均布内压等厚球壳局部塑性失稳研究
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摘要
球形容器(简称球罐)是存储和运输各种气体、液化气体、液体的压力容器，至今已广泛应用于石油、化工、石化、冶金、轻工、航天、核能、城建等部门。而它们在制造和使用过程中难免要产生缺陷，准确有效的评估这些缺陷对压力容器承载能力的影响，做到既保证压力容器安全，又要更大程度的挖掘其潜力，对于安全生产及提高经济效益有着重要的意义。
相关的力学问题是成功设计重要部分，本文旨在讨论球壳的塑性极限载荷分析问题，为压力容器在设计和使用的安全性、可靠性提供理论保证。本文首先采用有限元分析软件比较了几种典型工况薄球壳的弹塑性解，其次引入了实心圆轴扭转测定本构关系的概念和方法，并运用虚功原理来推倒大变形下薄球壳的极限载荷，通过两种方法的分析比较，为压力容器的设计和使用提供理论依据，对于指导实际的工程有很大的意义。
本文所处理的模型属于既有材料非线性，又有几何非线性。本文研究了无缺陷不同厚度球壳的三种工况和相同厚度有缺陷球壳的三种工况，再与虚功理论算法进行比较，根据塑性失稳点产生的特点，找出压力容器在加载过程中的局部塑性失稳点，由应变场、应力场以及径向位移对其加以监控，从而保证了压力容器在使用过程中的安全。
球壳在工程中有着广泛的应用，但对于球壳在内压很大时产生大变形的理论研究相对不足。本文通过有限元软件对球壳在发生大变形时进行了模拟，为球壳的设计提供了一些参考。
The spherical tank is a pressure vessel used for saving and transporting kinds of gas, liquefied gas and liquid. It has been widely used in such fields as petroleum, chemical industry, petrifaction, metallurgy, light industry, astronautics, nuclear power industry, and so on. Unfortunately, some defects will be encountered unavoidably when being manufactured and used. How to evaluate the impact of these defects on bearing capacity is a challenging problem. This is important for the security, enhancing the economic efficiency and excavating the potential bearing ability.
The corr(?)lated mechanics is the key for designing spherical tank successfully. This work aimed to analyze the plastic limit load of the spherical shell and provide some theoretical introductions for the designing of the spherical tank. Herein, various models of spherical shell with different thickness, different flaw and different loads were analyzed using finite element method. Moreover, the concept and method testing of stress-strain relation through twisting solid spherical shaft were introduced in this work. In succession, the virtual work principle was applied to deduce the limit load of the thin spherical shell under large deformation. These results were significant for the designing and using of the spherical tank, and also for introducing actual projects.
The problems here were geometrical nonlinear and material nonlinear questions. Different models with or without defects were analyzed and compared under three kinds of loads. These results were compared with those obtained though virtual work principle. The point accounting for the partial plastic instability was marked. This implied that we can guarantee the security and stability of the spherical tank through monitoring the stress or strain distribution and radial displacement.
The spherical shell has been widely used in engineering projects. But less fundamental studies devised theoretically on the large deformation of spherical
相关的力学问题是成功设计重要部分，本文旨在讨论球壳的塑性极限载荷分析问题，为压力容器在设计和使用的安全性、可靠性提供理论保证。本文首先采用有限元分析软件比较了几种典型工况薄球壳的弹塑性解，其次引入了实心圆轴扭转测定本构关系的概念和方法，并运用虚功原理来推倒大变形下薄球壳的极限载荷，通过两种方法的分析比较，为压力容器的设计和使用提供理论依据，对于指导实际的工程有很大的意义。
本文所处理的模型属于既有材料非线性，又有几何非线性。本文研究了无缺陷不同厚度球壳的三种工况和相同厚度有缺陷球壳的三种工况，再与虚功理论算法进行比较，根据塑性失稳点产生的特点，找出压力容器在加载过程中的局部塑性失稳点，由应变场、应力场以及径向位移对其加以监控，从而保证了压力容器在使用过程中的安全。
球壳在工程中有着广泛的应用，但对于球壳在内压很大时产生大变形的理论研究相对不足。本文通过有限元软件对球壳在发生大变形时进行了模拟，为球壳的设计提供了一些参考。
The spherical tank is a pressure vessel used for saving and transporting kinds of gas, liquefied gas and liquid. It has been widely used in such fields as petroleum, chemical industry, petrifaction, metallurgy, light industry, astronautics, nuclear power industry, and so on. Unfortunately, some defects will be encountered unavoidably when being manufactured and used. How to evaluate the impact of these defects on bearing capacity is a challenging problem. This is important for the security, enhancing the economic efficiency and excavating the potential bearing ability.
The corr(?)lated mechanics is the key for designing spherical tank successfully. This work aimed to analyze the plastic limit load of the spherical shell and provide some theoretical introductions for the designing of the spherical tank. Herein, various models of spherical shell with different thickness, different flaw and different loads were analyzed using finite element method. Moreover, the concept and method testing of stress-strain relation through twisting solid spherical shaft were introduced in this work. In succession, the virtual work principle was applied to deduce the limit load of the thin spherical shell under large deformation. These results were significant for the designing and using of the spherical tank, and also for introducing actual projects.
The problems here were geometrical nonlinear and material nonlinear questions. Different models with or without defects were analyzed and compared under three kinds of loads. These results were compared with those obtained though virtual work principle. The point accounting for the partial plastic instability was marked. This implied that we can guarantee the security and stability of the spherical tank through monitoring the stress or strain distribution and radial displacement.
The spherical shell has been widely used in engineering projects. But less fundamental studies devised theoretically on the large deformation of spherical
引文
[1] 韩伟基．中国球形容器建设回顾与展望．石油工程建设．1999．2．第1期
[2] 韩伟基．中国球形容器建设回顾与展望(续1)．石油工程建设．1999．4．第2期
[3] 邢静忠，柳春图．压力容器和管道随机局部减薄的有限元分析．工程力学增刊．2003：403-406页
[4] 黄涛，李国琛，洪友士，熊电元．材料分叉的数值分析．力学学报．1996．3．第2期
[5] 闫琨，何陵辉，刘人怀．表面应力引起的弹性薄膜形状分叉．应用数学和力学．2003．10．第24卷．第10期
[6] 王晓春．非线性有限元分析与分叉问题数值方法．西南交通大学学报．Vol．31 no3 June 1996
[7] 郑哲敏，周恒，张涵信，黄克智，白以龙．21世纪初的力学发展趋势．力学进展．1995．25(4)．433-449页
[8] 马宏伟，吴斌．弹性动力学及其数值方法．北京：中国建材工业出版社．2000：50-109页
[9] 徐秉业．弹塑性力学及其应用．北京：机械工业出版社．1984：53-102页
[10] 雷晋干，马亚南．分歧问题的逼近理论与数值方法．武汉：武汉大学出版社．1998：1-20页
[11] 朱正佑，程昌钧．分支问题的数值计算方法．兰州：兰州大学出版社．1989：1-32页
[12] [美]GR．布查南著，董文军，谢伟松译．有限元分析．北京：科学出版社．2002：1～110页
[13] Neale K W. A general variational teorem for the rate problem in elastic-plasticity. Int. J. Solid and Structures. Vol.8, 1972: 865-876P
[14] Neale K W. On the application of a variational pricinple for large-displacement elastic-plastic problems. Proc. IUTAM Symp. On Variational Method in the Mechanics of solids, S. Nemat-Nassered,??pergamon Press. 1978: 374-377P
[15] Storen S and Rice J R. Localized neching in thin sheets, J Mech. Phys. Solids. Vol.23, 1975: 421-441P
[16] Needleman A and Tvergaard V. Necking of bioxilly stretched elastic-plastic circular plates, J Mech. Phys. Solids. Vol.25, 1977: 159-183P
[17] 殷有权．固体力学非线性有限元引论．北京：北京大学出版社，清华大学出版社．1987
[18] Hutchinson J W. "Numerical strain analysis of elastic-plastic solids and structure[J] " ASME. 1973: 17-29P
[19] [美]S Timoshenko J. Gere Mechanics of materials[M], Van Nostrand Reinhold Company. 1972
[20] Christoffersen J and Huchinson J W. A class of phenomenological corner theories of plasticity, J Mech Phys Solids. Vol.27, 1979: 465-487P
[21] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part Ⅰ-yield criteeria and flow rules for porous ductile media, J. Eng. Meter. Tech. Vol.99, 1977: 2-15P
[22] Lemaitre J A. Continuous damage mechanics Model for ductile fracture, J. Enging. Mat.Tech. Vol. 107, 1985: 83-89P
[23] Lemaitre J.. How use damage mechanics, S. M. I, R. T. 7, Principal divison Leture, Chicago, 1983, Nucl. Eng. Des, 4th Special Issue on SMIRT-7. Vol. 80, No.2. june. 1984
[24] Chaboche j L. SurLutilisation des variables detat interne pour la descriptionclu comprotement visco-plastique, et dela rupture par endommagement, Commuication Prosentee au Symposium Franco-plolanais de Pheologie et de Mecanique, Cracovie, 27. Juino2 juillet. 1977
[25] 王勖成．有限单元法．北京：清华大学出版社．2003：1-120页
[26] 王焕定，王伟．有限单元法教程．哈尔滨：哈尔滨工业大学出版社．2003[27] [日]山田嘉昭．非线性有限元法基础．北京：清华大学出版社．1988
[28] Bellini P X Chulya A. An Improved Automatic Incremental Algorithm for the Efficient Solution of Nonlinear Finite Element Equations. Computers & Structures. 1987, 27: 625～630P
[29] Shi J. Computing Critical Points and Secondary Paths in Nonlinear Structural Stability Analysis by the Finite Element Method. Computers & Structures. 1996, 58: 203～220P
[30] Chan S L. A Nonlinear Numerical Method for Accurate Determination of Limit and Bifuration Points. Int. J. Num. Meth. Eng. 1993, 36: 2779～2790P
[31] 杨桂通．弹塑性力学．北京：人民教育出版社．198C
[32] Zhong Z H. Finite Element Procedures for Contact-Impact problems. Oxford University Press. 1993
[33] 黄克智，薛明德，陆明万．张量分析．北京：清华大学出版社．2003
[34] 老亮．中国古代材料力学史．国防科技大学出版社．1991
[35] 黄淑容，彭向和，秦义．实心试件大变形扭转实验的有限元模拟．重庆大学学报．2003．9．第9期
[36] 何蕴增，潘信吉．一种通过扭转试验确定塑性材料真实应力应变关系的方法[J]．船工科技．1987(4)：40-47页
[37] 何蕴增，邹广平，潘信吉．扭转冷作硬化的试验研究及分析[J]．实验力学．1994(3)：262-269页
[38] 陆明万，罗学富．弹性理论基础(第2版)．清华大学出版社，施普林格出版社．2001
[39] 何蕴增，邹广平．实心圆轴扭转测定本构关系的概念和方法．2003(9)：426-432页
[40] 周道祥，徐佩珠．压力容器凹坑应力的数值分析及工程算法[C]．压力容器．Vol8，no5，1991：34～38页
[41] [美]Saeed Moaveni著，王菘，董春敏，金云平等译．有限元分析——ANSYS理论与应用(第2版)．电子工业出版社．2005[42] A C U fural, Stresses in Plates and Shells, McGraw-Hill, New York. 1981
[43] 钟志华，李光耀．薄板冲压成型过程的计算机仿真和应用．北京．北京理工大学出版社．1998：1-50页
[44] 铁木辛柯，古地尔，徐芝纶，吴永镇译．弹性理论．北京：人民教育出版社．1964：1-70页
[45] 杜平安．结构有限元分析建模方法．北京：机械工业出版社．1998
[46] 许尚贤．机械结构中的有限元法．北京：高等教育出版社．1992
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[63] 龚曙光．ANSYS软件在应力分析设计中的应用．计算机辅助设计与制造．2001年第7期
[2] 韩伟基．中国球形容器建设回顾与展望(续1)．石油工程建设．1999．4．第2期
[3] 邢静忠，柳春图．压力容器和管道随机局部减薄的有限元分析．工程力学增刊．2003：403-406页
[4] 黄涛，李国琛，洪友士，熊电元．材料分叉的数值分析．力学学报．1996．3．第2期
[5] 闫琨，何陵辉，刘人怀．表面应力引起的弹性薄膜形状分叉．应用数学和力学．2003．10．第24卷．第10期
[6] 王晓春．非线性有限元分析与分叉问题数值方法．西南交通大学学报．Vol．31 no3 June 1996
[7] 郑哲敏，周恒，张涵信，黄克智，白以龙．21世纪初的力学发展趋势．力学进展．1995．25(4)．433-449页
[8] 马宏伟，吴斌．弹性动力学及其数值方法．北京：中国建材工业出版社．2000：50-109页
[9] 徐秉业．弹塑性力学及其应用．北京：机械工业出版社．1984：53-102页
[10] 雷晋干，马亚南．分歧问题的逼近理论与数值方法．武汉：武汉大学出版社．1998：1-20页
[11] 朱正佑，程昌钧．分支问题的数值计算方法．兰州：兰州大学出版社．1989：1-32页
[12] [美]GR．布查南著，董文军，谢伟松译．有限元分析．北京：科学出版社．2002：1～110页
[13] Neale K W. A general variational teorem for the rate problem in elastic-plasticity. Int. J. Solid and Structures. Vol.8, 1972: 865-876P
[14] Neale K W. On the application of a variational pricinple for large-displacement elastic-plastic problems. Proc. IUTAM Symp. On Variational Method in the Mechanics of solids, S. Nemat-Nassered,??pergamon Press. 1978: 374-377P
[15] Storen S and Rice J R. Localized neching in thin sheets, J Mech. Phys. Solids. Vol.23, 1975: 421-441P
[16] Needleman A and Tvergaard V. Necking of bioxilly stretched elastic-plastic circular plates, J Mech. Phys. Solids. Vol.25, 1977: 159-183P
[17] 殷有权．固体力学非线性有限元引论．北京：北京大学出版社，清华大学出版社．1987
[18] Hutchinson J W. "Numerical strain analysis of elastic-plastic solids and structure[J] " ASME. 1973: 17-29P
[19] [美]S Timoshenko J. Gere Mechanics of materials[M], Van Nostrand Reinhold Company. 1972
[20] Christoffersen J and Huchinson J W. A class of phenomenological corner theories of plasticity, J Mech Phys Solids. Vol.27, 1979: 465-487P
[21] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part Ⅰ-yield criteeria and flow rules for porous ductile media, J. Eng. Meter. Tech. Vol.99, 1977: 2-15P
[22] Lemaitre J A. Continuous damage mechanics Model for ductile fracture, J. Enging. Mat.Tech. Vol. 107, 1985: 83-89P
[23] Lemaitre J.. How use damage mechanics, S. M. I, R. T. 7, Principal divison Leture, Chicago, 1983, Nucl. Eng. Des, 4th Special Issue on SMIRT-7. Vol. 80, No.2. june. 1984
[24] Chaboche j L. SurLutilisation des variables detat interne pour la descriptionclu comprotement visco-plastique, et dela rupture par endommagement, Commuication Prosentee au Symposium Franco-plolanais de Pheologie et de Mecanique, Cracovie, 27. Juino2 juillet. 1977
[25] 王勖成．有限单元法．北京：清华大学出版社．2003：1-120页
[26] 王焕定，王伟．有限单元法教程．哈尔滨：哈尔滨工业大学出版社．2003[27] [日]山田嘉昭．非线性有限元法基础．北京：清华大学出版社．1988
[28] Bellini P X Chulya A. An Improved Automatic Incremental Algorithm for the Efficient Solution of Nonlinear Finite Element Equations. Computers & Structures. 1987, 27: 625～630P
[29] Shi J. Computing Critical Points and Secondary Paths in Nonlinear Structural Stability Analysis by the Finite Element Method. Computers & Structures. 1996, 58: 203～220P
[30] Chan S L. A Nonlinear Numerical Method for Accurate Determination of Limit and Bifuration Points. Int. J. Num. Meth. Eng. 1993, 36: 2779～2790P
[31] 杨桂通．弹塑性力学．北京：人民教育出版社．198C
[32] Zhong Z H. Finite Element Procedures for Contact-Impact problems. Oxford University Press. 1993
[33] 黄克智，薛明德，陆明万．张量分析．北京：清华大学出版社．2003
[34] 老亮．中国古代材料力学史．国防科技大学出版社．1991
[35] 黄淑容，彭向和，秦义．实心试件大变形扭转实验的有限元模拟．重庆大学学报．2003．9．第9期
[36] 何蕴增，潘信吉．一种通过扭转试验确定塑性材料真实应力应变关系的方法[J]．船工科技．1987(4)：40-47页
[37] 何蕴增，邹广平，潘信吉．扭转冷作硬化的试验研究及分析[J]．实验力学．1994(3)：262-269页
[38] 陆明万，罗学富．弹性理论基础(第2版)．清华大学出版社，施普林格出版社．2001
[39] 何蕴增，邹广平．实心圆轴扭转测定本构关系的概念和方法．2003(9)：426-432页
[40] 周道祥，徐佩珠．压力容器凹坑应力的数值分析及工程算法[C]．压力容器．Vol8，no5，1991：34～38页
[41] [美]Saeed Moaveni著，王菘，董春敏，金云平等译．有限元分析——ANSYS理论与应用(第2版)．电子工业出版社．2005[42] A C U fural, Stresses in Plates and Shells, McGraw-Hill, New York. 1981
[43] 钟志华，李光耀．薄板冲压成型过程的计算机仿真和应用．北京．北京理工大学出版社．1998：1-50页
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