考虑损伤的钢筋混凝土结构面向对象有限元分析
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摘要
钢筋混凝土结构是一种重要的工程结构。传统的钢筋混凝土有限元程序是采用面向过程的方法进行程序编制，由于数据与操作函数的分离，导致可扩展性差，难于维护等缺点。本文用面向对象的方法编制了钢筋混凝土有限元计算程序，并考虑弹塑性和损伤对结构的影响。
论文共分为六章，第一章介绍了论文课题提出的背景以及研究意义和面向对象技术应用于有限元的发展过程。
第二章主要介绍了非线性有限元分析的基本理论，建立了有限元弹塑性损伤本构模型。
第三章详细地讨论了面向对象有限元静力分析程序的设计与实现，利用面向对象的编程思想，结合有限元程序设计的特点和要求，编制了较为完整的结构有限元分析计算程序。充分利用了面向对象的特点，结合有限元的基本概念，将钢筋混凝土有限元的核心概念抽象成节点类、单元类、材料类、荷载类、矩阵类等基类以及混凝土材料类、钢筋材料类、四节点等参单元类等应用类。综合结构类负责管理和控制整个结构的计算分析过程。程序可以进行静力线性分析和静力弹塑性分析，还在弹塑性的基础上考虑了混凝土的损伤因素，进行静力弹塑性损伤分析，此外还分析了面向对象程序的消息传递机制，有限元程序的具体分析过程就是定义一系列的类对象并通过消息传递来解决特定问题的过程，程序还实现了部分后处理功能。包括结构形式图、结构剖分网格图、结构变形图、结构主应力图以及振型图等。
第四章利用层次设计的思想，实现了面向对象有限元分析动力程序部分，可以进行结构的模态分析以及动力响应分析，并介绍了有限元类库的发展和完善。
第五章结合具体算例进行了有限元分析计算，本文结果表明，面向对象的钢筋混凝土有限元程序调试周期短，代码重用率高，易于扩展与维护，便于实现良好的前后处理功能。本文的研究对钢筋混凝土非线性有限元分析作了有益的工作。
第六章是总结了结论与展望。
The reinforced concrete structure plays a great role in engineering. The traditional finite element program is oriented process, resulting in some disadvantage such as bad expansibility and difficult maintainability. Utilizing the method of object-oriented programming(OOP), this thesis has implemented the finite element calculation of reinforced concrete structure, considering the effects of elastic-plasticity and damage.
This thesis can be divided into six chapters. The first chapter introduces the background and significance of the research. In addition, the development history of OOP applied in FEM is also mentioned.
The basic theory of nonlinear finite element analysis is mainly introduced in the second chapter, at the same time, the finite element elastic-plasticity constitutive model considering damage is proposed in this part.
In the third chapter, the finite element static analysis is discussed and the program is designed and implemented. Based on the thinking of OOP, the author implements the finite element analysis program. Fully using the characters of OOP, combined with the basic notions of finite element method, the kernel notions of reinforced concrete finite element are abstracted into various basis classes, such as node class, element class, material class, load class, matrix class, and various application classes. The program can deal with static linear analysis and static elastic-plasticity analysis. Considering the damage factors of concrete, static elastic-plasticity damage analysis can also be carried out. Furthermore, parts of post-process are also implemented, including structure shape map, discrete structure mesh map, deformation map of structure, the first and third principle stress and vibration map.
Based upon the thinking of layer design, the forth chapter discusses and implements the dynamic analysis program of object oriented finite element which can be used to carry out the modal analysis and dynamic response analysis. The development and consummation of finite element class library is referred in the part.
In the fifth chapter, examples are utilized to verify the finite element program. The results show that the reinforced concrete finite element program based upon OOP has the advantages: short cycle in debugging, high recycle of codes, easy to expand and maintain, easy to realize excellent pre- and post-process.
At last, the conclusion and prospect are discussed.
论文共分为六章，第一章介绍了论文课题提出的背景以及研究意义和面向对象技术应用于有限元的发展过程。
第二章主要介绍了非线性有限元分析的基本理论，建立了有限元弹塑性损伤本构模型。
第三章详细地讨论了面向对象有限元静力分析程序的设计与实现，利用面向对象的编程思想，结合有限元程序设计的特点和要求，编制了较为完整的结构有限元分析计算程序。充分利用了面向对象的特点，结合有限元的基本概念，将钢筋混凝土有限元的核心概念抽象成节点类、单元类、材料类、荷载类、矩阵类等基类以及混凝土材料类、钢筋材料类、四节点等参单元类等应用类。综合结构类负责管理和控制整个结构的计算分析过程。程序可以进行静力线性分析和静力弹塑性分析，还在弹塑性的基础上考虑了混凝土的损伤因素，进行静力弹塑性损伤分析，此外还分析了面向对象程序的消息传递机制，有限元程序的具体分析过程就是定义一系列的类对象并通过消息传递来解决特定问题的过程，程序还实现了部分后处理功能。包括结构形式图、结构剖分网格图、结构变形图、结构主应力图以及振型图等。
第四章利用层次设计的思想，实现了面向对象有限元分析动力程序部分，可以进行结构的模态分析以及动力响应分析，并介绍了有限元类库的发展和完善。
第五章结合具体算例进行了有限元分析计算，本文结果表明，面向对象的钢筋混凝土有限元程序调试周期短，代码重用率高，易于扩展与维护，便于实现良好的前后处理功能。本文的研究对钢筋混凝土非线性有限元分析作了有益的工作。
第六章是总结了结论与展望。
The reinforced concrete structure plays a great role in engineering. The traditional finite element program is oriented process, resulting in some disadvantage such as bad expansibility and difficult maintainability. Utilizing the method of object-oriented programming(OOP), this thesis has implemented the finite element calculation of reinforced concrete structure, considering the effects of elastic-plasticity and damage.
This thesis can be divided into six chapters. The first chapter introduces the background and significance of the research. In addition, the development history of OOP applied in FEM is also mentioned.
The basic theory of nonlinear finite element analysis is mainly introduced in the second chapter, at the same time, the finite element elastic-plasticity constitutive model considering damage is proposed in this part.
In the third chapter, the finite element static analysis is discussed and the program is designed and implemented. Based on the thinking of OOP, the author implements the finite element analysis program. Fully using the characters of OOP, combined with the basic notions of finite element method, the kernel notions of reinforced concrete finite element are abstracted into various basis classes, such as node class, element class, material class, load class, matrix class, and various application classes. The program can deal with static linear analysis and static elastic-plasticity analysis. Considering the damage factors of concrete, static elastic-plasticity damage analysis can also be carried out. Furthermore, parts of post-process are also implemented, including structure shape map, discrete structure mesh map, deformation map of structure, the first and third principle stress and vibration map.
Based upon the thinking of layer design, the forth chapter discusses and implements the dynamic analysis program of object oriented finite element which can be used to carry out the modal analysis and dynamic response analysis. The development and consummation of finite element class library is referred in the part.
In the fifth chapter, examples are utilized to verify the finite element program. The results show that the reinforced concrete finite element program based upon OOP has the advantages: short cycle in debugging, high recycle of codes, easy to expand and maintain, easy to realize excellent pre- and post-process.
At last, the conclusion and prospect are discussed.
引文
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[2] 袁志芬．钢筋混凝土结构非线性有限元的分析．[西北农林科技大学硕士学位论文]，2001，3
[3] 宋玉普，赵国藩．钢筋混凝土结构分析中的有限单元法．大连理工大学出版社，1994
[4] 江见鲸．钢筋混凝土结构非线性有限元分析．陕西科学技术出版社，1994
[5] 沈聚敏，王传志，江见鲸．钢筋混凝土有限元与板壳极限分析．清华大学出版社，1993
[6] 吕西林，金国芳，吴晓涵．钢筋混凝土结构非线性有限元理论与应用．同济大学出版社，1997
[7] 封伯昊，张立翔，李桂青．混凝土损伤研究综述．昆明理工大学学报，2001，26(3)：21-30
[8] 何明，符晓陵，徐道远．混凝土的损伤模型．福州大学学报，1994，22(4)：109-114
[9] 余天庆．混凝土的分段线性损伤模型．岩石、混凝土断裂与强度，1985，2：14-16
[10] 钱济成，周建方．混凝土的两种损伤模型及其应用．和河海大学学报，1989，3：40-47
[11] K.E.Loland. Continuous damage model for load-response estimation of concrete. Cement and Concrete Research, 1998 (10): 392-402
[12] 余天庆．损伤理论及其在混凝土结构研究中的应用．桥梁建设，1986 (2-3)：45-58
[13] 清华大学抗震抗爆工程研究室．钢筋混凝土结构构件在冲击荷载下的性质．科学研究报告集第四集，清华大学出版社，1986
[14] Brooks J J., Al-Samaraie N. V. Fracture of concrete and Rock. S. P. Shah Ed, Elesevier Applied Science, 1989:397-408
[15] 李庆斌，张楚汉等．单压状态下混凝土的动力损伤本构模型．水利学报，1994 (3)：85-89
[16] 李庆斌，张楚汉，王光纶．单轴状态下混凝土的动力损伤本构模型．水利学报，1994，(12)：55-60
[17] 李庆斌．混凝土静、动力双剪本构模型．水利学报，1995(2)：27-34
[18] B.W.R.Forde, R.O.Foschi, S.F.Stiemer. Object-oriented finite element analysis. Computers & Structures. 2002, 34(3): 200-206
[19] G.L.Fenves. Object-oriented programming of the finite element method. Engineering with Computers. 1990, 6:1-15
[20] G.R.Miller. An Object-oriented approach to structural analysis and design. Computers & structures.1991, 40(1): 75-82
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