拱桥有限元设计计算原理及程序开发
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摘要
拱桥在我国有悠久的历史,是一种造型美观,经济耐久的传统桥梁结构形式。其主要是受压为主,拱内弯矩和剪力较小,所以圬工拱桥应用较广。虽然在已经达到的跨度上,拱桥不及悬索桥与斜拉桥,作为现代桥梁型式之一,当选择大跨度桥梁的桥型时,在目前比较常遇的200~600m跨度范围内,拱桥仍然是悬索桥与斜拉桥的竞争对手。而在中、小跨度领域,则只要有民间工匠的地方,就有条件修建拱桥。现阶段我国公路建设的重点是农村的村村通公路建设,拱桥的特点决定在农村公路建设中圬工拱桥将成为主要首选桥型。
过去拱桥计算都是采用计算手册,计算起来比较麻烦,有些地方是估算,不是很准确。随着计算机的应用,目前国内外可用于计算桥梁的有限元程序很多,例如:桥梁博士、MIDAS、ANSYS等,它们适应于各种桥型,其中包括计算拱桥内力。这些程序建模需要好长时间,对于对电脑操作,特别是建模不是很熟练的技术人员来说,应用十分不便。而且它们不止是针对一种桥型,应用起来没有桥梁通软件那样简单,快捷。本文内容是采用计算机和有限元有机结合,推导了拱桥有限元的单元刚度矩阵、体积力和表面力引起的单元节点矩阵和温度变化、拱脚变位、压力线偏离引起的节点阵等,依据有限元的计算原理和步骤提供了各种拱轴线下一般结构的内力计算程序,同时也可以根据需要划分单元计算内力;作者采用最小二乘法编写了便于拱轴优化的子程序,为拱桥设计拱轴线的优选提供了方便。另一方面,通过程序计算结果首先分析单元划分对结构内力的影响;然后对程序计算内力结果和理论结果进行对比分析;最后对新旧规范中活载的变化作对比分析,得出相关结论,同时总结新规范的具体变化,为桥梁工作者使用新规范提供参考。
文中所有的计算程序均利用Delphi开发,此程序属于桥梁通软件的一部分,充分体现了方便、快捷的特点。
Arch bridge has a long history in our country.It has a traditional bridge structure with the virtue of economy and ever lasting. Masonry arch bridges are widely used for they can bear high pressure, have less bending moment and shear force. Although arch bridge inferior to suspension bridge and staged-cable bridge in span. As a structure of modern bridge, arch bridge is a chiose when the bridge has a span of 200 to 600 meters. When the bridge has middle or small span, building arch bridge is an easy task when civilian craftsmen are available. Masonry arch bridges will be the first choice for its characteristic.
In the past, people calculated arch bridge with the help of manual. It is a complicated work, sometimes approximate calculation is needed and the result is not precise. Recently, many kinds of software to compute bridge are available at home and abroad such as Doctor Bridge, Midas and Anysis and so on. These softwares can be applied to various of bridge structures including arch bridge, but these softwares cost people much time to model the bridge structure and inconvenience those who are not familiar with computer.Further more, they can caculate more than one kind of bridge sturcture and are not concise to people who use the software named Qiaoliangtong . In this paper, combining computer and finite element methode, the Stiffness matrix of cell, the Force of Equivalent Node matrix of cell by the force of volume and surface, the Force of Equivalent Node matrix of cell by changed temperature, feet of the arch change and the compression line departure are derived. According to the compute principle and process of finite element, the paper provides program of counting internal force for many kinds of arch axes. At the same time, subprogram of optimizing arch axes using least squares method was programmed which is convenient to design arches axes. Meanwhile, partition cell infect to frame internal force according to the program result was analyzed. Couputed result and theoretical result are also compared. At last, the changes of variable action in new criterion and old criterion are also explained.
The program was developed by Delphi as a part of the program of QiaoLiangTong which have the characteristic of convenience.
过去拱桥计算都是采用计算手册,计算起来比较麻烦,有些地方是估算,不是很准确。随着计算机的应用,目前国内外可用于计算桥梁的有限元程序很多,例如:桥梁博士、MIDAS、ANSYS等,它们适应于各种桥型,其中包括计算拱桥内力。这些程序建模需要好长时间,对于对电脑操作,特别是建模不是很熟练的技术人员来说,应用十分不便。而且它们不止是针对一种桥型,应用起来没有桥梁通软件那样简单,快捷。本文内容是采用计算机和有限元有机结合,推导了拱桥有限元的单元刚度矩阵、体积力和表面力引起的单元节点矩阵和温度变化、拱脚变位、压力线偏离引起的节点阵等,依据有限元的计算原理和步骤提供了各种拱轴线下一般结构的内力计算程序,同时也可以根据需要划分单元计算内力;作者采用最小二乘法编写了便于拱轴优化的子程序,为拱桥设计拱轴线的优选提供了方便。另一方面,通过程序计算结果首先分析单元划分对结构内力的影响;然后对程序计算内力结果和理论结果进行对比分析;最后对新旧规范中活载的变化作对比分析,得出相关结论,同时总结新规范的具体变化,为桥梁工作者使用新规范提供参考。
文中所有的计算程序均利用Delphi开发,此程序属于桥梁通软件的一部分,充分体现了方便、快捷的特点。
Arch bridge has a long history in our country.It has a traditional bridge structure with the virtue of economy and ever lasting. Masonry arch bridges are widely used for they can bear high pressure, have less bending moment and shear force. Although arch bridge inferior to suspension bridge and staged-cable bridge in span. As a structure of modern bridge, arch bridge is a chiose when the bridge has a span of 200 to 600 meters. When the bridge has middle or small span, building arch bridge is an easy task when civilian craftsmen are available. Masonry arch bridges will be the first choice for its characteristic.
In the past, people calculated arch bridge with the help of manual. It is a complicated work, sometimes approximate calculation is needed and the result is not precise. Recently, many kinds of software to compute bridge are available at home and abroad such as Doctor Bridge, Midas and Anysis and so on. These softwares can be applied to various of bridge structures including arch bridge, but these softwares cost people much time to model the bridge structure and inconvenience those who are not familiar with computer.Further more, they can caculate more than one kind of bridge sturcture and are not concise to people who use the software named Qiaoliangtong . In this paper, combining computer and finite element methode, the Stiffness matrix of cell, the Force of Equivalent Node matrix of cell by the force of volume and surface, the Force of Equivalent Node matrix of cell by changed temperature, feet of the arch change and the compression line departure are derived. According to the compute principle and process of finite element, the paper provides program of counting internal force for many kinds of arch axes. At the same time, subprogram of optimizing arch axes using least squares method was programmed which is convenient to design arches axes. Meanwhile, partition cell infect to frame internal force according to the program result was analyzed. Couputed result and theoretical result are also compared. At last, the changes of variable action in new criterion and old criterion are also explained.
The program was developed by Delphi as a part of the program of QiaoLiangTong which have the characteristic of convenience.
引文
[1] 顾安邦、孙国柱等.公路桥涵设计手册 拱桥下册.北京:人民交通出版社.1994.
[2] 顾安邦、范立础 .桥梁工程下册.北京:人民交通出版社.2005.
[3] 戴崇安 .石拱桥施工 .北京:人民交通出版社 .1982.
[4] 刘培文、周卫 等.公路小桥涵设计示例 .北京:人民交通出版社 .2005.
[5] 王世槐 .圬工拱桥.北京:人民交通出版社.1983.
[6] 俞铭华、吴剑国等. 有限元法与面向对象编程 .北京:科学出版社 .2004.
[7]. 龙志飞、岑 松. 有限元法理论原理.程序.进展 .北京:中国水利水电出版社.2001
[8]. 王焕定、吴德伦等.有限单元法及计算程序 .北京:中国建筑工业出版社 .2004
[9]. 姚铃森. 桥梁工程.北京:人民交通出版社.1985.
[10] Meilir Page-Jones.UML 面向对象设计理论基础.北京:人民邮电出版社.2001.
[11] 项海帆、刘光栋著.拱结构的稳定与振动.北京:人民交通出版社.1991.
[12] 贺栓海.圆弧拱桥的挠度理论分析.西安:西安公路交通大学学报.1988年12月.
[13] 张德文.垂直悬杆刚性拉杆式刚拱的新设计方法.北京:人民交通出版社.1987
[14] 庄茁、岑 松 .有限元方法-固体力学 .北京:清华大学出版社 .2006.
[15] 龙驮球、包世华.结构力学.北京:高等教育出版社.1996.
[16] 罗定安.工程结构分析方法与程序设计.天津:天津大学出版社.1990.
[17] 赵更新.土木工程结构分析程序设计.北京:中国水利水电出版社.2002.
[18] 钱树人.程序设计语言原理.北京:高等教育出版社.2001.
[19] 姜晋庆、张绎.结构弹塑性有限元分析方法.北京:国防工业出版社.1992.
[20] 贺栓海 .拱桥挠度理论.北京:人民交通出版社.
[21]李庆扬、王能超、易大义.数值分析.北京:清华大学出版社.2001.
[22] Zeglinski G W,Han R P S,AitchisonP.Object oriented matrix classes for us in a finite element code using C++.International Journal for Numerical Memerical in Engineering 1992.37:3951-3937.
[23] Silvea E J,Mesquita R C ,Saldanha R R,et al.An Object-oriented finite-element program for electromagnetic field computation.IEEE transactions on magnetics ,1994.30:3618-3612.
[24] Babuska I,Siaho B A,Kalz L N.The P-version elemenl method.SLAM J Numer Anal,1981,18(3).
[25] 中交规划设计院《公路桥涵设计通用规范》(JTG D60-2004).北京.人民交通出版社.2004.
[26] 中交规划设计院《公路圬工桥涵设计规范》(JTG D61-2005). 北京.人民交通出版社.2005.
[27] 中交规划设计院《公路公路砖石及混凝土桥涵设计规范》(JTJ 002-85). 北京.人民交通出版社.1985.
[28] 中交规划设计院《公路桥涵设计通用规范》(JTJ 021-89). 北京.人民交通出版社.1989.
[2] 顾安邦、范立础 .桥梁工程下册.北京:人民交通出版社.2005.
[3] 戴崇安 .石拱桥施工 .北京:人民交通出版社 .1982.
[4] 刘培文、周卫 等.公路小桥涵设计示例 .北京:人民交通出版社 .2005.
[5] 王世槐 .圬工拱桥.北京:人民交通出版社.1983.
[6] 俞铭华、吴剑国等. 有限元法与面向对象编程 .北京:科学出版社 .2004.
[7]. 龙志飞、岑 松. 有限元法理论原理.程序.进展 .北京:中国水利水电出版社.2001
[8]. 王焕定、吴德伦等.有限单元法及计算程序 .北京:中国建筑工业出版社 .2004
[9]. 姚铃森. 桥梁工程.北京:人民交通出版社.1985.
[10] Meilir Page-Jones.UML 面向对象设计理论基础.北京:人民邮电出版社.2001.
[11] 项海帆、刘光栋著.拱结构的稳定与振动.北京:人民交通出版社.1991.
[12] 贺栓海.圆弧拱桥的挠度理论分析.西安:西安公路交通大学学报.1988年12月.
[13] 张德文.垂直悬杆刚性拉杆式刚拱的新设计方法.北京:人民交通出版社.1987
[14] 庄茁、岑 松 .有限元方法-固体力学 .北京:清华大学出版社 .2006.
[15] 龙驮球、包世华.结构力学.北京:高等教育出版社.1996.
[16] 罗定安.工程结构分析方法与程序设计.天津:天津大学出版社.1990.
[17] 赵更新.土木工程结构分析程序设计.北京:中国水利水电出版社.2002.
[18] 钱树人.程序设计语言原理.北京:高等教育出版社.2001.
[19] 姜晋庆、张绎.结构弹塑性有限元分析方法.北京:国防工业出版社.1992.
[20] 贺栓海 .拱桥挠度理论.北京:人民交通出版社.
[21]李庆扬、王能超、易大义.数值分析.北京:清华大学出版社.2001.
[22] Zeglinski G W,Han R P S,AitchisonP.Object oriented matrix classes for us in a finite element code using C++.International Journal for Numerical Memerical in Engineering 1992.37:3951-3937.
[23] Silvea E J,Mesquita R C ,Saldanha R R,et al.An Object-oriented finite-element program for electromagnetic field computation.IEEE transactions on magnetics ,1994.30:3618-3612.
[24] Babuska I,Siaho B A,Kalz L N.The P-version elemenl method.SLAM J Numer Anal,1981,18(3).
[25] 中交规划设计院《公路桥涵设计通用规范》(JTG D60-2004).北京.人民交通出版社.2004.
[26] 中交规划设计院《公路圬工桥涵设计规范》(JTG D61-2005). 北京.人民交通出版社.2005.
[27] 中交规划设计院《公路公路砖石及混凝土桥涵设计规范》(JTJ 002-85). 北京.人民交通出版社.1985.
[28] 中交规划设计院《公路桥涵设计通用规范》(JTJ 021-89). 北京.人民交通出版社.1989.