一种新的薄壁杆件单元扭转刚度矩阵

本文提出一种新的薄壁杆件单元扭转刚度矩阵,它能够计及二次剪应力对翘曲变形的影响,并适用于任意剖面(包括开口,闭口和混合剖面)的薄壁杆件。计算表明,这个新的扭转刚度矩阵有相当好的精确度,可以代替Kawai或Gunnlaugsson-Pedersen的刚度矩阵,用于薄壁杆件的有限元静动力分析。     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

薄壁杆约束扭转的单肢解析化分析方法

针对薄壁杆件约柬扭转的基本受力反应分析问题,采用与符拉索夫的经典约束扭转理论截然不同的立论途径,将自由扭转刚度视为调整因素,而将剥离了该抗力效应的薄壁杆件基本体系作为主要分析对象,推导出基于翘曲理论并考虑了自由扭转刚度影响的杆件刚度方程及结问荷载的等效措施.此外,提出了基于微段薄壁杆简化单刚的有效数值化分析方法.上述研究表明,对于钢构件等具有薄壁构型截面形式的杆件,这种单肢解析化分析方法无需进行复杂的截面特性如弯、翘曲惯矩或弯、形心坐标等的分析,力与变形的表达简洁、直接,本文的抗力性能分析和表述方式可为薄壁构件的稳定及畸变等研究提供新的思路切入点.     

薄壁杆系结构的梁元分析模型

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型，在空间梁元分析模型^[3]的基础上，采用了一种改进的位移模式，考察了薄壁杆件可能发生的拉压，剪切，弯曲，扭转和翘曲等各变形形式以及它们的耦合效应，得出了相应的单元形函数，同时从工程应变的定义出发，采用Taylor级数展开的方法，建立了单元的五阶近似正交变表达式，并建立了相应的薄壁单元刚度方程，从而得出了局部坐标系下单元刚度矩阵的显式，根据本文所导出的薄壁梁元分析模型，编制了相应的结构计算程序，通过算例验证了本文所推导的单元刚度矩阵，同时通过与传统空间梁元计算模型计算结果的比较，阐述了截面翘曲对薄壁杆系结构的影响。     

大型渡槽动力建模研究

根据渡槽系薄壁杆件结构的特点,提出了渡槽薄壁结构空间动力分析模型。采用空间梁段单元进行离散,考虑渡槽横向、竖向、纵向、自由扭转和约束扭转变形,由能量原理推导给出了渡槽槽身结构的单元刚度矩阵、质量矩阵的显示表达式;渡槽支架采用空间梁单元模拟;渡槽支架与槽身联贯的盆式橡胶支认采用弹性元件单元模拟。文中具体计算了某大型渡槽的模态,计算结果表明：该模型计算渡槽结构的固有频率与理论解和用大型结构分析程序SAP计算的结果良好接近。本文模型计算简单,使用方便,是大型渡槽动力分析的实用模型。     

基于新型广义位移的箱形梁扭转单元及应用

为了改进变截面连续箱梁桥的扭转分析理论，将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角，选取自由翘曲转角扭率作为广义位移，提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发，推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数，以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析，结果表明，双力矩影响线与弯矩影响线较为类似，按双力矩影响线进行最不利荷载加载时最大应力值偏小；应力增大系数在集中荷载作用截面出现极值，均发生在腹板与顶板交点处；利用偏载放大系数来考虑扭转附加效应时，不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。     

开口薄壁梁的扭转理论与应用

以Vlasov薄壁构件理论为基础, 推导了开口薄壁构件一阶扭转理论. 该理论考虑了翘曲剪应力对截面转角的影响, 截面的转角分为自由翘曲转角和约束剪切转角, 在约束扭转中, St.Venant扭矩仅仅与自由翘曲转角有关, 而翘曲扭矩仅与约束剪切转角有关. 利用半逆解方法求出了约束扭转中薄壁构件的St.Venant扭矩表达公式; 依据能量方法, 建立了约束剪切转角和翘曲扭矩之间的关系, 并提出了翘曲剪切系数概念, 给出了一阶扭转理论的微分方程. 为了有效求解微分方程, 给出了求解微分方程的初参数法方程和相应的影响函数矩阵; 当St.Venant扭矩可以忽略时, 得到与一阶弯曲理论(Timoshenko梁理论)相似的一阶扭转理论简化形式. 最后利用算例证明了一阶扭转理论和简化理论的有效性.      

薄壁箱梁的翘曲连续性条件

基于薄壁杆件理论,分析了薄壁箱梁弯曲剪流和约束扭转翘曲剪流计算时的翘曲连续性 条件. 从翘曲连续性条件出发,推导了薄壁箱梁约束扭转翘曲剪流的一般公式,此外,还指 出了有关文献中的错误并进行了更正. 最后对一个悬臂箱梁的约束扭转翘曲剪流进行了计算 比较.     

复室开闭口混合薄壁截面翘曲座标的计算

本文试图对复室开闭口混合薄壁截面翘曲座标的计算作一简介。应用了广义扇形座标计算的原则,对二种类型的上述截面的计算,作了示例。翘曲座标值,仍以计算公式表示之。本文并简述了复室混合截面薄壁杆件和复室闭合截面薄壁杆件扭转计算的异同。     

钢框架高等分析中考虑局部屈曲的子结构法

将相对自由度概念引入三维实体等参数单元,得到了16结点相对自由度壳元的插值表达式,并基于更新拉格朗日构型的虚位移原理推导了该壳单元的刚度矩阵。在单元刚度矩阵形成以后采用子结构法对内部结点自由度进行聚缩,根据薄壁构件相关假定并考虑截面翘曲因素的影响,通过边界结点的位移协调条件把壳单元组装成每端7个自由度的薄壁梁-柱单元参与整体分析,可以考虑板件局部屈曲的影响;突破了传统分析的紧凑型截面限制,并通过算例证明了本文方法的精确度和有效性。     

Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams

The dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli–Euler beam element whose elastic and inertia axes are not coincident by directly solving the governing differential equations of motion of the beam element. Bernoulli–Euler beam theory is used, and the cross section of the beam does not have any symmetrical axes. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix method is used for calculation of exact natural frequencies and mode shapes of the nonsymmetrical thin-walled beams. Numerical results are given for a specific example of thin-walled beam under a variety of end conditions, and exact numerical solutions are tabulated for natural frequencies and solutions calculated by the other method are also tabulated for comparison. The effects of axial force and warping stiffness are also discussed.     

Dynamic analysis of 3-D beam elements including warping and shear deformation effects

In this paper the dynamic analysis of 3-D beam elements restrained at their edges by the most general linear torsional, transverse or longitudinal boundary conditions and subjected in arbitrarily distributed dynamic twisting, bending, transverse or longitudinal loading is presented. For the solution of the problem at hand, a boundary element method is developed for the construction of the 14 × 14 stiffness matrix and the corresponding nodal load vector of a member of an arbitrarily shaped simply or multiply connected cross section, taking into account both warping and shear deformation effects, which together with the respective mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach that is only boundary discretization is used. Both free and forced transverse, longitudinal or torsional vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance. Numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the dynamic analysis of a space frame. Moreover, the discrepancy in the dynamic analysis of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members.     

A new super convergent thin walled composite beam element for analysis of box beam structures

In this paper, a new composite thin wall beam element of arbitrary cross-section with open or closed contour is developed. The formulation incorporates the effect of elastic coupling, restrained warping, transverse shear deformation associated with thin walled composite structures. A first order shear deformation theory is considered with the beam deformation expressed in terms of axial, spanwise and chordwise bending, corresponding shears and twist. The formulated locking free element uses higher order interpolating polynomial obtained by solving static part of the coupled governing differential equations. The formulated element has super convergent properties as it gives the exact elemental stiffness matrix. Static and free vibration analyses are performed for various beam configuration and compared with experimental and numerical results available in current literature. Good correlation is observed in all cases with extremely small system size. The formulated element is used to study the wave propagation behavior in box beams subjected to high frequency loading such as impact. Simultaneous existence of various propagating modes are graphically captured. Here the effect of transverse shear on wave propagation characteristics in axial and transverse directions are investigated for different ply layup sequences.     

Buckling of short beams with warping effect included

A beam theory for the stability analysis of short beam that includes shear deformation and warping of the cross-section is developed. The warping of the cross-section is taken to be an independent kinematics quantity and corresponding force resultants are defined. For the beam subjected to the external loading only at the ends of the beam, equilibrium equations have been obtained by the principle of virtual work. The variations of lateral displacement, rotational angle of the cross-section and the multiplier of the warping shape along the beam axis are solved in closed form and expressed in terms of deformation quantities at the ends of the beam. Based on this beam theory, the lateral stiffness of the beam sustained an axial compression force and a lateral shear force at one end is explicitly derived, from which the equation of the buckling load is established and the buckling load can be solved. When the effect of cross-section warping is neglected, the derived lateral stiffness and buckling load converge to the solutions of the Haringx theory.     

一种考虑初始缺陷影响的非线性梁单元

在目前广泛应用的梁单元中,尚缺乏全面考虑以下四种因素影响的粱单元：(1)轴力的影响;(2)剪切交形的影响;(3)初始弯曲的影响;(4)弯曲变形对轴向应变的影响,即弓形效应。事实上,以上四种非线性因素都会对钢框架结构的稳定和极限承载力有影响,需同时考虑。本文将致力于推导同时考虑以上四种因素影响的平面梁单元的平衡微分方程,最后得到精确的粱单元刚度矩阵,并研究以上四种因素对钢框架构件及钢框架结构的影响。     

箱形梁剪力滞和剪切效应引起的附加挠度分析

将箱形梁腹板剪切变形纳入初等梁挠曲变形,在全截面上引入剪力滞翘曲修正系数,重新定义了剪力滞翘曲位移模式。选取剪力滞效应引起的附加挠度为广义位移,计算外力势能时考虑剪力滞广义位移的影响,应用能量变分法建立了反映剪力滞和剪切效应的控制微分方程,并导出了均布荷载作用下简支箱梁和两跨连续箱梁剪力滞和剪切效应附加挠度的解析解。数值算例表明,本文方法计算的总挠度值与有限元数值解吻合良好,从而验证了本文方法的合理性。算例箱梁剪切附加挠度明显大于剪力滞附加挠度;简支箱梁跨中截面的剪切和剪力滞附加挠度分别占初等梁挠度的2.50%和1.97%,两跨连续箱梁距中支点9l/16截面分别占27.45%和16.87%。     

Stress resultants plasticity with general closest point projection

In this paper, general closest point projection algorithm is derived for the elastoplastic behavior of a cross-section of a beam finite element. For given section deformations, the section forces (stress resultants) and the section tangent stiffness matrix are obtained as the response for the cross-section. Backward Euler time integration rule is used for the solution of the nonlinear evolution equations. The solution yields the general closest projection algorithm for stress resultants plasticity model. Algorithmic consistent tangent stiffness matrix for the section is derived. Numerical verification of the algorithms in a mixed formulation beam finite element proves the accuracy and robustness of the approach in simulating nonlinear behavior.