishment carbon fiber concretes flaw body's electric heating theoretical model carries on the solution to the model interior temperature field, the research and the analysis with the green function method and drawn the corresponding conclusion, And revolved this question to carry on the related exploring theoretical analysis and the research.
The main achievement and the innovation place of are as follows:
(1) The heat conduction temperature anatomic model with internal heat source were established.
(2) Obtained the Joule heat generation's analytic expression of electric heating object with ellipse flaw through analysis steady permanent electric field theory.
(3) Adopting approximate processing, this paper presents an approximate method of obtaining the temperature field by Green's function, and gives the solution of electric heating object with ellipse flaw.
(4) Through analytical study different material natural parameter(mainly is the electronic resistivity and the thermal conductivity ) and different flaw size which have had the influence to the temperature change , and drawn the corresponding conclusion, which has the guiding sense to the infrared detection .
This article studies involves to mechanics, the electricity, the concretes material study, heat transfer theory and so on multi-disciplinary, its achievement to enhances the conventional concretes infrared non-destructive inspection the efficiency and the precision, promotes the infrared thermal imagery to have certain practical significance in the concrete structure non-destructive inspection application, moreover applies to the carbon fiber concretes in the essential construction structure, and realizes the damage real-time monitor to have the instruction function.)
引文
[1]宋显辉,潘志橼,王建军,等.碳纤维混凝土局部损伤检测的实验研究[J].武汉理工大学学报,2004,26(3):44-46
[2]欧进萍,大型桥梁应加强监测与控制,经济参考,2004,7(20).
[3]黄莉,李卓球,宋显辉,钱红兵.碳纤维混凝土中裂纹的红外热像检测方法与机理研究[J].实验力学,2003,18(3):403-408
[4]王厚亮,李建保,碳纤维树脂板内部缺陷的红外检测,红外技术2000.5.49-53
[5]孙格靓,王厚亮,炭纤维增强混凝土构件的内部缺陷红外热像技术检测,炭素技术,2000.04:47-53
[6]王厚亮,李建保,碳纤维树脂板内部缺陷的红外检测,红外技术2000.5.49-53
[7]Akbar Darabi Xavier Maldague.Neural network based defect detection and depth estimation in TNDE.NDT & E International.Vol.35.p.165-175,2002
[8]Toshimitsu Ishii Terurni Inagaki,Detection of internal defect in materials by infrared thermography and its numerical simulation,非破坏检查,2002.51(4):223-230
[9]Kenji Aono Satoru Oikawa Makoto Asakawa,Study on inner defects inspection of concrete structure by infrared thermography,非破坏检查,2003.6:338-344
[10]Takahide Sakagami,Shiro Kubo.Applications of pulse heating thermography and lock-in thermography to quantitative nondestructive evaluations.Infrared physics & Technology.2002.Vol.43.P.211-218
[11]唐祖全,李卓球,导电混凝土融雪化冰机理分析,混凝土,2001年07期
[12]唐祖全,李卓球,碳纤维导电混凝土电热升降温规律研究,华中科技大学学报(城市科学版),2002.9:7-9
[13]侯作富,李卓球,唐祖全,融雪化冰用碳纤维混凝土的导电性能研究,武汉理工大学学报,2002.8:32-35
[14]侯作富.融雪化冰用碳纤维导电混凝土的研制及应用研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2003
[15]唐祖全.碳纤维机敏混凝土路面机构融雪化冰性能研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2002
[16]Shui Zhonghe,Li Jizhong,Huang Fengping,Yan Depo,Study on the electrical properties of carbon fiber-cement composites,J.Wuhan University of Technology(Mater.Sci.Edition),1995,10(4):37-41.
[17]Xie Ping,Gu Ping,Beaudoin J J.Electrical Percolation Phenomena in Cement Composites Containing Conductive Fibres.Journal of Materials Science,1996,31(15):4093-4097
[18]侯作富,李卓球,王建军,裂纹对碳纤维水泥基复合材料性能的影响[J].华中科技大学学报,2007.6:46-48
[19]侯作富,李卓球,于建军,碳纤维水泥基复合材料电阻变化规律研究[J].武汉理工大学学报,2007.7:30-32
[20]黄莉,龙曦,李卓球,碳纤维混凝土电热红外无损检测的灵敏性分析[J].武汉理工大学学报,2005:
[21]Xuli Fu,D.D.L.Chung.Effects of Silica Fume,Later,Methylcellulose,and Carbon Fibers on the Thermal Conductivity and Specific Heat of Cement Paste.Cement and Concrete Research,1997,27(12):1799-1804.
[22]Yunsheng Xu,D.D.L.Chung.Effects of Sand Addition on the Specific Heat and Thermal Conductivity of Cement.Cement and Concrete Research,2000,30(1):59-61.
[23]Yunsheng Xu,D.D.L.Chung.Cement of High Specific Heat and High Thermal Conductivity,Obtained by Using Silane and Silica Fume as Admixtures.Cement and Concrete Research,2000,30(7):1175-1178
[24]侯作富.融雪化冰用碳纤维导电混凝土的研制及应用研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2003
[25]唐祖全.碳纤维机敏混凝土路面机构融雪化冰性能研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2002
[26]杨强生 浦保荣 高等传热学[M]上海:上海交通大学出版社,2001.7
[27]姚端正 数学物理方法学习指导[M]北京:科学出版社,2001.4
[28]张洪济 热传导[M]高等教育出版社,1992
[29]徐永斌,何国瑜.工程电磁场基础.北京:北京航空航天大学出版社,1992
[30]邱景辉,李在清,王宏,王欣.电磁场与电磁波.哈尔滨:哈尔滨工业大学出版社,2001
[31]陈乃云,魏东北,李一枚.电磁场与电磁波.北京:中国铁道出版社出版社,2001
[32]刘晓利,矩形绕流问题的分析解,弹道学报,1999.12:45-49
[33]刘晓利,三角形绕流问题的分析解,南京理工大学学报,1999.12:499-502
[34]郑建华,复分析,北京:清华大学出版社,2000.3
[35]张洪济,热传导[M]高等教育出版社,1992
[36]张雄.机敏混凝土内热源红外检测及其机理研究:[硕士学位论文].武汉:武汉理工大学工程结构与力学系,2004
[37]俞昌铭(主译)热传导[M]北京:高等教育出版社,1984.7
[38] Beck J V. Green's function solution for transient heat conduction problems. International Journal of Heat and Mass Transfer, 1984, V27,1235-1244
[39] Beck J V, Cole K D, Haji-Sheikh A, Litkouhi B, Heat Conduction Using Green's Functions, Hemisphere, Washington, DC, 1992
[40] Stakgold I, Green's Functions and Boundary Value Problems, Willey-Interscience, New York, 1979
[41] Kevin D Cole, David H Y Yen. Green's functions, temperature and heat flux in the rectangle. International journal of heat and mass transfer. 2001.vol44: 3883-3894
[42] Conde J C, Lusquinos F, Gonzalez P. Temperature distribution in a material heated by laser radiation: modeling and application. Surface engineering, Surface instrumentation & Vacuum technology. 2002.vacuum64: 359-366
[43] Hyperbolic type transport equations, Physica A Statistical and Theoretical Physics, 1995.Vol. 220. P.165-172
[44] Marcin Janicki, Gilbert De Mey, Andrzej Napieralski. Application of Green's functions for analysis of transient thermal states in electronic circuits, Microelectronics Journal, 2002.Vol. 33, P733-738
[45] Barletta A and Zanchini E, Hyperbolic heat conduction and thermal resonances in a cylindrical solid carrying a steady-periodic electric field, International Journal of Heat and Mass Transfer, 1996 .Vol.39.P.1307-1315
[46] Zhi-gang Feng, efstathios, e.michaelides. The use of modified Green's functions in unsteady heat transfer. 1997.vol.40.No.12: 2997-3002
[2]欧进萍,大型桥梁应加强监测与控制,经济参考,2004,7(20).
[3]黄莉,李卓球,宋显辉,钱红兵.碳纤维混凝土中裂纹的红外热像检测方法与机理研究[J].实验力学,2003,18(3):403-408
[4]王厚亮,李建保,碳纤维树脂板内部缺陷的红外检测,红外技术2000.5.49-53
[5]孙格靓,王厚亮,炭纤维增强混凝土构件的内部缺陷红外热像技术检测,炭素技术,2000.04:47-53
[6]王厚亮,李建保,碳纤维树脂板内部缺陷的红外检测,红外技术2000.5.49-53
[7]Akbar Darabi Xavier Maldague.Neural network based defect detection and depth estimation in TNDE.NDT & E International.Vol.35.p.165-175,2002
[8]Toshimitsu Ishii Terurni Inagaki,Detection of internal defect in materials by infrared thermography and its numerical simulation,非破坏检查,2002.51(4):223-230
[9]Kenji Aono Satoru Oikawa Makoto Asakawa,Study on inner defects inspection of concrete structure by infrared thermography,非破坏检查,2003.6:338-344
[10]Takahide Sakagami,Shiro Kubo.Applications of pulse heating thermography and lock-in thermography to quantitative nondestructive evaluations.Infrared physics & Technology.2002.Vol.43.P.211-218
[11]唐祖全,李卓球,导电混凝土融雪化冰机理分析,混凝土,2001年07期
[12]唐祖全,李卓球,碳纤维导电混凝土电热升降温规律研究,华中科技大学学报(城市科学版),2002.9:7-9
[13]侯作富,李卓球,唐祖全,融雪化冰用碳纤维混凝土的导电性能研究,武汉理工大学学报,2002.8:32-35
[14]侯作富.融雪化冰用碳纤维导电混凝土的研制及应用研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2003
[15]唐祖全.碳纤维机敏混凝土路面机构融雪化冰性能研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2002
[16]Shui Zhonghe,Li Jizhong,Huang Fengping,Yan Depo,Study on the electrical properties of carbon fiber-cement composites,J.Wuhan University of Technology(Mater.Sci.Edition),1995,10(4):37-41.
[17]Xie Ping,Gu Ping,Beaudoin J J.Electrical Percolation Phenomena in Cement Composites Containing Conductive Fibres.Journal of Materials Science,1996,31(15):4093-4097
[18]侯作富,李卓球,王建军,裂纹对碳纤维水泥基复合材料性能的影响[J].华中科技大学学报,2007.6:46-48
[19]侯作富,李卓球,于建军,碳纤维水泥基复合材料电阻变化规律研究[J].武汉理工大学学报,2007.7:30-32
[20]黄莉,龙曦,李卓球,碳纤维混凝土电热红外无损检测的灵敏性分析[J].武汉理工大学学报,2005:
[21]Xuli Fu,D.D.L.Chung.Effects of Silica Fume,Later,Methylcellulose,and Carbon Fibers on the Thermal Conductivity and Specific Heat of Cement Paste.Cement and Concrete Research,1997,27(12):1799-1804.
[22]Yunsheng Xu,D.D.L.Chung.Effects of Sand Addition on the Specific Heat and Thermal Conductivity of Cement.Cement and Concrete Research,2000,30(1):59-61.
[23]Yunsheng Xu,D.D.L.Chung.Cement of High Specific Heat and High Thermal Conductivity,Obtained by Using Silane and Silica Fume as Admixtures.Cement and Concrete Research,2000,30(7):1175-1178
[24]侯作富.融雪化冰用碳纤维导电混凝土的研制及应用研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2003
[25]唐祖全.碳纤维机敏混凝土路面机构融雪化冰性能研究:[博士学位论文].武汉:武汉理工大学工程结构与力学系,2002
[26]杨强生 浦保荣 高等传热学[M]上海:上海交通大学出版社,2001.7
[27]姚端正 数学物理方法学习指导[M]北京:科学出版社,2001.4
[28]张洪济 热传导[M]高等教育出版社,1992
[29]徐永斌,何国瑜.工程电磁场基础.北京:北京航空航天大学出版社,1992
[30]邱景辉,李在清,王宏,王欣.电磁场与电磁波.哈尔滨:哈尔滨工业大学出版社,2001
[31]陈乃云,魏东北,李一枚.电磁场与电磁波.北京:中国铁道出版社出版社,2001
[32]刘晓利,矩形绕流问题的分析解,弹道学报,1999.12:45-49
[33]刘晓利,三角形绕流问题的分析解,南京理工大学学报,1999.12:499-502
[34]郑建华,复分析,北京:清华大学出版社,2000.3
[35]张洪济,热传导[M]高等教育出版社,1992
[36]张雄.机敏混凝土内热源红外检测及其机理研究:[硕士学位论文].武汉:武汉理工大学工程结构与力学系,2004
[37]俞昌铭(主译)热传导[M]北京:高等教育出版社,1984.7
[38] Beck J V. Green's function solution for transient heat conduction problems. International Journal of Heat and Mass Transfer, 1984, V27,1235-1244
[39] Beck J V, Cole K D, Haji-Sheikh A, Litkouhi B, Heat Conduction Using Green's Functions, Hemisphere, Washington, DC, 1992
[40] Stakgold I, Green's Functions and Boundary Value Problems, Willey-Interscience, New York, 1979
[41] Kevin D Cole, David H Y Yen. Green's functions, temperature and heat flux in the rectangle. International journal of heat and mass transfer. 2001.vol44: 3883-3894
[42] Conde J C, Lusquinos F, Gonzalez P. Temperature distribution in a material heated by laser radiation: modeling and application. Surface engineering, Surface instrumentation & Vacuum technology. 2002.vacuum64: 359-366
[43] Hyperbolic type transport equations, Physica A Statistical and Theoretical Physics, 1995.Vol. 220. P.165-172
[44] Marcin Janicki, Gilbert De Mey, Andrzej Napieralski. Application of Green's functions for analysis of transient thermal states in electronic circuits, Microelectronics Journal, 2002.Vol. 33, P733-738
[45] Barletta A and Zanchini E, Hyperbolic heat conduction and thermal resonances in a cylindrical solid carrying a steady-periodic electric field, International Journal of Heat and Mass Transfer, 1996 .Vol.39.P.1307-1315
[46] Zhi-gang Feng, efstathios, e.michaelides. The use of modified Green's functions in unsteady heat transfer. 1997.vol.40.No.12: 2997-3002