A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Stability Analysis of Spatial Cubic Spline Geometric Nonlinear Beam Element Considering the Second-Order Effect

To analyze the stability problem of spatial beam structure more accurately, a spatial cubic spline geometric nonlinear beam dement was proposed considering the seeond-order effect. The deformation field was built with cubic spline function, and its curvature degree of freedom （DOF） was eliminated by static condensation method. Then we got the geometric nonlinear stiffness matrix of the new spatial two.node Euler-Bernouili beam dement. Several examples proved calculation accuracy of the critical load by meshing a bar to one element using the method of this paper was equivalent to mesh a bar to 3 or 4 traditional nonlinear beam dements.

Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Determination of reasonable finished state of self-anchored suspension bridges

A systematic and generic procedure for the determination of the reasonable finished state of self-anchored suspension bridges is proposed, the realization of which is mainly through adjustment of the hanger tensions. The initial hanger tensions are first obtained through an iterative analysis by combining the girder-tower-only finite element(FE) model with the analytical program for shape finding of the spatial cable system. These initial hanger tensions, together with the corresponding cable coordinates and internal forces, are then included into the FE model of the total bridge system, the nonlinear analysis of which involves the optimization technique. Calculations are repeated until the optimization algorithm converges to the most optimal hanger tensions(i.e. the desired reasonable finished bridge state). The "temperature rigid arm" is introduced to offset the unavoidable initial deformations of the girder and tower, which are due to the huge axial forces originated from the main cable. Moreover, by changing the stiffness coefficient K in the girder-tower-only FE model, the stiffness proportion of the main girder, the tower or the cable subsystem in the whole structural system could be adjusted according to the design intentions. The effectiveness of the proposed method is examined and demonstrated by one simple tutorial example and one self-anchored suspension bridge.

Cable flexural rigidity influence on suspension bridges static properties

In order to figure out the cable flexural rigidity influence on suspension bridges,a contrast model experiment is made:a chain cable model with no flexural rigidity and a wire cable model with some flexural rigidity.And then,four finite element models of a same long-span suspension bridge with different cable element are set up to be analyzed.Both experimental and numerical simulation results show that,with the increase of the span and the decrease of sag-span ratio,the influence of the cable flexural rigidity is significant.The difference of nodes displacement reaches more than 10 cm in construction analysis,which will bring some trouble to the construction.And the difference of the maximum section edge normal stress may reach 15%,which may have an adverse impact onto the bridge.Therefore,considering the cable flexural rigidity is necessary on some analysis of suspension bridges.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

New tangent stiffness matrix for geometrically nonlinear analysis of space frames

A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.

A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section

Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in total Lagarange(TL) and the corresponding stiffness matrix are formulated.Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss.Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method.Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.

宽幅双边钢箱钢-混组合梁构造优化

为研究双边钢箱钢-混组合梁的优化设计,以某双塔双索面自锚式悬索桥的宽幅双边钢箱钢-混组合梁为研究对象,建立实体模型及杆系模型,分析横梁及次纵梁构造参数的改变对组合梁受力性能的影响,提出各构件合理优化方案。研究结果表明:增大次纵梁间距,对结构影响较小,可优化组合梁结构;减小横梁上翼缘板厚度有助于改善横梁下翼缘板及腹板受力,达到组合梁优化目的;上翼缘板板厚从25 mm减小至20 mm,同时下翼缘板板厚从20 mm增加至25 mm,横梁下翼缘板应力得到明显改善,即横梁下翼缘板板厚大于横梁上翼缘板板厚对组合梁结构更有利。

Improved Discrete Element Method for Linear and Nonlinear Dynamic Analysis of 3-D Beam Structures

Based on the combination of multi body dynamics and structural dynamics, a new model of discrete element with flexible connector is developed. It is applicable to the eigenfrequency and geometric nonlinear dynamic response analysis of three dimensional beam structures. It is pointed out that both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off diagonal in a general case. A special discrete element, zero length rigid element, is introduced to simulate the node at which multiple elements are jointed together. It may also be efficient when the axes of adjacent elements are not in the same line. The formulation of stiffness matrix is established while nonlinearity is taken into consideration. Given examples show that the model is successful in eigenvalue calculation and geometric nonlinear response analysis.

悬索桥抖振响应随跨度的非线性演变分析

设计了11组不同跨度悬索桥有限元模型.通过风洞实验得到主梁截面的气动三分力系数,运用Matlab工具箱生成B类风场脉动风速时程后得到桥梁抖振力.在此基础上,分析了结构动力特性的变化规律、计算了按几何线性和几何非线性考虑的11个模型的抖振响应.结果表明,随着跨度增大,悬索桥3个方向的自振频率逐渐降低,抖振位移均方根逐渐增大.对于竖向与扭转响应,线性与非线性均方根之间的差值均随跨度逐渐增大;对于侧向响应,两者之间的差值随跨度变化较小,表明几何非线性主要影响了悬索桥竖向和扭转方向上的抖振响应.为探索抖振响应随主跨跨度的演变规律,首先通过频谱分析得到各主要模态的共振响应和背景响应的贡献,然后分析了2类贡献的变化规律,最后拟合得到了主要模态的抖振位移均方根随跨度的变化公式.以一座实际桥梁为数值算例计算了其抖振响应,并将结果与本文拟合公式进行了对比,验证了拟合公式的实用性,可快速估算悬索桥在B类风场中的抖振响应.

横州大桥索塔上横梁高支架支撑体系测试分析

大跨度桥梁索塔横梁支架支撑体系测试分析是保障桥梁施工安全的关键手段。横州大桥为主跨400 m的单跨双铰钢箱梁悬索桥,桥塔上横梁采用牛腿支架法施工。文章设计了上横梁施工牛腿高支架支撑体系,开展了施工过程中支架体系受力实测,建立了分步施工有限元模型,并计算、分析了上横梁施工过程中支架支撑体系的结构安全性。结果表明:横梁已浇筑结构在张拉预应力形成刚度后,能够与支架支撑体系共同承载并分担大部分的后期荷载,引起钢管支架各测点在腹板浇筑及后续施工中实测应变发展相对较小;数值模型计算应变结果与实测结果总体吻合良好,可较好地应用于支架支撑体系上横梁分步施工的计算分析;所提出的支架支撑体系能够较好地满足大桥上横梁施工的安全性要求。

基于索-梁结构的斜拉桥非线性振动仿真研究

本文建立了索-梁结构的有限元模型,对斜拉桥线性和非线性振动问题进行研究.首先对结构进行模态分析,发现结构振动表现出全局模态,局部模态以及混合模态,且索梁两者之间固有频率相互影响,对低阶频率影响较大,对高阶频率影响较小.其次,应用有限元软件对索-梁结构的自由振动和强迫振动进行仿真研究.结果表明:整个自由振动过程中频率有先增大后减小的趋势,且最终小于真实频率;在强迫振动中,观察到了丰富的非线性振动现象,包括索的亚谐波共振和内共振,与以往的实验和理论研究结果定性上得到验证;为斜拉桥全桥非线性动力学分析提供参考.

抗风缆对人行悬索桥荷载试验的影响分析

本文以某人行悬索桥为研究对象,分析不同抗风缆状态对桥梁检测工作的影响。分析结果表明:人行悬索桥抗风缆内力状态不同对桥梁静载试验期间的理论值存在较大影响,故理论计算时需考虑抗风缆对桥梁的刚度影响以及试验荷载对桥梁结构的非线性影响;人行悬索桥抗风缆对静载试验期间加劲梁纵向变形影响较大,且抗风缆成桥内力大小与加劲梁纵向约束效果呈正相关。因此,对抗风缆松动或未设置抗风缆的柔性人行悬索桥,在静载试验期间应密切监测梁端位移,防止纵向位移过大对桥梁伸缩缝装置或加劲梁支座造成破坏。

基于共旋坐标法的悬索桥几何非线性正装计算分析及软件开发

给出了基于共旋坐标法的几何非线性计算流程,推导了按共旋坐标法的梁杆单元在总体坐标系下的几何非线性切线刚度矩阵,经过比较证明了和Saafan给出的几何非线性切线刚度矩阵一致。同时单元切线刚度矩阵元素完全对称,并且可以用于直接组集总刚度矩阵,不需要经过旋转变换。根据无应力长度为未知量的成桥找形计算和已知无应力长度的几何非线性正装计算的互逆性,应用基于几何非线性正装计算算法开发的几何非线性分析程序,对含梁杆索混合单元的悬索结构进行了正装计算,其中梁单元和杆单元按共旋坐标法计算,主缆单元按只受拉的索单元计算。几何非线性正装计算的线形和内力跟成桥找形的结果能闭合,验证了找形所得线形的平衡状态以及几何非线性程序的正确性。

钢筋混凝土T梁受弯性能试验与数值模拟研究

为了研究钢筋混凝土T梁的受弯性能,笔者设计了全长3.6m的T梁试验模型,采用模型试验与有限元分析方法开展研究。研究结果表明,混凝土T梁的受弯破坏模式与混凝土矩形梁不同,表现为主钢筋屈服、荷载不再增长;T梁破坏时,受压区混凝土已经进入塑性阶段,但是并未达到极限压应变;采用非线性有限元分析得到的受弯破坏模式、荷载-变形曲线与试验测试结果吻合较好,极限荷载模拟值与试验值的相对误差为4.52%,文中采用的有限元模拟方法能够准确模拟钢筋混凝土T梁的受弯行为。

大跨人行悬索桥非线性静风稳定性分析

基于风洞试验所测加劲梁静力三分力系数,在综合考虑静风荷载非线性、结构几何非线性基础上,采用双重迭代计算分析方法对主跨420 m大跨窄人行悬索桥进行静风稳定性全过程分析。结果表明,结构变形随风速变化呈明显非线性,静风失稳形态弯曲扭转空间耦合变形特征显著;较公路桥大跨人行悬索桥主缆提供的扭转刚度比重更大,跟踪两主缆跨中应力随风速变化情况可定义静风失稳临界风速及与分析静风失稳原因;非零初始风攻角会降低静风失稳临界风速;中央扣及抗风缆均能提高静风失稳临界风速。施加中央扣措施,失稳形态为主梁结构弯扭失稳;施加抗风缆措施,失稳形态为抗风拉索、抗风缆应力松弛导致局部结构失稳。该研究可为大跨窄桥静风稳定性能及提高静风稳定性提供科学依据及参考。

预应力高强混凝土梁极限承载力分析

针对高强混凝土材料力学行为的特殊性,考虑材料非线性的影响,通过将普通钢筋均匀“涂抹”于混凝土中,建立综合本构关系矩阵,将由此形成的普通钢筋与混凝土匀质材料整体离散为实体单元,并将预应力钢筋离散为独立的一维单元,用有限元法对预应力高强混凝土T型梁进行了极限承载力分析研究,给出了梁受力全过程p-f曲线,分析了其受力变形和破坏特点。为方便结构工程师参考,还对影响预应力高强混凝土梁极限承载力的主要结构参数(配筋率、高跨比等)进行了分析计算,推荐了这些参数的合理取值范围。

三维杆系结构的几何非线性有限元分析

为了更准确地描述杆系结构的几何非线性性能,建立了一种基于三维梁单元有限元分析的计算方法。引入了考虑两方向曲率和扭转角变化的坐标转换矩阵来描述任意增量下的单元平移和转动;采用了包括轴向变形和扭转的非线性项的刚度矩阵来考虑高阶非线性项的影响。应用广义位移控制法进行增量迭代,编制了相应的三维梁单元非线性计算程序NL_Beam3D。通过对几个例子进行的分析,验证了该方法可较好地考虑结构几何非线性。