索杆梁膜结构体系动力算法优化、特性研究及程序开发
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摘要
索杆梁膜结构由于其造型新颖丰富、构思巧妙、性能优良而越来越受到人们的青睐,被广泛的应用于各类建筑中,显示出巨大的生命力和广阔的应用前景。众多学者对这类结构进行了非常深入的理论研究,但大多还停留在结构找形、荷载静力分析、风振响应等方面,对结构本身的动力特性研究较少。
在计算工具方面,目前国内学者在对索杆梁膜结构进行动力分析时多采用一些大型的通用有限元设计软件,比如ANSYS,SAP2000等。这些设计软件虽然具有很好的计算效率和计算精度,但为了保证良好的通用性,会在单元选择、杆件材料定义、弹性支座设置等方面给索杆梁膜结构的求解带来一些不必要的麻烦。而MSTCAD作为国内主要的空间结构设计与分析软件,虽然具有更为专业化的结构设计与静力计算功能,但在动力分析方面却还存在着很大的空白。本文运用VC++语言编制了索杆梁膜结构的动力分析程序,集成到空间结构设计与分析软件MSTCAD中,并对伞形索膜结构的动力特性进行了系统深入的研究。
本文回顾了索杆梁膜空间结构的发展历程和研究现状,简单介绍了面向对象的编程方法和有限元计算分析方法。
推导了弹性结构的基本动力方程。列出了索杆单元、梁系单元、三角形膜单元的协调质量矩阵和集中单元矩阵,对阻尼矩阵进行了定义和分类。简单介绍了结构的自振特性和动力响应问题。
对广义特征值问题及求解方法做了简要介绍,讨论了传统子空间迭代算法在求解索杆梁膜结构时存在的几点困难,并在此基础上运用移位和更新初始向量技术,提出改进的子空间迭代算法。通过编制动力程序进行算例比较,验证了新算法在求解大型多自由度结构时更高的计算效率和更好的稳定性能。
在LDLT三角分解、向量重正交及丢根判断等步骤上,对Lanczos算法进行了多步优化,同时提出了新的丢根判断方法——模态比较法,并给出算例对优化效果进行了验证。
基于Lanczos算法编制了索杆梁膜动力分析程序,并以多个工程实例为计算模型,与ANSYS计算结果进行了比较验证,体现本文程序的高精度和高效率。
对振型分解反应谱算法进行了推导,指出用其计算索杆梁膜结构体系的几点不足,提出了新的地震效应算法——修正振型分解反应谱算法,并对其推导得到了该算法的两种计算形式,同时对反应谱的效应组合方法展开了探讨。
分析了伞性索膜结构的自振频率和振型,并分别研究了索膜应力比、膜面应力、矢高比等三个主要参数对结构基频和前10阶自振频率的影响。以大量理论数值为依据,
Cable-Strut-Beam-Membrane structure (CSBM) is accepted by more and more researchers for its novelty, ingenious idea and efficiencies. So it is applied in kinds of structures, and shows great vitality and applied future in great span. Lots of researchers have done lots of deep theory research for this special kind of structure. However it still remains in the field of form finding、 static load analysis、 wind-induced vibration, and there is less theory research in the dynamic characteristic.And talking of analyzing tools, researchers in the main land usually use some universal finite element softwares in analyzing the CSBM, such as ANSYS, SAP2000 and so on. Although these kinds of analyzing software owns good calculating efficiency and high calculating precision. But in ordering to make sure the universal application, it brings lots of troubles in choosing element, in defining the beam material characteristic and in setting the elasticity support in analyzing the CABM. Being the important large-space structure designing and analyzing software, although MSTCAD has professional function of structure designing and static force calculating, it still remains great blanks in dynamic analyzing. In this article, dynamic program for CABM is designed by VC++ language, and integrated into MSTCAD. The dynamic characteristic of umbrella-shaped cable-membrane structure is systematically research.This article traced back to the developed history and research condition of CASM, and introduced the Object-Oriented Programming method and Finite Element Method.The article deduced the basic dynamic equation of elastic structure and listed lumped mass matrix and consistent mass matrix for the CASM. It also defined and classified the damping matrix and introduced the problems of structural natural frequency and dynamic response.The calculate method of generalized eigenvalue is simply introduced and it analyses the problems which is encountered in traditional method of subspace iteration method in calculating the CSBM. Compared by dynamic program, it was proved the better calculating efficiency and better stability of the new method in calculating large structures.Lanczos method is optimized in LDLT triangular decomposition 、 vector reorthogonalization and result judgement. At the same time a new method of result judgement is brought forward, and named mode compare method. The example proves the optimized results of the method.
Based on Lanczos method, the CSBM program is designed. According to comparing with ANSYS by analyzing results of several project cases, good efficiency and high precision of the program which is discussed in the article is shown.With deducing the mode decomposition response spectrum method, its several deficiencies in calculating CSBM is pointed out. As a new method for seismic response, the revised mode decomposition response spectrum method is proposed. Furthermore the response combination method of spectrum is discussed.The natural frequency and vibration of the CSBM is analyzed, and the article did different researches in the effect on the structure frequency by three main parameters, such as stress ratio of cable-membrane, membrane stress, rise-span ratio and so on, in separately. By large amount of theory numerical value, a fitting equation of the first frequency for the CSBM is given and proved by calculated model.
在计算工具方面,目前国内学者在对索杆梁膜结构进行动力分析时多采用一些大型的通用有限元设计软件,比如ANSYS,SAP2000等。这些设计软件虽然具有很好的计算效率和计算精度,但为了保证良好的通用性,会在单元选择、杆件材料定义、弹性支座设置等方面给索杆梁膜结构的求解带来一些不必要的麻烦。而MSTCAD作为国内主要的空间结构设计与分析软件,虽然具有更为专业化的结构设计与静力计算功能,但在动力分析方面却还存在着很大的空白。本文运用VC++语言编制了索杆梁膜结构的动力分析程序,集成到空间结构设计与分析软件MSTCAD中,并对伞形索膜结构的动力特性进行了系统深入的研究。
本文回顾了索杆梁膜空间结构的发展历程和研究现状,简单介绍了面向对象的编程方法和有限元计算分析方法。
推导了弹性结构的基本动力方程。列出了索杆单元、梁系单元、三角形膜单元的协调质量矩阵和集中单元矩阵,对阻尼矩阵进行了定义和分类。简单介绍了结构的自振特性和动力响应问题。
对广义特征值问题及求解方法做了简要介绍,讨论了传统子空间迭代算法在求解索杆梁膜结构时存在的几点困难,并在此基础上运用移位和更新初始向量技术,提出改进的子空间迭代算法。通过编制动力程序进行算例比较,验证了新算法在求解大型多自由度结构时更高的计算效率和更好的稳定性能。
在LDLT三角分解、向量重正交及丢根判断等步骤上,对Lanczos算法进行了多步优化,同时提出了新的丢根判断方法——模态比较法,并给出算例对优化效果进行了验证。
基于Lanczos算法编制了索杆梁膜动力分析程序,并以多个工程实例为计算模型,与ANSYS计算结果进行了比较验证,体现本文程序的高精度和高效率。
对振型分解反应谱算法进行了推导,指出用其计算索杆梁膜结构体系的几点不足,提出了新的地震效应算法——修正振型分解反应谱算法,并对其推导得到了该算法的两种计算形式,同时对反应谱的效应组合方法展开了探讨。
分析了伞性索膜结构的自振频率和振型,并分别研究了索膜应力比、膜面应力、矢高比等三个主要参数对结构基频和前10阶自振频率的影响。以大量理论数值为依据,
Cable-Strut-Beam-Membrane structure (CSBM) is accepted by more and more researchers for its novelty, ingenious idea and efficiencies. So it is applied in kinds of structures, and shows great vitality and applied future in great span. Lots of researchers have done lots of deep theory research for this special kind of structure. However it still remains in the field of form finding、 static load analysis、 wind-induced vibration, and there is less theory research in the dynamic characteristic.And talking of analyzing tools, researchers in the main land usually use some universal finite element softwares in analyzing the CSBM, such as ANSYS, SAP2000 and so on. Although these kinds of analyzing software owns good calculating efficiency and high calculating precision. But in ordering to make sure the universal application, it brings lots of troubles in choosing element, in defining the beam material characteristic and in setting the elasticity support in analyzing the CABM. Being the important large-space structure designing and analyzing software, although MSTCAD has professional function of structure designing and static force calculating, it still remains great blanks in dynamic analyzing. In this article, dynamic program for CABM is designed by VC++ language, and integrated into MSTCAD. The dynamic characteristic of umbrella-shaped cable-membrane structure is systematically research.This article traced back to the developed history and research condition of CASM, and introduced the Object-Oriented Programming method and Finite Element Method.The article deduced the basic dynamic equation of elastic structure and listed lumped mass matrix and consistent mass matrix for the CASM. It also defined and classified the damping matrix and introduced the problems of structural natural frequency and dynamic response.The calculate method of generalized eigenvalue is simply introduced and it analyses the problems which is encountered in traditional method of subspace iteration method in calculating the CSBM. Compared by dynamic program, it was proved the better calculating efficiency and better stability of the new method in calculating large structures.Lanczos method is optimized in LDLT triangular decomposition 、 vector reorthogonalization and result judgement. At the same time a new method of result judgement is brought forward, and named mode compare method. The example proves the optimized results of the method.
Based on Lanczos method, the CSBM program is designed. According to comparing with ANSYS by analyzing results of several project cases, good efficiency and high precision of the program which is discussed in the article is shown.With deducing the mode decomposition response spectrum method, its several deficiencies in calculating CSBM is pointed out. As a new method for seismic response, the revised mode decomposition response spectrum method is proposed. Furthermore the response combination method of spectrum is discussed.The natural frequency and vibration of the CSBM is analyzed, and the article did different researches in the effect on the structure frequency by three main parameters, such as stress ratio of cable-membrane, membrane stress, rise-span ratio and so on, in separately. By large amount of theory numerical value, a fitting equation of the first frequency for the CSBM is given and proved by calculated model.
引文
[1] 刘锡良.现代空间结构.天津大学出版社.2003.
[2] 浙江大学建筑工程学院,浙江大学建筑设计研究院.空间结构.中国计划出版社 2003.
[3] 吴晓涵.面向对象结构分析程序设计.科学出版社.2002.
[4] 胡宁.索杆膜空间结构协同分析理论及风振响应研究.浙江大学博士学位论文.2003.
[5] 王荣.索杆梁膜体系动力程序设计及其动力特性研究.浙江大学硕士学位论文.2004.
[6] 年有增.索杆张力结构失稳模态与极限承载力研究.浙江大学硕士学位论文.2004.
[7] 曹国辉.索杆梁模结构体系的协同找形分析研究及程序设计.浙江大学硕士学位论文.2004.
[8] .R.B.Fuller. Tensile-Integrity Structures. US Patent3, 063, 521, 1962.
[9] R.B.Fuller. Synergetics Explorations in the Geometry of Thinking. Collier Macmillan Pubishers. London. 1975.
[10] R.Motro. Tensegrity Systems and Geodesic Domes. Int. J. Space Structures. 1990.
[11] D.G. Emmerich. Constructions de Reseaux Autotendands. Brevet No. 1,377, 290, 1963.
[12] D.G. emmerich. Self-tensioning Spherical Structures: Single and Double Layer Spheroids. Int. j. Space structures. 1990.
[13] O.Vilnay. Structures Made of Infinite Regular Tensegric Nets. IASS Bulletin. 1977.
[14] O.Vilnay. Cable Nets and Tensegric Shells: Analysis and Design Application. Ellis Horword, Chichester. 1990.
[15] 胡宁,罗尧治,董石麟.108m×90m柱面网壳整体提升施工方法.科技通报.2003.
[16] 卓新.空间结构施工方法研究和施工全过程力学分析.浙江大学博士论文.2001.
[17] 肖炽,徐春强.网壳结构外扩法安装.第十届空间结构学术会议论文集.2002.
[18] 孙旭光.网壳结构滑移法施工全过程分析及监测.浙江大学硕士论文.2005.
[19] 赵仁孝,宋根由.空间网架结构施工可靠性分析及其监控技术.工程力学.96增刊.
[20] 翟振锋.光纤光栅传感技术在网架结构健康检测中的应用研究.浙江大学硕士论文.2005.
[21] 杨维国,刘智敏.薄膜体系找形设计中二次找形方法的提出及其力学原理.工程力学.2005.
[22] 卫东,沈世钊.薄膜结构裁剪分析新方法.建筑结构.2002.
[23] 向阳,沈世钊.薄膜结构的使用裁剪设计方法.空间结构.1999.
[24] 膜构造建筑物构造设计手引.计算例集.日本膜构造协会.
[25] 张华,单建.索膜结构的抖振动力特性研究.工程力学.2004.
[26] 余志祥,赵雷.张拉膜结构自振特性研究.西南交通大学学报.2004.
[27] 王勖成,邵敏.有限单元法基本原理和数值方法.清华大学出版社.2002.
[28] R.Courant. Variational Method for Solutions of Problems of Equilibrium and Vibrations. Bull. AN. Math. Soc. 1943.
[29] M.J.Turner, R.W.Clough, L.C.Topp. Stiffness and Deflection Analysis of Complex Structures. J. Aero. Sci. 1956.
[30] R.W. Clough. The Finite Element Method in Plane Stress Analysis. Proc. 2nd ASME Conference on Electronic Computation, Pittsburgh, Pa. 1960.
[31] J.F. Besseling. The Complete Analogy between the Matrix Equations and the Continuous Field Equations of Structural Analysis. International Symposium on Analogue and Digital Techniques Applied to Aeronautics, Liege, Belgium. 1963
[32] J.R. Melosh. Basis for the Derivation of Matrics for the Direct Stiffness Method. AIAAJ. 1963.
[33] R.E.Jones. A Generalization of the Direct Stiffness Method of Structural Analysis. AIAAJ. 1964.
[2] 浙江大学建筑工程学院,浙江大学建筑设计研究院.空间结构.中国计划出版社 2003.
[3] 吴晓涵.面向对象结构分析程序设计.科学出版社.2002.
[4] 胡宁.索杆膜空间结构协同分析理论及风振响应研究.浙江大学博士学位论文.2003.
[5] 王荣.索杆梁膜体系动力程序设计及其动力特性研究.浙江大学硕士学位论文.2004.
[6] 年有增.索杆张力结构失稳模态与极限承载力研究.浙江大学硕士学位论文.2004.
[7] 曹国辉.索杆梁模结构体系的协同找形分析研究及程序设计.浙江大学硕士学位论文.2004.
[8] .R.B.Fuller. Tensile-Integrity Structures. US Patent3, 063, 521, 1962.
[9] R.B.Fuller. Synergetics Explorations in the Geometry of Thinking. Collier Macmillan Pubishers. London. 1975.
[10] R.Motro. Tensegrity Systems and Geodesic Domes. Int. J. Space Structures. 1990.
[11] D.G. Emmerich. Constructions de Reseaux Autotendands. Brevet No. 1,377, 290, 1963.
[12] D.G. emmerich. Self-tensioning Spherical Structures: Single and Double Layer Spheroids. Int. j. Space structures. 1990.
[13] O.Vilnay. Structures Made of Infinite Regular Tensegric Nets. IASS Bulletin. 1977.
[14] O.Vilnay. Cable Nets and Tensegric Shells: Analysis and Design Application. Ellis Horword, Chichester. 1990.
[15] 胡宁,罗尧治,董石麟.108m×90m柱面网壳整体提升施工方法.科技通报.2003.
[16] 卓新.空间结构施工方法研究和施工全过程力学分析.浙江大学博士论文.2001.
[17] 肖炽,徐春强.网壳结构外扩法安装.第十届空间结构学术会议论文集.2002.
[18] 孙旭光.网壳结构滑移法施工全过程分析及监测.浙江大学硕士论文.2005.
[19] 赵仁孝,宋根由.空间网架结构施工可靠性分析及其监控技术.工程力学.96增刊.
[20] 翟振锋.光纤光栅传感技术在网架结构健康检测中的应用研究.浙江大学硕士论文.2005.
[21] 杨维国,刘智敏.薄膜体系找形设计中二次找形方法的提出及其力学原理.工程力学.2005.
[22] 卫东,沈世钊.薄膜结构裁剪分析新方法.建筑结构.2002.
[23] 向阳,沈世钊.薄膜结构的使用裁剪设计方法.空间结构.1999.
[24] 膜构造建筑物构造设计手引.计算例集.日本膜构造协会.
[25] 张华,单建.索膜结构的抖振动力特性研究.工程力学.2004.
[26] 余志祥,赵雷.张拉膜结构自振特性研究.西南交通大学学报.2004.
[27] 王勖成,邵敏.有限单元法基本原理和数值方法.清华大学出版社.2002.
[28] R.Courant. Variational Method for Solutions of Problems of Equilibrium and Vibrations. Bull. AN. Math. Soc. 1943.
[29] M.J.Turner, R.W.Clough, L.C.Topp. Stiffness and Deflection Analysis of Complex Structures. J. Aero. Sci. 1956.
[30] R.W. Clough. The Finite Element Method in Plane Stress Analysis. Proc. 2nd ASME Conference on Electronic Computation, Pittsburgh, Pa. 1960.
[31] J.F. Besseling. The Complete Analogy between the Matrix Equations and the Continuous Field Equations of Structural Analysis. International Symposium on Analogue and Digital Techniques Applied to Aeronautics, Liege, Belgium. 1963
[32] J.R. Melosh. Basis for the Derivation of Matrics for the Direct Stiffness Method. AIAAJ. 1963.
[33] R.E.Jones. A Generalization of the Direct Stiffness Method of Structural Analysis. AIAAJ. 1964.