高层建筑结构扭转耦联振动自振特性的超元法

提出了高层建筑结构扭转耦联振动自振特性简化计算的超元法,将纵横向各片抗侧力结构简化处理成一根等效柱,空间协同分析时,采用超元法(每个单元由多根杆组成)计算等效柱的侧移刚度矩阵,即得各片抗侧力结构的侧移刚度矩阵,从而组集整个结构的侧移刚度矩阵和扭转刚度矩阵,然后,代入扭转耦联无阻尼自由振动方程,用现有数值分析方法可方便求出结构的自振特性.该法自由度成数倍减少,不论是框架、框-剪结构,还是剪力墙结构,计算侧移刚度矩阵具有统一算式,计算简便.     

箱形薄壁结构在翘曲扭转下的截面非线性分析

针对广泛应有于公路行业的钢筋混凝土薄壁构件,本文详细地推导了其在翘曲扭转作用下的截面应力和截面力的具体表达式;综合考虑了混凝土和钢筋对截面整体刚度矩阵的贡献,进一步推导了在翘曲扭转作用下钢筋混凝土薄壁结构截面非线性分析的表达式,对翘曲变形产生的纵向应力采用了有效的研究分析手段.     

大型渡槽结构地震响应分析

大型渡槽槽身采用薄壁杆件结构,渡槽支架与槽身采用盆式橡胶支座连接,根据此结构特点,提出了大型渡槽结构地震响应分析模型.该模型综合考虑了渡槽槽身横向弯扭耦合振动、约束扭转变形、渡槽支架变形和盆式橡胶支座等对渡槽动力响应的影响.采用能量原理给出了渡槽梁段单元的刚度矩阵、质量矩阵和阻尼矩阵的表达式.具体计算了某大型渡槽的地震响应,计算结果表明本文模型计算渡槽结构的地震时程响应与大型结构分析程序SAP93计算的结果十分接近,但本文方法相当简单,计算工作量小,使用方便,是大型渡槽结构地震响应计算的实用模型.     

筒中筒结构在扭矩作用下的超元法

提出筒中筒结构在扭矩作用下的超元法,即是对外框筒及楼板连续化处理以后,视整个结构为一个悬臂杆,然后按楼层划分成超级单元,导出超级单元的刚度矩阵,用矩阵位移法分析.用该法分析变刚度筒中筒结构的扭转问题,自由度很少,计算简便.     

薄壁箱梁的挠曲扭转有限元分析

本文根据薄壁杆件的约束扭转理论和有限元方法,推导了薄壁箱梁的约束扭转刚度矩阵.将此刚度矩阵与一般实体杆件的单元刚度矩阵相组合,并注意到薄壁箱梁截面形心和扭心的差别后导出了建立在形心坐标系下的新的薄壁箱梁弯扭组合刚度矩阵,以便工程应用.此外,对薄壁箱梁非节点载荷的处理方法进行了简要说明.最后用本文推导的新的刚度矩阵分析了某一具有非对称断面的两跨薄壁箱形连续梁.     

偏心支撑压弯构件稳定性分析

对压弯构件在跨中设置侧向支撑和扭转支撑时的稳定性进行研究 ,先就一般情况建立平衡微分方程 ,推导出压弯构件的稳定临界方程 ,在此稳定临界方程的基础上对偏心支撑压弯构件进行详细的分析 ,得到了使压弯构件计算长度减半的扭转支撑临界刚度表达式和侧向支撑临界刚度表达式 ,导出了判断支撑是否能使压弯构件计算长度减半的临界荷载偏心。此外还分析了非完全支撑时支撑刚度和构件承载力的关系 ,以及侧向支撑、扭转支撑及两者联合作用对构件承载力的影响 ,推出了上面所有分析的解析式     

基于能量变分剪切效应空间梁单元刚度矩阵及荷载列阵推导

为了系统研究空间梁单元考虑剪切变形影响时的刚度矩阵及荷载列阵,将能量变分原理应用于空间梁的单元分析。建立了考虑剪切效应的空间梁单元位移函数,利用最小势能原理导出了这种空间梁单元的刚度矩阵和荷载列阵的表达式,显式积分得到单元刚度矩阵,同时计算了平面内部分非节点荷载作用下的等效节点荷载,修正了相关文献中的部分错误。计算结果表明:该方法所得到的单元刚度矩阵与相关文献中其他方法的计算结果完全一致,为编制空间巨型结构的有限元程序奠定基础,对推算其他类型单元刚度矩阵及其荷载列阵也具有理论意义和应用价值。     

基于矩阵求逆理论的曲梁单元刚度矩阵解析解

基于矩阵求逆理论,提出矩阵求逆的综合法。弹性核法求解曲梁单元的刚度矩阵时,由于柔度矩阵的每个元素表达式繁琐,难以直接求逆得到曲梁单元的刚度矩阵。既有相关文献均指出采用数值方法求逆可得出曲梁单元的刚度矩阵。应用矩阵求逆的综合法,推导出曲梁单元刚度矩阵的解析解,并通过算例分析比较,证明了公式的正确性。由此,在编制曲梁杆系梁段有限元的计算程序时,解析解的应用不但简化了程序的编写,而且节约了计算机工作单元,提高了计算精度。     

一种控制结构位移比及扭转效应的方法

《建筑抗震设计规范》规定,在进行高层建筑结构设计时,在计算位移比时应该考虑偶然偏心的影响。本文通过变换位移比计算的另一种表达式,阐明位移比所表达的普遍物理意义,指出结构抗侧刚度与扭转效应存在着一定关系,并通过算例说明适当削弱结构的抗侧刚度有助于控制结构的扭转效应。     

基于等参元理论的钢筋混凝土任意截面的刚度计算

根据有限单元法中的等参元理论,把笛卡尔坐标系下的任意形状截面变换为自然坐标系下的规则形状单元,导出自然坐标系下的钢筋混凝土截面的应变场和刚度矩阵表达式,使用高斯积分法计算截面刚度矩阵各个元素,从而建立计算任意形状截面刚度的通用计算模型。计算过程简单、算法可移植性好、精度较高。用所提出方法对钢筋混凝土双向偏压截面进行非线性全过程分析,计算结果与试验结果吻合良好。     

薄壁钢梁的曲线纤维优化设计工具

研究了用曲线纤维实现变刚度概念的薄壁组合梁可能的性能改进。钢梁的截面为封闭截面,模型中考虑了一些非典型作用如材料各向异性、横向剪力、翘曲限制和非均匀扭转的影响。控制方程由扩展的Hamilton原理导出,运用扩展的Galerkin方法对控制方程求解。给定几何特性和材料特性情况下,优化设计了承受不同荷载组合钢梁以承受最大极限承载力。给出了变刚度梁相对于常规的恒刚度梁的改进之处。     

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.     

On the behavior of thin walled composite beams with stochastic properties under matrix cracking damage

Thin walled composite beam structures are prone to damage which results in change in the performance of these structures. The change in the performance due to damage may get confused with the variation in the performance due uncertainties in the properties of these structures. Here, the performances of the thin walled composite beam under matrix cracking damage having material uncertainties are studied. The cross-sectional stiffness properties are obtained using thin walled beam formulation, which is based on a mixed force and displacement method. The stochastic behaviors of material properties are obtained from previous experimental and analytical studies. The effects of matrix cracking are introduced through the changes in the extension, extension–bending and bending matrices of composites. The effects of matrix cracking on out-of-plane bending, inplane bending and torsion cross-sectional properties are studied at different crack densities for stochastic material properties. Further, the effects of matrix cracking and uncertainties on measurable properties such as deflections and frequencies are studied. Results show that the beam responses at different crack densities get mixed due to the material uncertainties. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms.     

任意形状薄壁钢截面双轴压弯恢复力分析

为适应高耸结构非线性分析的需要，将任意形状薄壁钢截面划分成适当数目的薄壁直边，通过建立薄壁边截面的面内弯矩及轴力与相应变形之间的广义本构关系合成整个截面的双轴压弯恢复力模型。     

Curvilinear fiber optimization tools for design thin walled beams

An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton's principle. Also the extended Galerkin's method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load. Improvements of variable-stiffness beams over conventional, constant-stiffness beams are also demonstrated.     

Coupled flexural–torsional dynamic stiffness matrix of an elastically supported axially loaded beam with shear resistant in‐fill

The dynamic stiffness matrix of an axially loaded elastically supported uniform beam with doubly asymmetric cross‐section that exhibits coupling between flexural and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The beam comprises a thin‐walled outer section that encloses, and works compositely with, a core of shear resistant in‐fill material. The outer layer provides flexure, warping and Saint–Venant rigidity, while the inner layer provides both Saint–Venant and shear rigidity. A three‐parameter Winkler model is used to describe the distributed elastic support. Hamilton's principle is used to derive the partial differential equations governing the free vibration of the beam, together with the associated natural boundary conditions. This gives rise to three coupled equations that are subsequently combined into a single, 12th order, ordinary differential equation. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick–Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using abaqus software. Copyright © 2014 John Wiley & Sons, Ltd.     

Zur Entwicklung der Steifigkeitsmatrizen für dünnwandige Stäbe

On the development of stiffness matrices for thin‐walled members. A glance into the early development of element stiffness matrices for thin‐walled members is given in the present paper and their most mature shapes are shown. Those shapes, the most general and later reduced to two particular forms, refer to the specifics of the classical Vlasov theory of thin‐walled bars [1] as well as to the Bornscheuer systematics of the cross‐sectional properties involved [2]. Appropriate modifications of the relevant matrices are performed and their coordinate system dependence is demonstrated.     

考虑隅角点承托刚性影响薄壁曲线箱梁的空间计算分析

根据薄壁曲线箱梁受载行为 ,为曲梁力学行为的特点 ,考虑其隅角处承托刚性的影响 ,将曲线箱梁板件视为曲线板梁 ,隅角处承托视为曲线梁元 ,由此提出了考虑隅角承托刚性影响薄壁曲线箱梁空间计算的曲线板梁有限单元法     

边梁对板柱结构侧向刚度影响的研究

板柱结构的周边布置边梁可以提高结构的抗震性能。采用等代框架法分析带边梁的板柱结构发现,边梁的抗扭刚度对内框架的侧向刚度影响较小。在边框架中,等代梁的抗弯刚度比边梁的抗弯刚度大,影响因素有板与边梁的抗弯刚度比、受扭构件与板抗弯刚度的比等,给出了边梁抗弯刚度增大系数的计算方法。