高层钢框架结构体系稳定分析的样条函数方法
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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。
With many advantages, steel structure is more and more widely used in construction, now has become one of China's major structural system. Compared with the reinforced concrete structure, steel structure has some advantages, such as high strength, light weight, good anti-seismic performance, design flexibility, easy construction, short construction period, in line with industrial requirements, meet the requirements of sustainable development and so on. Steel frame, one of the most popular styles of steel structure, is flexible in column arrangement, large in column space, excellent in plastic performance, good for anti-seismic, simple in construction and widely used in many high-rise buildings.
Since steel has high strength and excellent ductility, frame members is slender, thin-walled and light in high-rise steel frame system. In axial compression or bending, the structure may be local or global instability, and then stability factors control the ultimate strength of steel frame and its components. So stability analysis is very important while analyzing steel frames.
Among so many methods for structure stability analysis, the finite element method is widely used. But traditional finite element method has much unknown quantity, resource occupation and calculation. Much finite element software can not track the loading path in many cases. The real ultimate stability state can not be achieved.
This thesis aims to study the spline function methods for high-rise steel frame structure stability analysis. The main works includes:
(1) Based on Kirchhoff thin-plate theory, the spline element-free method (SEFM) computation format for elastic thin plate stability analysis is established. The spline element-free method computation format for the stability analysis of thick/thin plate is established based on Mindlin-Reissner theory, which takes deflection and shear strains as the independent field variables. The critical force is determined by eigenvalue buckling. The general program is composed by C language. The results of examples shows that this method has many advantages such as high precision, rapid convergence, less degree of freedom, no shear locking phenomenon, easy to be programmed, applicable for the stability analysis of the plate with various boundaries and various thickness. It can be used to analyze the plate in frame structure.
(2) Using beam-to-column theory and stable function, the stiffness matrix of beam-to-column which considered geometric nonlinear is developed. The computation format of QR method for the geometric nonlinear stability analysis of plan steel frame is conducted and adopted to programming by C language. The examples show that the effecting of geometry nonlinear to the stability analysis of steel frames can not be neglected. QR method has simple computation format and high precision, not only can calculate the critical load of whole instability of structure, but also can track the entire loading path. QR method has great advantages on steel frame stability analysis.
(3) Based on the geometric nonlinear stability analysis, taking both material nonlinearity and geometric nonlinearity into account, using the stiffness matrix of beam-to-column developed in this thesis, the nonlinear stability analysis incremental stiffness equation by load incremental method is established. Plastic hinge model is used to establish the QR method format for double nonlinear stability analysis of steel frame. The Euler-modified-Newton method is used to solve the nonlinear equations. The tangent stiffness method is applied to trace the nonlinear equilibrium path of the structure. General computer program is composed by C language. Through typical examples, the effecting of material nonlinearity to structure stability is analyzed, which proofs the feasibility and superiority of QR method for double nonlinear stability analysis of steel frame. QR method has simple computation format, less unknown and high precision, do not need to modify the computational grid and the degree of freedom of structure to meet the appearance of plastic hinges, takes the overall instability as the termination condition. So the subsequent incremental calculation will not be terminated by local buckling damage.
(4) A software of steel frame structure stability analysis which programmed by the algorithm of this thesis is introduced. It can be used to analyze the stability of plane frame and plate. Then takes the Guangxi Tobacco Industrial Co., Ltd. Research and Development Center Building as example, uses that software to analyze its stability, assess the stability of the structure.
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。
With many advantages, steel structure is more and more widely used in construction, now has become one of China's major structural system. Compared with the reinforced concrete structure, steel structure has some advantages, such as high strength, light weight, good anti-seismic performance, design flexibility, easy construction, short construction period, in line with industrial requirements, meet the requirements of sustainable development and so on. Steel frame, one of the most popular styles of steel structure, is flexible in column arrangement, large in column space, excellent in plastic performance, good for anti-seismic, simple in construction and widely used in many high-rise buildings.
Since steel has high strength and excellent ductility, frame members is slender, thin-walled and light in high-rise steel frame system. In axial compression or bending, the structure may be local or global instability, and then stability factors control the ultimate strength of steel frame and its components. So stability analysis is very important while analyzing steel frames.
Among so many methods for structure stability analysis, the finite element method is widely used. But traditional finite element method has much unknown quantity, resource occupation and calculation. Much finite element software can not track the loading path in many cases. The real ultimate stability state can not be achieved.
This thesis aims to study the spline function methods for high-rise steel frame structure stability analysis. The main works includes:
(1) Based on Kirchhoff thin-plate theory, the spline element-free method (SEFM) computation format for elastic thin plate stability analysis is established. The spline element-free method computation format for the stability analysis of thick/thin plate is established based on Mindlin-Reissner theory, which takes deflection and shear strains as the independent field variables. The critical force is determined by eigenvalue buckling. The general program is composed by C language. The results of examples shows that this method has many advantages such as high precision, rapid convergence, less degree of freedom, no shear locking phenomenon, easy to be programmed, applicable for the stability analysis of the plate with various boundaries and various thickness. It can be used to analyze the plate in frame structure.
(2) Using beam-to-column theory and stable function, the stiffness matrix of beam-to-column which considered geometric nonlinear is developed. The computation format of QR method for the geometric nonlinear stability analysis of plan steel frame is conducted and adopted to programming by C language. The examples show that the effecting of geometry nonlinear to the stability analysis of steel frames can not be neglected. QR method has simple computation format and high precision, not only can calculate the critical load of whole instability of structure, but also can track the entire loading path. QR method has great advantages on steel frame stability analysis.
(3) Based on the geometric nonlinear stability analysis, taking both material nonlinearity and geometric nonlinearity into account, using the stiffness matrix of beam-to-column developed in this thesis, the nonlinear stability analysis incremental stiffness equation by load incremental method is established. Plastic hinge model is used to establish the QR method format for double nonlinear stability analysis of steel frame. The Euler-modified-Newton method is used to solve the nonlinear equations. The tangent stiffness method is applied to trace the nonlinear equilibrium path of the structure. General computer program is composed by C language. Through typical examples, the effecting of material nonlinearity to structure stability is analyzed, which proofs the feasibility and superiority of QR method for double nonlinear stability analysis of steel frame. QR method has simple computation format, less unknown and high precision, do not need to modify the computational grid and the degree of freedom of structure to meet the appearance of plastic hinges, takes the overall instability as the termination condition. So the subsequent incremental calculation will not be terminated by local buckling damage.
(4) A software of steel frame structure stability analysis which programmed by the algorithm of this thesis is introduced. It can be used to analyze the stability of plane frame and plate. Then takes the Guangxi Tobacco Industrial Co., Ltd. Research and Development Center Building as example, uses that software to analyze its stability, assess the stability of the structure.
引文
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