连续折线索单元及其应用研究
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摘要
随着工程技术的不断进步,以及材料工艺的发展,带有预应力拉索的结构越来越多地应用在民用建筑领域中的大跨度工程中,如体育馆、体育场、表演场、会展中心等。
连续折线索单元就是在这种工程实际应用的背景下产生并发展的。本文中所描述和使用的连续折线索单元,是以有限单元方法的思想与非线性固体力学理论为基础发展的,用以模拟连续协同受拉而又不在同一直线上具有可滑动节点的一系列线性索段的仿真工具。
荷载缓和体系是英国学者在上世纪八十年代提出的结构设计概念。本文将连续折线索单元应用于荷载缓和体系,并针对典型荷载缓和体系进行了算例分析,得到了较好的结果,体现了连续折线索单元对于荷载缓和体系分析的可用性和正确性。
本文以北京工业大学北京2008奥运会羽毛球馆弦支穹顶结构为参考,自行建立了弦支穹顶有限元模型,并对于该模型分别以间断索单元与连续折线索单元模拟环索进行了相应的静动力分析。两种模型在预应力、荷载作用、结构非线性屈曲分析与地震时程响应分析中几乎得出完全相同的结果与结论。在荷载作用下结构顶部首先发生屈曲,地震作用下,最外圈杆件与斜索是结构的最不利部位。
在线性屈曲分析中,间断索模型与连续索模型表现出较为明显的差异。两种模型的线性屈曲形式、线性屈曲特征值、振型、固有频率均不相同。间断索模型的模态类型较为丰富,而连续索模型则是外圈杆件更容易发生屈曲和振动;间断环索的各阶屈曲特征值均高于连续环索模型,固有频率也是如此。这说明采用间断环索的弦支穹顶结构与抗屈曲性能要强于连续环索弦支穹顶,刚度也更大一些。
综上,连续折线索单元应用于荷载缓和体系与弦支穹顶结构分析是较为有效的,既通过与间断索单元荷载分析得出几乎相同的结论证明了自身的正确性,又通过线性模态分析与线性屈曲分析的差别体现了自身的特点。
With the development of engineering technology and material, prestress cable stuctures are more and more used in long span civil engineering structures, for example gymnasium station, meeting hall, exhibition center, show hall and etc.
Sliding cable element is created and developed in the above engineering background. The sliding cable element which is described and used in this paper is developed on the base of finite element method and nonlinear solid mechanics. The element which contains sliding nodes can simulate the cables with consistent stress. And the cables are not necessarily in the same line.
The concept of structure design called load relieving system is created by English scholars in 1980s. This paper analyses load relieving system with sliding cable element. An example model of typical load relieving system is analyzed and a satisfactory result is get which partly proves the sliding cable element is correct and effective.
A finite element model is created which have great reference to the suspendome structure of the gymnasium of Olympic badminton game in 2008. Static analysis and dynamic analysis are made with both disconnected hoop cable element and continuous hoop cable cable element.
The two models with different cable elements perform exactly the same in prestress analysis, load analysis, nonlinear buckling analysis and time-history analysis. The buckling happens firstly at the top part of the dome. The most dangerous part of the structure is the ragged edge radial members and cables.
Different results are acquaired when eigenvalue buckling analysis and modal analysis are performed. Buckling shape, buckling eigenvalue, natural frequency and modal shape of two models are all different. The model with disconnect hoop cable element has more various buckling shapes and modal shapes, while the model with continuous hoop cable element seems to be more likely to buckle and vibrate at outer members. The buckling eigenvalue of the model with disconnect hoop cable element is higher than that of the model with continuous hoop cable element, and so is the natural frequency. It shows that the model with disconnect hoop cable element is harder to buckle than the other model and has more stiffness too.
From above, it shows that the application of sliding cable element in the load relieving system and suspendome system is effective. The rightness of sliding cable element is proved by getting the same result with disconnect cable element and the individual character is also exhibited by different performance in eigenvalue buckling analysis and modal analysis at the same time.
连续折线索单元就是在这种工程实际应用的背景下产生并发展的。本文中所描述和使用的连续折线索单元,是以有限单元方法的思想与非线性固体力学理论为基础发展的,用以模拟连续协同受拉而又不在同一直线上具有可滑动节点的一系列线性索段的仿真工具。
荷载缓和体系是英国学者在上世纪八十年代提出的结构设计概念。本文将连续折线索单元应用于荷载缓和体系,并针对典型荷载缓和体系进行了算例分析,得到了较好的结果,体现了连续折线索单元对于荷载缓和体系分析的可用性和正确性。
本文以北京工业大学北京2008奥运会羽毛球馆弦支穹顶结构为参考,自行建立了弦支穹顶有限元模型,并对于该模型分别以间断索单元与连续折线索单元模拟环索进行了相应的静动力分析。两种模型在预应力、荷载作用、结构非线性屈曲分析与地震时程响应分析中几乎得出完全相同的结果与结论。在荷载作用下结构顶部首先发生屈曲,地震作用下,最外圈杆件与斜索是结构的最不利部位。
在线性屈曲分析中,间断索模型与连续索模型表现出较为明显的差异。两种模型的线性屈曲形式、线性屈曲特征值、振型、固有频率均不相同。间断索模型的模态类型较为丰富,而连续索模型则是外圈杆件更容易发生屈曲和振动;间断环索的各阶屈曲特征值均高于连续环索模型,固有频率也是如此。这说明采用间断环索的弦支穹顶结构与抗屈曲性能要强于连续环索弦支穹顶,刚度也更大一些。
综上,连续折线索单元应用于荷载缓和体系与弦支穹顶结构分析是较为有效的,既通过与间断索单元荷载分析得出几乎相同的结论证明了自身的正确性,又通过线性模态分析与线性屈曲分析的差别体现了自身的特点。
With the development of engineering technology and material, prestress cable stuctures are more and more used in long span civil engineering structures, for example gymnasium station, meeting hall, exhibition center, show hall and etc.
Sliding cable element is created and developed in the above engineering background. The sliding cable element which is described and used in this paper is developed on the base of finite element method and nonlinear solid mechanics. The element which contains sliding nodes can simulate the cables with consistent stress. And the cables are not necessarily in the same line.
The concept of structure design called load relieving system is created by English scholars in 1980s. This paper analyses load relieving system with sliding cable element. An example model of typical load relieving system is analyzed and a satisfactory result is get which partly proves the sliding cable element is correct and effective.
A finite element model is created which have great reference to the suspendome structure of the gymnasium of Olympic badminton game in 2008. Static analysis and dynamic analysis are made with both disconnected hoop cable element and continuous hoop cable cable element.
The two models with different cable elements perform exactly the same in prestress analysis, load analysis, nonlinear buckling analysis and time-history analysis. The buckling happens firstly at the top part of the dome. The most dangerous part of the structure is the ragged edge radial members and cables.
Different results are acquaired when eigenvalue buckling analysis and modal analysis are performed. Buckling shape, buckling eigenvalue, natural frequency and modal shape of two models are all different. The model with disconnect hoop cable element has more various buckling shapes and modal shapes, while the model with continuous hoop cable element seems to be more likely to buckle and vibrate at outer members. The buckling eigenvalue of the model with disconnect hoop cable element is higher than that of the model with continuous hoop cable element, and so is the natural frequency. It shows that the model with disconnect hoop cable element is harder to buckle than the other model and has more stiffness too.
From above, it shows that the application of sliding cable element in the load relieving system and suspendome system is effective. The rightness of sliding cable element is proved by getting the same result with disconnect cable element and the individual character is also exhibited by different performance in eigenvalue buckling analysis and modal analysis at the same time.
引文
[1]彭伟贤,荷载缓和体系中缓和装置及其计算理论的研究:[硕士学位论文],浙江:浙江大学,2005
[2]黄刚,吴会鹏,高博青,谢忠良,荷载缓和体系的研究现状,空间结构,2006,1(12)
[3]单建,易军,郑勤刚,荷载缓和体系的受力性能研究,工程力学,1999,3(16)
[4] C.Meiboume,P,Bullman. Load relieving roof systems. In: Proc Int Conf. on Non-conventional Structures. London, 1987(2):1-6
[5]李旲,荷载缓和体系的理论分析与实验研究:[硕士学位论文],天津:天津大学,1999
[6]单建,蓝天,动力松弛法在张拉结构静力分析中的应用,东南大学学报,1994,24(3)
[7]崔晓强,郭彦林,广东奥林匹克体育场火炬计算分析,钢结构,2003,18(63),43～45
[8]姚裕昌,张桂先,荷载缓冲装置和平面索网抗风,第四届全国现代结构工程学术研讨会论文集,2004,393～396
[9]闫翔宇,陈志华,可呼吸结构的工程应用研究,第四届全国现代结构工程学术研讨会论文集,2004,425～428
[10]沈世钊,悬索结构(第二版),北京,中国建筑工业出版社,2006
[11]秦雅丽,弦支穹顶结构施工方法研究与施工过程分析:[硕士学位论文],天津:天津大学,2007
[12]刘学春,预应力弦支穹顶结构稳定性分析及优化设计:[硕士学位论文],北京:北京工业大学,2006
[13]尹德钰,刘善维,钱若军,网壳结构设计,北京:中国建筑工业出版社,1996
[14]左晨然,弦支穹顶结构的静力与稳定性分析:[硕士学位论文],天津:天津大学,2002
[15]张晓峰,2008奥运羽毛球馆弦支穹顶结构整体稳定及动力性能研究:[硕士学位论文],北京:北京工业大学,2006
[16]陈骥,钢结构稳定理论与设计(第二版),北京:科学出版社,2003
[17]尹越,单层球面网壳结构的稳定性研究:[博士学位论文],天津:天津大学,1999
[18]中华人民共和国建设部,JGJ61-2003,网壳结构技术规程,中华人民共和国行业标准, 2003-8-1
[19]中华人民共和国建设部,GB50205-2001,钢结构工程施工质量验收规范,中华人民共和国国家标准,北京:中国计划出版社,2002-3-1
[20]刘锡良,现代空间结构,天津:天津大学出版社,2002,1~2
[21]陈志华,弦支穹顶结构体系,第一届全国现代结构工程学术研讨会论文集,天津,2001,243~246
[22]陈志华,张拉整体结构的理论分析与试验研究:[博士学位论文],天津:天津大学,1995
[23]殷有泉,固体力学非线性有限元引论,北京:北京大学出版社,1987,122～127.
[24]宋天霞,郭建生,杨元明,非线性固体计算力学,武汉:华中科技大学出版社,2002,135～156.
[25] Ted Belytschko,Wing Kam Liu,Brian Moran,Nonlinear Finite Elements for Continua and Structures,England:John Wiley & Sons Ltd.,2000,65～86.
[26] ANSYS Release 9.0 Documentation. Canonsburg: ANSYS, Inc., 2005.
[27] B. Zhou, M.L. Accorsi, J.W. Leonard. Finite Element Formulation for Modeling Sliding Cable Elements. Computers & Structures, 82 (2004) 271～280.
[28] ABAQUS Version 6.5 Documentation. Providence: ABAQUS, Inc., 2005.
[29]庄茁,ABAQUS有限元软件6.4版入门指南,北京:清华大学出版社,2004.
[30]庄茁,张帆,岑松,ABAQUS非线性有限元分析与实例,北京:科学出版社,2005
[31]曹树谦,振动结构模态分析——理论、实验与应用,天津:天津大学出版社,2001
[32]冯振昌,索穹顶结构静动力性能研究:[硕士学位论文],天津:天津大学,2006
[33]赵建波,连续折线索单元的理论分析及张拉整体塔结构试验研究:[硕士学位论文],天津:天津大学,2006
[34]王晓明,索变长计算,计算结构力学及应用,1992, 9(2): 135~139
[35]单建,易军,郑勤刚,荷载缓和体系的研究与应用前景,第八届空间结构学术会议论文集,1997: 311~316
[36]唐建民,沈祖炎,悬索结构分析的滑移单元法,计算力学学报,1999(5):143~149
[37]郭彦林,崔晓强,滑动索系结构的统一分析方法——冷冻-升温法,工程力学,2003, 20(4): 156~160
[38]崔晓强,郭彦林,叶可明,滑动环索连接节点在弦支穹顶结构中的应用,同济大学学报(自然科学版),2004, 32(10): 1300~1303
[39]武建华,苏文章,四节点索单元的悬索结构非线性有限元分析,重庆建筑大学学报,2005,12(6):55~58
[40]唐建民,沈祖炎,钱若军,索穹顶结构非线性分析的曲线索单元有限元法,同济大学学报(自然科学版),1996(01):6~10
[2]黄刚,吴会鹏,高博青,谢忠良,荷载缓和体系的研究现状,空间结构,2006,1(12)
[3]单建,易军,郑勤刚,荷载缓和体系的受力性能研究,工程力学,1999,3(16)
[4] C.Meiboume,P,Bullman. Load relieving roof systems. In: Proc Int Conf. on Non-conventional Structures. London, 1987(2):1-6
[5]李旲,荷载缓和体系的理论分析与实验研究:[硕士学位论文],天津:天津大学,1999
[6]单建,蓝天,动力松弛法在张拉结构静力分析中的应用,东南大学学报,1994,24(3)
[7]崔晓强,郭彦林,广东奥林匹克体育场火炬计算分析,钢结构,2003,18(63),43～45
[8]姚裕昌,张桂先,荷载缓冲装置和平面索网抗风,第四届全国现代结构工程学术研讨会论文集,2004,393～396
[9]闫翔宇,陈志华,可呼吸结构的工程应用研究,第四届全国现代结构工程学术研讨会论文集,2004,425～428
[10]沈世钊,悬索结构(第二版),北京,中国建筑工业出版社,2006
[11]秦雅丽,弦支穹顶结构施工方法研究与施工过程分析:[硕士学位论文],天津:天津大学,2007
[12]刘学春,预应力弦支穹顶结构稳定性分析及优化设计:[硕士学位论文],北京:北京工业大学,2006
[13]尹德钰,刘善维,钱若军,网壳结构设计,北京:中国建筑工业出版社,1996
[14]左晨然,弦支穹顶结构的静力与稳定性分析:[硕士学位论文],天津:天津大学,2002
[15]张晓峰,2008奥运羽毛球馆弦支穹顶结构整体稳定及动力性能研究:[硕士学位论文],北京:北京工业大学,2006
[16]陈骥,钢结构稳定理论与设计(第二版),北京:科学出版社,2003
[17]尹越,单层球面网壳结构的稳定性研究:[博士学位论文],天津:天津大学,1999
[18]中华人民共和国建设部,JGJ61-2003,网壳结构技术规程,中华人民共和国行业标准, 2003-8-1
[19]中华人民共和国建设部,GB50205-2001,钢结构工程施工质量验收规范,中华人民共和国国家标准,北京:中国计划出版社,2002-3-1
[20]刘锡良,现代空间结构,天津:天津大学出版社,2002,1~2
[21]陈志华,弦支穹顶结构体系,第一届全国现代结构工程学术研讨会论文集,天津,2001,243~246
[22]陈志华,张拉整体结构的理论分析与试验研究:[博士学位论文],天津:天津大学,1995
[23]殷有泉,固体力学非线性有限元引论,北京:北京大学出版社,1987,122～127.
[24]宋天霞,郭建生,杨元明,非线性固体计算力学,武汉:华中科技大学出版社,2002,135～156.
[25] Ted Belytschko,Wing Kam Liu,Brian Moran,Nonlinear Finite Elements for Continua and Structures,England:John Wiley & Sons Ltd.,2000,65～86.
[26] ANSYS Release 9.0 Documentation. Canonsburg: ANSYS, Inc., 2005.
[27] B. Zhou, M.L. Accorsi, J.W. Leonard. Finite Element Formulation for Modeling Sliding Cable Elements. Computers & Structures, 82 (2004) 271～280.
[28] ABAQUS Version 6.5 Documentation. Providence: ABAQUS, Inc., 2005.
[29]庄茁,ABAQUS有限元软件6.4版入门指南,北京:清华大学出版社,2004.
[30]庄茁,张帆,岑松,ABAQUS非线性有限元分析与实例,北京:科学出版社,2005
[31]曹树谦,振动结构模态分析——理论、实验与应用,天津:天津大学出版社,2001
[32]冯振昌,索穹顶结构静动力性能研究:[硕士学位论文],天津:天津大学,2006
[33]赵建波,连续折线索单元的理论分析及张拉整体塔结构试验研究:[硕士学位论文],天津:天津大学,2006
[34]王晓明,索变长计算,计算结构力学及应用,1992, 9(2): 135~139
[35]单建,易军,郑勤刚,荷载缓和体系的研究与应用前景,第八届空间结构学术会议论文集,1997: 311~316
[36]唐建民,沈祖炎,悬索结构分析的滑移单元法,计算力学学报,1999(5):143~149
[37]郭彦林,崔晓强,滑动索系结构的统一分析方法——冷冻-升温法,工程力学,2003, 20(4): 156~160
[38]崔晓强,郭彦林,叶可明,滑动环索连接节点在弦支穹顶结构中的应用,同济大学学报(自然科学版),2004, 32(10): 1300~1303
[39]武建华,苏文章,四节点索单元的悬索结构非线性有限元分析,重庆建筑大学学报,2005,12(6):55~58
[40]唐建民,沈祖炎,钱若军,索穹顶结构非线性分析的曲线索单元有限元法,同济大学学报(自然科学版),1996(01):6~10