Q460高强钢焊接工字形截面单伸臂梁整体稳定性能与设计方法研究

为研究Q460高强钢焊接工字形截面单伸臂梁的整体稳定性能以及完善规范中关于此类构件的设计方法,进行了6根集中荷载作用下Q460高强钢焊接工字形截面单伸臂梁的整体稳定性能试验,测量了试件的初始几何缺陷和截面残余应力。试验结果表明：当单伸臂梁整体失稳的控制梁段位于简支跨时,单伸臂梁的整体稳定承载力随伸臂长度比的增大而减小,截面高宽比较伸臂长度比对单伸臂梁整体稳定承载力的影响更大。在试验基础上,运用有限元程序创建考虑初始几何缺陷和残余应力的有限元模型对试验进行模拟,模拟结果与试验结果吻合良好;基于试验验证的有限元模型,分析荷载形式、荷载比例、简支跨长度、伸臂跨长度和截面高宽比等因素对Q460高强钢焊接工字形截面单伸臂梁整体稳定承载力的影响规律。基于特征值屈曲分析结果,回归出单伸臂梁的弹性屈曲临界弯矩计算公式,并通过对试验结果和有限元参数分析结果的回归提出了Q460高强钢焊接工字形截面单伸臂梁的极限弯矩计算公式。     

从 Levinson 高阶梁理论的一致变分到高次翘曲梁理论

将矩形截面梁的截面翘曲位移设定为3次Legendre多项式的形式,利用弹性力学平面应力问题分项的不完全的广义变分原理,导出高次翘曲梁理论,得到形式简单易求解的方程。由于引入轴向拉伸的情况,使梁的平面内变形问题得以统一;计及了梁表面剪切荷载的作用,并严格满足表面剪应力边界条件;通过引入轴向位移约束参考点间距离的概念对梁端翘曲约束作更精致地描述,且使得该理论包含了变分一致或者不一致的高阶剪切梁理论。该理论的推导还表明,Levinson梁理论的变分不一致仅仅局限于有转角约束的梁端。通过算例,将高次翘曲梁理论与弹性力学平面应力问题以及Timoshenko梁理论、Levinson梁理论进行比较,初步显示出该理论的优越性。     

弹性约束下Timoshenko夹层梁的热屈曲行为研究

综合考虑构件轴线伸长和1阶横向剪切变形等条件下,建立横向受热作用且周围有弹性支承约束的夹层梁几何非线性精确数学模型。利用打靶法数值方法获得了两端转角弹簧与横向弹性地基共同约束时夹层梁的静态热过屈曲数值解。改变梁端转角弹簧刚度,获得不同的临界屈曲温度;当改变夹层梁物性参数时,给出平均升温参数与水平轴向压力之间的关系曲线;当两端转角弹簧刚度和弹性地基刚度同时给定时,分析非均匀升温参数与夹层梁热过屈曲和热弯曲组合变形之间的关系。     

基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究

基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。     

中间约束轴向运动梁横向非线性振动

聚焦于中间弹性约束对轴向运动梁横向非线性振动的影响。应用哈密顿原理,建立带有中间弹簧支撑的轴向运动梁的动力学控制方程。通过Galerkin截断方法数值计算了简支边界梯型截面轴向运动梁的固有频率,并数值计算得到梁的稳态响应。着重讨论了中间约束弹簧的刚度、系统的轴向运动速度、不同Galerkin截断阶数对系统固有频率、非线性受迫振动稳态响应的影响。研究发现,中间约束弹簧显著改变轴向运动梁的横向振动特性,而且轴向运动的速度能够改变中间弹簧对系统横向振动的影响。     

有侧移半刚性连接组合框架柱的有效长度系数

利用三层柱的框架模型,考虑了节点的非线性弯矩-转角关系、楼板的组合效应、梁端和柱远端不同边界情况等因素对柱的有效长度系数的影响,推导了有侧移半刚性连接组合框架柱的有效长度系数方程式,并分析了GB50017-2003规范附录D求解的精确性,最后用两个实例:门式组合框架和三层两跨组合框架,研究了荷载大小和非线性弯矩-转角关系对柱有效长度系数的影响。研究表明,对于有侧移半刚性连接组合框架柱,当柱远端处于不同边界条件时,用GB50017-2003规范附录D求得的有效长度系数设计柱偏于安全;节点初始刚度对有效长度系数影响较明显。研究结果可供工程设计参考。     

解析型弹性地基Timoshenko梁单元

采用双参数弹性地基模型和Timoshenko深梁模型,建立了弹性地基一般梁挠度控制方程,求解得到了挠度方程解析通解,构建了双参数弹性地基深梁的挠度、截面弯曲转角及剪切角的解析位移形函数。建立了梁模型、梁基模型等两种势能泛函,利用最小势能原理,构造了两个双参数弹性地基深梁单元,给出了单元列式。分析表明:梁模型单元在均布荷载作用下误差为0.221%,非均布荷载作用下误差为0;梁基模型单元在均布荷载作用下误差为0,在两端集中力作用下误差为6.597%,在跨中集中力作用下误差为102.716%;同时,该文提出的双参数Timoshenko梁模型单元不存在剪切闭锁的问题。     

爆炸荷载作用下承重柱的弹性动力响应分析

为了建立爆炸荷载作用下承重柱构件的弹性动力响应分析方法,进一步奠定研究承重柱非线性抗爆响应和破坏形态的理论基础,该文将承重柱简化为承受轴向荷载的约束梁构件,并基于经典Timoshenko梁理论,通过建立等效频率矩阵、等效荷载向量矩阵以及修正的等效质量矩阵,采用变量分离法联立方程求解,推导出承受恒定轴力的Timoshenko梁在任意横向爆炸荷载作用下的弹性动力响应的解析解;并以此弹性解析方法为基础,进一步分析讨论了爆炸荷载作用下,长细比、初始轴向应变、端部约束条件及荷载参数等因素对承重柱弹性动态响应的影响,研究结果对钢柱或钢筋混凝土柱(RC柱)的抗爆分析与设计有参考作用。     

半刚接钢框架的弹性屈曲研究

本文通过对梁的转角位移方程的修正,以考虑节点柔性对钢框架屈曲强度的影响,并建立了半钢接框架梁柱单元刚度矩阵。在此基础上,分析研究了半刚性连续在不同初始转动刚度下,单层单跨有侧移钢框架的屈曲荷载,得出了相关的结论。     

基于截面组合法和截面弹簧刚度考虑跨内塑性铰的钢框架高等分析

采用截面组合法推导工字形或H形截面的屈服方程, 并在端部和跨内分别假想有一个零长度的弹簧考虑截面的刚度, 提出了有分布荷载作用的杆件仅使用一个单元就能准确模拟跨内塑性铰的钢框架高等分析方法。通过对引入的非节点自由度进行凝聚, 使得所提出的单元与常规单元具有相同的节点自由度。该方法还利用稳定函数考虑单元的剪切变形和几何非线性、初始屈服方程中考虑残余应力、折减弹性模量法考虑初始缺陷。算例结果表明, 采用所提出的方法可得到高效率和高精度的结果。     

Theory and numerics of three‐dimensional beams with elastoplastic material behaviour

A theory of space curved beams with arbitrary cross‐sections and an associated finite element formulation is presented. Within the present beam theory the reference point, the centroid, the centre of shear and the loading point are arbitrary points of the cross‐section. The beam strains are based on a kinematic assumption where torsion‐warping deformation is included. Each node of the derived finite element possesses seven degrees of freedom. The update of the rotational parameters at the finite element nodes is achieved in an additive way. Applying the isoparametric concept the kinematic quantities are approximated using Lagrangian interpolation functions. Since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells. Due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load‐carrying capacity of beam structures. Copyright © 2000 John Wiley & Sons, Ltd.     

A hybrid force/stiffness matrix method for the analysis of thin-walled composite frames

A novel method for the analysis of frames constructed of thin-walled members of anisotropic composite materials is presented in this paper. The method accounts for non-isotropic coupling effects that exist in composite material beams due to the anisotropy of the composite material laminates that form the thin-walled cross section. The method also accounts for warping effects known to be significant in thin-walled members. The analysis is performed by the direct stiffness matrix method utilizing a new approach that divides each thin-walled member of the frame into one-dimensional warping-beam superelements and non-warping conventional beam elements. The element stiffness matrices for these two one-dimensional beam elements are obtained by a numerical procedure that is based on the classical force method analysis. The stiffness matrices of both beam elements are 12 × 12 matrices corresponding to the six degrees of freedom per node required for conventional space frame analysis. The remarkable feature of this representation is that warping is accounted for without introducing additional degrees of freedom to account for the bimoment and warping twist in the members. This is accomplished by use of the warping-beam superelement that linearizes the regions of non-uniform torsion in the thin-walled beam. Examples of space frame structures constructed of thin-walled composite material I-beams are presented to demonstrate the method. Results of analyses using the proposed method are compared with those obtained from two-dimensional finite element models.     

梁杆结构二阶效应分析的一种新型梁单元

推导了一种计及梁杆二阶效应的新型两结点梁单元。首先依据插值理论构造了三结点Euler-Bernoulli梁单元的位移场:使用五次Hermite插值函数建立梁单元的侧向位移场,二次Lagrange插值函数建立梁单元的轴向位移场,进而由非线性有限元理论推导了单元的线性刚度矩阵和几何刚度矩阵,然后使用静力凝聚方法消除三结点梁单元中间结点的自由度,从而得到一种考虑轴力效应的新型两结点梁单元。实例分析表明,此新型梁单元具有很高的计算精度,使用此单元进行梁杆结构分析可获得相当准确的二阶位移和内力。     

大跨度斜拉桥空间振动计算分析

本文提出了一种分析列车、大跨度钢桁梁斜拉桥系统空间振动的方法.文中采用21个自由度的列车空间振动模型,对斜拉桥桁架、桥塔、拉索分别采用桁段有限单元、空间梁元、空间杆元来模拟,计算了列车以不同车速通过大跨度斜拉桥的空间振动响应,所得结果可供设计参考.     

An improved theory and finite-element model for laminated composite and sandwich beams using first-order zig-zag sublaminate approximations

A new beam finite element based on a new discrete-layer laminated beam theory with sublaminate first-order zig-zag kinematic assumptions is presented and assessed for thick and thin laminated beams. The model allows a laminate to be represented as an assemblage of sublaminates in order to increase the model refinement through the thickness, when needed. Within each sublaminate, discrete-layer effects are accounted for via a modified form of DiSciuva's linear zig-zag laminate kinematics, in which continuity of interfacial transverse shear stresses is satisfied identically. In the computational model, each finite element represents one sublaminate. The finite element is developed with the topology of a fournoded rectangle, allowing the thickness of the beam to be discretized into several elements, or sublaminates, if necessary, to improve accuracy. Each node has three engineering degrees of freedom, two translations and one rotation. Thus, this element can be conveniently implemented into general purpose finite-element codes. The element stiffness coefficients are integrated exactly, yet the element exhibits no shear locking due to the use of a consistent interdependent interpolation scheme. Numerical performance of the current element is investigated for an arbitrarily layered beam, a symmetrically layered beam and a sandwich beam with low and high aspect ratios. The comparisons of numerical results with elasticity solutions show that the element is very accurate and robust.     

A TORSIONAL SPRING-LIKE BEAM ELEMENT FOR THE DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS

A new finite element beam formulation for modelling flexible multibody systems undergoing large rigid-body motion and large deflections is developed. In this formulation, the motion of the ‘nodes’ is referred to a global inertial reference frame. Only Cartesian position co-ordinates are used as degrees of freedom. The beam element is divided into two subelements. The first element is a truss element which gives the axial response. The second element is a torsional spring-like bending element which gives the transverse bending response. D'Alembert principle is directly used to derive the system's equations of motion by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to determine the flexible deformations of the element and to extract those deformations from the total element motion. The equations of motion are solved along with constraint equations using a direct iterative integration scheme. Two numerical examples which were presented in earlier literature are solved to demonstrate the features and accuracy of the new method.     

A finite element for edge-cracked beam columns

The stiffness matrix is derived for a finite element representing a beam column with rectangular cross section and a single edge crack. The element has zero length, and the standard nodal degrees of freedom associated with beam-column elements. To illustrate its capabilities, the element is used to model propagation of multiple cracks in a self-loaded fixed beam.