高层钢框架结构体系稳定分析的样条函数方法

发布时间：2018-02-11 09:26

本文关键词： 钢框架结构稳定分析样条无单元法 QR法几何非线性材料非线性双重非线性程序设计　出处：《广西大学》2014年博士论文　论文类型：学位论文

【摘要】：钢结构具有众多优点,在我国工程建设中的应用越来越广泛,已经是我国主要的结构体系之一。与钢筋混凝土结构相比,钢结构具有强度大、自重轻、抗震性能好、设计灵活、施工方便、工期短、符合产业化要求、符合可持续发展的要求等优点。钢框架是钢结构中最常用的一种结构形式,柱网布置灵活,可采用较大的柱距,而且塑性变形能力强,抗震性好,施工简便,广泛地用于多高层建筑。在高层钢框架结构体系中,钢材强度很高,具有极好的延性,钢构件壁薄修长,构造轻巧。在轴压或压弯作用下,结构可能出现局部或整体失稳,稳定因素控制钢框架和构件的极限承载力。稳定分析是对钢框架进行分析时不可忽略的一个重要环节。在对结构进行稳定分析的众多方法中,有限单元法运用较为广泛。但是运用传统的有限元法分析高层钢框架的稳定问题时,存在未知量多、计算量大、占用资源多等不足。目前比较常见的一些有限元软件在很多情况下无法跟踪结构的加载平衡路径,得不到真正的稳定极限状态。本文旨在研究高层钢框架结构体系稳定分析的样条函数方法,主要作了以下方面工作： (1)基于Kirchhoff薄板理论,建立弹性薄板稳定分析的样条无单元法(SEFM)计算格式；基于Mindlin-Reissner中厚度板理论,把板的挠度和剪应变作为独立的场变量,建立了厚／薄板稳定分析的通用样条无单元法的计算格式；应用特征值失稳来判断临界力。用C语言设计相应的通用程序,通过典型算例说明样条无单元法适用于不同厚度、不同边界的板的稳定分析,且具有精度高、收敛快、自由度少、无剪切闭锁现象、程序简便等优点。可用于框架结构体系中的板的稳定分析。 (2)采用平衡微分方程及稳定函数推导了考虑几何非线性影响的梁柱单元的刚度矩阵。建立了平而钢框架几何非线性性稳定分析的QR法计算格式,用C语言编制了平面钢框架的儿何非线性稳定分析的QR法计算程序。通过算例分析说明几何非线性对钢框架结构稳定的影响不能忽略,而QR法的计算格式简单,而且精度高,不但可以计算结构整体失稳的临界荷载,而且跟踪整个加载路径,在钢框架的稳定分析方面很有优势。 (3)在几何非线性稳定分析的基础上,同时考虑材料非线性和几何非线性,应用本文推导的梁柱单元刚度矩阵,用荷载增量法建立结构非线性分析的增量刚度方程,采用塑性铰模型,建立钢框架双重非线性稳定分析的QR法计算格式,采用Euler-修正的Newton法求解非线性方程组,用切线刚度法跟踪结构的整个非线性平衡路径,并用C语言设计了相应的通用计算程序。通过典型的算例分析,分析了材料非线性对结构稳定的影响,证明了钢框架双重非线性稳定分析的QR法的可行性和优越性。QR法计算格式简单,未知量少,计算精度高,不会因为塑性铰的出现修正结构的计算网格和自由度,以结构的整体失稳作为程序计算的终止条件,不会因为局部失稳破坏而影响后续的增量计算。 (4)利用本文算法编制钢框架结构体系稳定性分析的软件包,可用于平面框架及楼板的稳定性分析。以目前广西最高的钢结构商务大楼-广西中烟工业有限责任公司研发中心办公楼为工程实例,利用软件包对其进行稳定分析,评定该结构的稳定性能。
[Abstract]:The steel frame is one of the main structural systems in our country . Compared with the reinforced concrete structure , the steel structure has the advantages of large strength , light weight , good aseismatic performance , flexible design , convenient construction , short construction period , meeting industrialization requirements , meeting the requirements of sustainable development , etc . The steel frame is one of the most commonly used structural forms in the steel structure , and has the advantages of high column spacing , strong plastic deformation capability , good shock resistance , simple and convenient construction , and is widely used for many high - rise buildings . In the high - rise steel frame structure system , the strength of the steel is very high , it has excellent ductility , the wall of the steel member is thin and long , and the structure is light . Under the action of axial compression or bending , the structure may be locally or integrally unstable , and the stability factor controls the ultimate bearing capacity of the steel frame and the component . The stability analysis is an important link which can not be neglected in the analysis of the steel frame . The finite element method is widely used in many methods for the stability analysis of the structure . However , the traditional finite element method is used to analyze the stability of the high - rise steel frame . The purpose of this paper is to study the spline function method for the stability analysis of high - rise steel frame structure system , which mainly works as follows : ( 1 ) Based on the thin plate theory , a spline - free method ( SEFM ) method for the stability analysis of elastic thin plates is established . Based on the theory of the thickness plate , the paper establishes a general spline non - element method for the stability analysis of thick / thin plates based on the theory of the thickness plate in Minlin - Reissner . It has the advantages of high precision , fast convergence , few degrees of freedom , no shear locking , simple procedure and the like , and can be used in the stability analysis of the plates in the frame structure system . ( 2 ) The stiffness matrix of beam - column units considering geometric nonlinearity is derived by using equilibrium differential equations and stable functions . The QR method for the stability analysis of the geometrical nonlinear stability of the steel frame is established . The QR method for the nonlinear stability analysis of the plane steel frame is compiled by C language . The calculation method of QR method is simple , and the precision is high , which not only can calculate the critical load of the whole instability of the structure , but also trace the whole loading path , and has the advantage in the stability analysis of the steel frame . ( 3 ) On the basis of geometric nonlinear stability analysis , considering the nonlinear and geometric nonlinearity of materials , the stiffness matrix of the beam - column element deduced from this paper is applied , and the incremental stiffness equation of the structure nonlinear analysis is established by the load increment method . ( 4 ) A software package for stability analysis of steel frame structure system is developed by using the algorithm , which can be applied to the stability analysis of plane frame and floor .

【学位授予单位】：广西大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU973.13

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