一种索穹顶结构初始预应力分布确定的新方法——预载回弹法
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摘要
对索穹顶结构初始预应力分布的确定进行了研究,提出一种新方法—预载回弹法。该方法首先对索穹顶施加一个预设荷载,提取有利于抵抗预设荷载的内力分布。将该组内力作为预应力施加至结构上,并撤除预载,使结构回弹,通过两阶段变弹性模量迭代计算,收敛后可获得索穹顶结构的整体可行预应力分布。该方法通过施加对称荷载,即可自动实现单元的分组,便于整体可行预应力的判定,并可直接获得多自应力模态结构的优化初始预应力分布。通过算例证明预载回弹法具有很高的精度、较快的收敛速度,求得的整体可行预应力分布直接适用于实际工程应用。
The determination of the initial prestress distribution of cable domes is studied and a new method named the Preload and Rebound Method is proposed. A preload is applied to the cable dome first to get the internal force distribution which helps resist the preload. After the preload is removed, the internal force is then applied to the structure as prestress, making the structure rebound. Through the two-stage iterative calculation by using changing elastic modulus, the integrity feasible prestressing distribution of the cable dome is achieved after convergence. By applying a symmetric load, this method automatically groups the members and easily distinguishes the integrity feasible prestressing distribution. The optimized initial prestress distribution of the structure with multi-self-equilibrium stress modes is also directly gained. This method is proved to be accurate and converge fast by several examples. The integrity feasible prestressing distribution obtained through this method can be directly applied to engineering practice.
The determination of the initial prestress distribution of cable domes is studied and a new method named the Preload and Rebound Method is proposed. A preload is applied to the cable dome first to get the internal force distribution which helps resist the preload. After the preload is removed, the internal force is then applied to the structure as prestress, making the structure rebound. Through the two-stage iterative calculation by using changing elastic modulus, the integrity feasible prestressing distribution of the cable dome is achieved after convergence. By applying a symmetric load, this method automatically groups the members and easily distinguishes the integrity feasible prestressing distribution. The optimized initial prestress distribution of the structure with multi-self-equilibrium stress modes is also directly gained. This method is proved to be accurate and converge fast by several examples. The integrity feasible prestressing distribution obtained through this method can be directly applied to engineering practice.
引文
[1]Geiger D H,Stefaniuk A,Chen D.The design and construction of two cable domes for the Korea Olympics[C]//Proceedings of the IASS Symposium:Shells,Membranes and Space Frame.Osaka,1986,2:265―272.
[2]Levy M P.The Georgia dome and beyond achieving lightweight-long span structures[C]//Proceedings of the IASS-ASCE International Symposium:Spatial,Lattice and Tension Structures.New York,1994:560―562.
[3]Pellegrino S,Calladine C R.Matrix analysis of statically and kinematically indaterminate frameworks[J].International Journal of Solids and Structures,1986,22(4):409―428.
[4]Pellegrino S.Structural computations with the singular value decomposition of the equilibrium matrix[J].International Journal of Solids and Structures,1993,30(21):3025―3035.
[5]董石麟,袁行飞.肋环型索穹顶初始预应力分布的快速计算法[J].空间结构,2003,9(2):3―8,19.Dong Shilin,Yuan Xingfei.A quick calculation method for initial prestress distribution of Geiger domes[J].Spatial Structures,2003,9(2):3―8,19.(in Chinese)
[6]董石麟,袁行飞.葵花型索穹顶初始预应力分布的简捷算法[J].建筑结构学报,2004,25(6):9―14.Dong Shilin,Yuan Xingfei.A simplified calculation method for initial prestress distribution of sunflower-patterned cable domes[J].Journal of Building Structures,2004,25(6):9―14.(in Chinese)
[7]董石麟,王振华,袁行飞.Levy型索穹顶考虑自重的初始预应力简捷计算法[J].工程力学,2009,26(4):1―6.Dong Shilin,Wang Zhenhua,Yuan Xingfei.A simplified calculation method for initial prestress of Levy cable domes with the consideration of self-weight[J].Engineering Mechanics,2009,26(4):1―6.(in Chinese)
[8]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33―37,61.Yuan Xingfei,Dong Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33―37,61.(in Chinese)
[9]袁行飞,董石麟.索穹顶结构的新形式及其初始预应力确定[J].工程力学,2005,22(2):22―26.Yuan Xingfei,Dong Shilin.New forms and initial prestress calculation of cable domes[J].Engineering Mechanics,2005,22(2):22―26.(in Chinese)
[10]曾文平,王元清,张勇,等.索穹顶结构的预应力设计方法[J].工业建筑,2002,32(9):24―26.Zeng Wenping,Wang Yuanqing,Zhang Yong,et al.The method of prestress design for cable dome[J].Industrial Construction,2002,32(9):24―26.(in Chinese)
[11]阚远,叶继红.动力松弛法在索穹顶结构形状确定中的应用[J].工程力学,2007,24(9):50―55.Kan Yuan,Ye Jihong.Form finding of cable domes by modified dynamic relaxation[J].Engineering Mechanics,2007,24(9):50―55.(in Chinese)
[12]Schek H J.The force density method for form finding and computation of general networks[J].Computer Methods in Applied Mechanics and Engineering,1974,3(1):115―134.
[13]Barnes M R.Form finding and analysis of tension structures by dynamic relaxation[J].International Journal of Space Structures,1999,14(2):89―104.
[14]袁行飞,董石麟.索穹顶结构几何稳定性分析[J].空间结构,1999,5(1):3―9.Yuan Xingfei,Dong Shilin.Analysis of geometric stability for cable domes[J].Spatial Structures,1999,5(1):3―9.(in Chinese)
[15]陈联盟,袁行飞,董石麟.索杆张力结构自应力模态分析及预应力优化[J].土木工程学报,2006,39(2):11―15.Chen Lianmeng,Yuan Xingfei,Dong Shilin.Selfstress mode analysis and optimal prestress design of cable-strut tension structures[J].China Civil Engineering Journal,2006,39(2):11―15.(in Chinese)
[2]Levy M P.The Georgia dome and beyond achieving lightweight-long span structures[C]//Proceedings of the IASS-ASCE International Symposium:Spatial,Lattice and Tension Structures.New York,1994:560―562.
[3]Pellegrino S,Calladine C R.Matrix analysis of statically and kinematically indaterminate frameworks[J].International Journal of Solids and Structures,1986,22(4):409―428.
[4]Pellegrino S.Structural computations with the singular value decomposition of the equilibrium matrix[J].International Journal of Solids and Structures,1993,30(21):3025―3035.
[5]董石麟,袁行飞.肋环型索穹顶初始预应力分布的快速计算法[J].空间结构,2003,9(2):3―8,19.Dong Shilin,Yuan Xingfei.A quick calculation method for initial prestress distribution of Geiger domes[J].Spatial Structures,2003,9(2):3―8,19.(in Chinese)
[6]董石麟,袁行飞.葵花型索穹顶初始预应力分布的简捷算法[J].建筑结构学报,2004,25(6):9―14.Dong Shilin,Yuan Xingfei.A simplified calculation method for initial prestress distribution of sunflower-patterned cable domes[J].Journal of Building Structures,2004,25(6):9―14.(in Chinese)
[7]董石麟,王振华,袁行飞.Levy型索穹顶考虑自重的初始预应力简捷计算法[J].工程力学,2009,26(4):1―6.Dong Shilin,Wang Zhenhua,Yuan Xingfei.A simplified calculation method for initial prestress of Levy cable domes with the consideration of self-weight[J].Engineering Mechanics,2009,26(4):1―6.(in Chinese)
[8]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33―37,61.Yuan Xingfei,Dong Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33―37,61.(in Chinese)
[9]袁行飞,董石麟.索穹顶结构的新形式及其初始预应力确定[J].工程力学,2005,22(2):22―26.Yuan Xingfei,Dong Shilin.New forms and initial prestress calculation of cable domes[J].Engineering Mechanics,2005,22(2):22―26.(in Chinese)
[10]曾文平,王元清,张勇,等.索穹顶结构的预应力设计方法[J].工业建筑,2002,32(9):24―26.Zeng Wenping,Wang Yuanqing,Zhang Yong,et al.The method of prestress design for cable dome[J].Industrial Construction,2002,32(9):24―26.(in Chinese)
[11]阚远,叶继红.动力松弛法在索穹顶结构形状确定中的应用[J].工程力学,2007,24(9):50―55.Kan Yuan,Ye Jihong.Form finding of cable domes by modified dynamic relaxation[J].Engineering Mechanics,2007,24(9):50―55.(in Chinese)
[12]Schek H J.The force density method for form finding and computation of general networks[J].Computer Methods in Applied Mechanics and Engineering,1974,3(1):115―134.
[13]Barnes M R.Form finding and analysis of tension structures by dynamic relaxation[J].International Journal of Space Structures,1999,14(2):89―104.
[14]袁行飞,董石麟.索穹顶结构几何稳定性分析[J].空间结构,1999,5(1):3―9.Yuan Xingfei,Dong Shilin.Analysis of geometric stability for cable domes[J].Spatial Structures,1999,5(1):3―9.(in Chinese)
[15]陈联盟,袁行飞,董石麟.索杆张力结构自应力模态分析及预应力优化[J].土木工程学报,2006,39(2):11―15.Chen Lianmeng,Yuan Xingfei,Dong Shilin.Selfstress mode analysis and optimal prestress design of cable-strut tension structures[J].China Civil Engineering Journal,2006,39(2):11―15.(in Chinese)