肋环型球面网壳结构的静动力分析
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摘要
球面网壳结构由于受力合理、用料经济、造型美观，能覆盖较大空间，近十年来发展速度惊人，其发展前景广阔，是一种理想的空间结构形式。目前网壳结构的研究主要集中在静力稳定性能，对其抗震性能研究进行的较少。为此，本文采用有限元方法，对肋环型局部双层、铝合金双层球面网壳结构进行了静、动力分析。主要包括以下几个方面的内容：
1．对肋环型局部双层球面网壳结构进行了稳定性分析。在大跨度结构中，将单、双层网壳结合起来形成的一种结构形成—周边双层中部单层的球面网壳结构，可充分发挥两种结构形式的优点。本文采用钢、铰接模型，即单层部分采用空间梁单元，双层部分采用空间杆单元，应用弧长法跟踪了网壳结构的平衡路径，总结了此类网壳结构的失稳规律，并且得出了结构由单层过渡到双层时临界荷载的变化规律。
2．分析了肋环型铝合金双层球面网壳结构的自振特性，考虑了结构多种参数的影响，并且与同种结构形式的钢网壳进行了对比。
3．采用时程分析法对肋环型铝合金双层球面网壳结构进行了地震分析，得出了结构在地震荷载作用下的位移、轴向应力的变化曲线，并且与谱分析结果以及相应的钢网壳作了比较。同时考虑了几何非线性的影响，在几何非线性的影响下分析结构随跨度、矢跨比、网格频数等参数受地震荷载的响应情况，对工程应用提出有科学价值的建议。
Spherical reticulated shell is of great prospect because of its economy, large span. In the recent ten years, reticulated shell structure develops very quickly. Most researches of reticulated shell focuses on static stability behaviors, but not on seismic behaviors. Thus, in this paper ,FEM is adopted to do static and dynamic analysis of partial double layer and aluminum alloy double layer spherical reticulated shell. The following content are mainly considered:
1. Analysis of stability behaviors of partial double-layer cable dome is done. The advantages of two different structural types can be fully developed by combining the single-layer spherical dome and the double-layer square pyramid space grids into a new structural type. The equilibrium path is traced using the arc-length scheme with the rigid-pin-joint model in which the spatial beam elements are used in single-layer parts and spatial truss elements are used in the double-layer parts. Thus the stability behavior is summarized and the critical load is obtained.
2. The vibration natural frequency of aluminum alloy double-layer cable dome is analyzed and several factors of the reticulated shell are considered as well.
3. Seismic response analysis is done by using time history analysis method in aluminum alloy double-layer cable dome and the displacement and the axis stress of the structure under the seismic response are obtained and the results are compared with the ones of the spectrum analysis. In addition, based on the analysis of several factors including the single-double-layer span ratios, the height-to-span ratios and the pipe types, the nonlinear analysis gives important suggestion to engineering application.
1．对肋环型局部双层球面网壳结构进行了稳定性分析。在大跨度结构中，将单、双层网壳结合起来形成的一种结构形成—周边双层中部单层的球面网壳结构，可充分发挥两种结构形式的优点。本文采用钢、铰接模型，即单层部分采用空间梁单元，双层部分采用空间杆单元，应用弧长法跟踪了网壳结构的平衡路径，总结了此类网壳结构的失稳规律，并且得出了结构由单层过渡到双层时临界荷载的变化规律。
2．分析了肋环型铝合金双层球面网壳结构的自振特性，考虑了结构多种参数的影响，并且与同种结构形式的钢网壳进行了对比。
3．采用时程分析法对肋环型铝合金双层球面网壳结构进行了地震分析，得出了结构在地震荷载作用下的位移、轴向应力的变化曲线，并且与谱分析结果以及相应的钢网壳作了比较。同时考虑了几何非线性的影响，在几何非线性的影响下分析结构随跨度、矢跨比、网格频数等参数受地震荷载的响应情况，对工程应用提出有科学价值的建议。
Spherical reticulated shell is of great prospect because of its economy, large span. In the recent ten years, reticulated shell structure develops very quickly. Most researches of reticulated shell focuses on static stability behaviors, but not on seismic behaviors. Thus, in this paper ,FEM is adopted to do static and dynamic analysis of partial double layer and aluminum alloy double layer spherical reticulated shell. The following content are mainly considered:
1. Analysis of stability behaviors of partial double-layer cable dome is done. The advantages of two different structural types can be fully developed by combining the single-layer spherical dome and the double-layer square pyramid space grids into a new structural type. The equilibrium path is traced using the arc-length scheme with the rigid-pin-joint model in which the spatial beam elements are used in single-layer parts and spatial truss elements are used in the double-layer parts. Thus the stability behavior is summarized and the critical load is obtained.
2. The vibration natural frequency of aluminum alloy double-layer cable dome is analyzed and several factors of the reticulated shell are considered as well.
3. Seismic response analysis is done by using time history analysis method in aluminum alloy double-layer cable dome and the displacement and the axis stress of the structure under the seismic response are obtained and the results are compared with the ones of the spectrum analysis. In addition, based on the analysis of several factors including the single-double-layer span ratios, the height-to-span ratios and the pipe types, the nonlinear analysis gives important suggestion to engineering application.
引文
[1] 沈祖炎，陈扬骥．网架与网壳[M]．上海．同济大学出版社，1997
[2] 沈祖炎，严慧．空间网架结构[M]．贵州．贵人民出版社，1987．
[3] 董石麟，钱若军．空间网格结构分析理论与计算方法．中国建筑工业出版社，第1版，2000．
[4] 符立勇，杨从娟．大跨度空间结构-网壳结构的历史与发展．工程建设与设计，第五期，2002．
[5] Civil Engineer International 1997.11, Fabric Architecture 1999.1.2
[6] Th.von.Karman, H.s.Tsien,The Bucking of Spherical Shells byExtemal Pressure, J.aero.Sci.7,pp.43-50.
[7] 中华人民共和国国家标准，建筑结构抗震设计规范,GBJ11-89,中国建筑工业出版社，1990．
[8] 朱伯龙，张琨联，建筑结构抗震设计原理，同济大学出版社，1994
[9] 中华人民共和国行业标准，工程抗震术语标准，中国建筑工业出版社，1995．
[10] E.I.Brimelow,Aluminum in Building,London,1957
[11] 钱基宏、赵鹏飞等，大跨度铝穹顶网壳结构的研究，第九届空间结构学术会议论文集，2000．9．13～2000．9．17，浙江，萧山．
[12] 姚念亮、杨联萍，铝合金格构结构的发展与应用，第九届空间结构学术会议论文集，2000．9．13～2000．9．17，浙江，萧山．
[13] Aluminum Association, Specification for Aluminum Structures,First Edn,1976.
[14] Aluminum Association, Specification for Aluminum Structures, Second Edn, 1994.
[15] 史志利，李忠献，随机地震动场多点激励．地震工程与工程震动．第23卷第4期2003．8
[16] Makowsi Z S. Three Dimensional Strnctures,im view of their achievements in the past,can we forcast their influence upon modem engineering and light-weight large-span structures?Proceedings jof the IASS Intenational Symposium on Shell and Spatial Structures,Singapore, 1997,1:55～68
[17] 蓝天．空间结构的十年—从中国看世界．第六届空间结构学术会议论文集，北京：地震出版社，1992，1-8
[18] Makowski Z S. Analysis design and constrrction of braced domes[M]. London and New York: Granada publishing Ltd, Nicolls publishing Co, 1984.
[19] Gioncu V. Special issue on stability of space structures [J]. hat J of Space Stuctures, [1992,7(4):243-368
[20] 董石鳞，沈祖炎．新型空间结构论文集[M]．杭州：浙江大学出版社，1994．
[21] 尹德钰，刘善维，钱若军．网壳结构设计[M]．北京：中国建筑工业出版社，1996
[22] 陈务军，董石麟．局部双层网壳的体系与稳定性能研究[R]．博士后研究报告，上海交通大学空间结构研究中心，2000．
[23] 夏开全，董石麟．局部双层网壳结构的几何非线性分析[J]．空间结构，1999，5(2)：29-37．
[24] 夏开全，董石鳞．刚接与铰接混合连接杆系结构的几何非线性分析[J]．计算力学学报，2001，18(1)：103-107．
[25] 陈务军，董石麟，付功义，等．非线性分析广义增量法算法研究[J]．工程力学，2001，1 8(3)：28-33
[26] W.T Koiter, The stability of Elestic Equilibrium,Thesis, Delft,1945(Eenglish Translation NASA TT-F·10833,1967).
[27] J.M.Thompsom, Aasic Principles in the General Theory of Elastic Stability, J.Mechanics and Physics of Solids,Vol. 11,1963,pp. 13-20
[28] M.A.Crisfield. A Fast Incremental/Iterative Solution Procedure that Handle"Snap_Through".Computers and Structures, 1981,13:55-62.
[29] 关富玲，高博青．单层网壳的稳定性分析．工程力学，1996，13(3)：93-104
[30] 陈昕，王娜．空间梁单元的切线刚度矩阵．哈而滨建筑工程学院学报，1993，26(3)，24-29．
[31] 龚景海，刘锡良．网壳结构稳定分析程序．工程力学增刊，1998：633-637
[32] J.H.Argyris,P.C.Dumme.On Large Displacement-Small Strain Analysis of Structure with Rotational Degrees of Freedom. Computer Methods in Applied Mechanics and Engineering, 1978,14:405-451,15:99-135.
[33] 沈世钊，陈昕．网壳结构稳定性．科学出版社．1999．
[34] W.F. Chen, E.M.Lui.Structural Stability Theory and Implementation.New
York,Elsevier Science Publishing Co.,Inc., 1987
[35] M.A.Crisfield. An Arc-Length Method Including Line Searches and Accelerations.International Journal for Numercial Methods in Engineering, 1983,19:1269-12889
[36] 尹德钰，刘善维，钱若军．网壳结构设计[M]．中国建筑工业出版社
[37] 曾银枝，钱若军．铝合金穹顶的试验研究．空间结构第6卷第4期：47-52．
[38] 曹资，薛素铎，王珺．单层与双层柱面网壳基频时用实际图表[J]．建筑结构第32卷第7期：42-44．
[39] ANSYS动力学分析指南，模态分析．
[40] Clough R W, Pinzien J.Dynamics of structures.McGraw-Hill,Inc, 1993
[41] 罗永峰、季跃等，铝合金结构轴心压杆稳定性研究，2001，29(4)
[42] ECCS European Recommendation for Aluminum Alloy Structures[s]．First edu,1978．
[43] 王肇民，高耸结构设计手册，中国建筑工业出版社，1995．
[44] Bathe K.J.Finete Element Procedures in Engineering Analysis [M].Prentice-Hall,Inc.,Englewood Cliffs,New Jersey, 1982
[45] 陈兴冲，韩建平，王琳．工程结构抗震设计[M]．重庆大学出版社．
[46] R.W.Clough,J.Penzien.DYNAMICS OF STRRCTURES.McCmw-Hill Inc,1975.
[47] N.M.Newmark, E.ROSENBLUETH.FUNDAMENTALS OF EARTHQUAKE ENGNEERING Prentice-Hall, Inc. Englewood CLIFFS, N.J. 1971.
[48] 叶继红，单层网壳结构的动力稳定分析：[博士论文]．上海：同济大学图书馆，1995
[49] Clough R W, Pinzien J.Dynamics of structures.McGraw-Hill,Inc, 1993
[50] ANSYS入门手册，美国ANSYS公司广州办事处．
[51] 胡聿贤．地震工程学[M]．地震出版社(北京)，1988．
[52] 冯云用，李明瑞．复杂结构的弹性地震反应分析[J]．地震工程与工程震动，
1991, 11 (1): 78-87.
[53] Moehle JP, editor. Preliminary report on the seismologicaland engineering aspects of the January 17, 1994 northbridgeearthquake, arthquake engineering research centerreport no. UCB/EERC-94/01, Berkeley, CA: University of California; 1994.
[54] EQE International. The January 17, 1995 Kobe earthquake.San Francisco: EQE International;
[2] 沈祖炎，严慧．空间网架结构[M]．贵州．贵人民出版社，1987．
[3] 董石麟，钱若军．空间网格结构分析理论与计算方法．中国建筑工业出版社，第1版，2000．
[4] 符立勇，杨从娟．大跨度空间结构-网壳结构的历史与发展．工程建设与设计，第五期，2002．
[5] Civil Engineer International 1997.11, Fabric Architecture 1999.1.2
[6] Th.von.Karman, H.s.Tsien,The Bucking of Spherical Shells byExtemal Pressure, J.aero.Sci.7,pp.43-50.
[7] 中华人民共和国国家标准，建筑结构抗震设计规范,GBJ11-89,中国建筑工业出版社，1990．
[8] 朱伯龙，张琨联，建筑结构抗震设计原理，同济大学出版社，1994
[9] 中华人民共和国行业标准，工程抗震术语标准，中国建筑工业出版社，1995．
[10] E.I.Brimelow,Aluminum in Building,London,1957
[11] 钱基宏、赵鹏飞等，大跨度铝穹顶网壳结构的研究，第九届空间结构学术会议论文集，2000．9．13～2000．9．17，浙江，萧山．
[12] 姚念亮、杨联萍，铝合金格构结构的发展与应用，第九届空间结构学术会议论文集，2000．9．13～2000．9．17，浙江，萧山．
[13] Aluminum Association, Specification for Aluminum Structures,First Edn,1976.
[14] Aluminum Association, Specification for Aluminum Structures, Second Edn, 1994.
[15] 史志利，李忠献，随机地震动场多点激励．地震工程与工程震动．第23卷第4期2003．8
[16] Makowsi Z S. Three Dimensional Strnctures,im view of their achievements in the past,can we forcast their influence upon modem engineering and light-weight large-span structures?Proceedings jof the IASS Intenational Symposium on Shell and Spatial Structures,Singapore, 1997,1:55～68
[17] 蓝天．空间结构的十年—从中国看世界．第六届空间结构学术会议论文集，北京：地震出版社，1992，1-8
[18] Makowski Z S. Analysis design and constrrction of braced domes[M]. London and New York: Granada publishing Ltd, Nicolls publishing Co, 1984.
[19] Gioncu V. Special issue on stability of space structures [J]. hat J of Space Stuctures, [1992,7(4):243-368
[20] 董石鳞，沈祖炎．新型空间结构论文集[M]．杭州：浙江大学出版社，1994．
[21] 尹德钰，刘善维，钱若军．网壳结构设计[M]．北京：中国建筑工业出版社，1996
[22] 陈务军，董石麟．局部双层网壳的体系与稳定性能研究[R]．博士后研究报告，上海交通大学空间结构研究中心，2000．
[23] 夏开全，董石麟．局部双层网壳结构的几何非线性分析[J]．空间结构，1999，5(2)：29-37．
[24] 夏开全，董石鳞．刚接与铰接混合连接杆系结构的几何非线性分析[J]．计算力学学报，2001，18(1)：103-107．
[25] 陈务军，董石麟，付功义，等．非线性分析广义增量法算法研究[J]．工程力学，2001，1 8(3)：28-33
[26] W.T Koiter, The stability of Elestic Equilibrium,Thesis, Delft,1945(Eenglish Translation NASA TT-F·10833,1967).
[27] J.M.Thompsom, Aasic Principles in the General Theory of Elastic Stability, J.Mechanics and Physics of Solids,Vol. 11,1963,pp. 13-20
[28] M.A.Crisfield. A Fast Incremental/Iterative Solution Procedure that Handle"Snap_Through".Computers and Structures, 1981,13:55-62.
[29] 关富玲，高博青．单层网壳的稳定性分析．工程力学，1996，13(3)：93-104
[30] 陈昕，王娜．空间梁单元的切线刚度矩阵．哈而滨建筑工程学院学报，1993，26(3)，24-29．
[31] 龚景海，刘锡良．网壳结构稳定分析程序．工程力学增刊，1998：633-637
[32] J.H.Argyris,P.C.Dumme.On Large Displacement-Small Strain Analysis of Structure with Rotational Degrees of Freedom. Computer Methods in Applied Mechanics and Engineering, 1978,14:405-451,15:99-135.
[33] 沈世钊，陈昕．网壳结构稳定性．科学出版社．1999．
[34] W.F. Chen, E.M.Lui.Structural Stability Theory and Implementation.New
York,Elsevier Science Publishing Co.,Inc., 1987
[35] M.A.Crisfield. An Arc-Length Method Including Line Searches and Accelerations.International Journal for Numercial Methods in Engineering, 1983,19:1269-12889
[36] 尹德钰，刘善维，钱若军．网壳结构设计[M]．中国建筑工业出版社
[37] 曾银枝，钱若军．铝合金穹顶的试验研究．空间结构第6卷第4期：47-52．
[38] 曹资，薛素铎，王珺．单层与双层柱面网壳基频时用实际图表[J]．建筑结构第32卷第7期：42-44．
[39] ANSYS动力学分析指南，模态分析．
[40] Clough R W, Pinzien J.Dynamics of structures.McGraw-Hill,Inc, 1993
[41] 罗永峰、季跃等，铝合金结构轴心压杆稳定性研究，2001，29(4)
[42] ECCS European Recommendation for Aluminum Alloy Structures[s]．First edu,1978．
[43] 王肇民，高耸结构设计手册，中国建筑工业出版社，1995．
[44] Bathe K.J.Finete Element Procedures in Engineering Analysis [M].Prentice-Hall,Inc.,Englewood Cliffs,New Jersey, 1982
[45] 陈兴冲，韩建平，王琳．工程结构抗震设计[M]．重庆大学出版社．
[46] R.W.Clough,J.Penzien.DYNAMICS OF STRRCTURES.McCmw-Hill Inc,1975.
[47] N.M.Newmark, E.ROSENBLUETH.FUNDAMENTALS OF EARTHQUAKE ENGNEERING Prentice-Hall, Inc. Englewood CLIFFS, N.J. 1971.
[48] 叶继红，单层网壳结构的动力稳定分析：[博士论文]．上海：同济大学图书馆，1995
[49] Clough R W, Pinzien J.Dynamics of structures.McGraw-Hill,Inc, 1993
[50] ANSYS入门手册，美国ANSYS公司广州办事处．
[51] 胡聿贤．地震工程学[M]．地震出版社(北京)，1988．
[52] 冯云用，李明瑞．复杂结构的弹性地震反应分析[J]．地震工程与工程震动，
1991, 11 (1): 78-87.
[53] Moehle JP, editor. Preliminary report on the seismologicaland engineering aspects of the January 17, 1994 northbridgeearthquake, arthquake engineering research centerreport no. UCB/EERC-94/01, Berkeley, CA: University of California; 1994.
[54] EQE International. The January 17, 1995 Kobe earthquake.San Francisco: EQE International;