纯压钢管拱稳定临界荷载计算的等效柱法

以均布荷载下的抛物线钢管拱为研究对象,在考虑双重非线性的有限元分析基础上,讨论了完善拱和有初始几何缺陷的拱的弹性失稳和弹塑性失稳的特性,提出纯压钢管拱稳定临界荷载计算的等效柱法.分析结果表明,矢跨比是计算拱临界荷载的重要影响因素,而现有等效柱法中没有考虑这一因素的影响,为此,提出等效柱的稳定系数中考虑矢跨比影响的计算方法.有初始几何缺陷的拱将发生极值点失稳,且极值点荷载要小于分支屈曲临界荷载,为此提出缺陷拱等效柱法考虑缺陷影响的计算方法.给出了钢管拱失稳临界荷载等效柱法计算的相应公式和实用表格.与双重非线性有限元计算结果对比表明,提出的等效柱法能方便且较精确地估算钢管拱的非线性临界荷载.     

均布压力作用下圆弧双铰拱对称和反对称失稳的折迭突变和尖点突变模型

建立了径向均布压力作用下圆弧双铰拱正对称失稳和反对称失稳的折迭和尖点突变模型，模型可以很好地描述这两个失稳过程的各种性态，求解拱失稳时的临界荷载，给出拱屈曲后路径与荷载的初步关系。     

拱暨索拱面内稳定性研究的传递矩阵法

为探究拱桥面内稳定问题求解的新途径,应用传递矩阵法对径向均布荷载作用下的圆拱面内屈曲微分方程进行解答,利用边界条件导出其特征方程,从而求得其屈曲荷载。同时,结合力法以及拱上荷载集度与轴力的关系,将该理论方法推广到承受集中荷载的变截面拱以及索拱组合结构的稳定分析中,并和有限元ANSYS计算结果进行对比,验证了本文理论和方法的正确性。最后,研究了不同荷载工况下的边界条件、圆心角和截面惯性矩对拱结构面内稳定性的影响。结果表明,索拱结构的面内稳定性优于纯拱结构。     

动支座对拱结构抗爆承载力的影响

建立了具有动支座拱的计算模型,该模型考虑了竖向的弹性支承和阻尼支承、水平向弹性支承和扭转约束等柔性支承形式。基于大变形动力微分方程并利用有限差分方法,研究了动支座拱在爆炸荷载作用下的动力响应,并分析动支座对结构承载力的影响。研究表明:动支座对拱的抗爆承载能力有较大影响,不同形式的柔性支承对拱承载力的影响截然不同,竖向弹性支承能够使爆炸荷载作用下拱的弯矩峰值减小,并且使到达峰值的时间增加,提高了拱的抗爆或承受瞬态荷载的能力。而水平弹性支承使拱的内力值和相对位移值增大,对结构的承载力不利。     

钢管混凝土圆弧桁架拱平面内徐变稳定分析

核心混凝土的徐变会增加钢管混凝土拱肋的屈曲前变形,降低结构的稳定承载力,因此只有计入屈曲前变形的影响,才能准确得到钢管混凝土拱的徐变稳定承载力。基于圆弧形浅拱的非线性屈曲理论,采用虚功原理,建立了考虑徐变和剪切变形双重效应的管混凝土圆弧桁架拱的平面内非线性平衡方程,求得两铰和无铰桁架拱发生反对称分岔屈曲和对称跳跃屈曲的徐变稳定临界荷载。探讨了钢管混凝土桁架拱核心混凝土徐变随修正长细比、圆心角和加载龄期对该类结构弹性稳定承载力的影响,为钢管混凝土桁架拱长期设计提供理论依据。     

跨中集中荷载作用下弹性约束圆弧拱的稳定性分析

研究了跨中集中荷载作用下两端由不同转动刚度弹性约束的铰支圆弧拱的面内稳定性。由变形几何关系、变分原理得到了拱的非线性平衡方程,建立了外荷载、结构内力、径向位移的对应关系,通过定义拱的深浅参数和约束刚度参数进行分析,并得到了跳跃屈曲和分岔屈曲的发生条件及存在区间。通过数值分析可知本文方法所得屈曲路径和屈曲荷载与有限元法所得结论吻合良好,极值点、临界荷载相对差值在1%左右。对不同结构参数区间圆弧拱在集中荷载作用下的屈曲路径和临界荷载进行了分析,结果表明约束刚度对屈曲路径和临界荷载起决定性的作用,深浅参数决定屈曲发生条件、屈曲形式、极值点对数。     

哑铃型钢管混凝土拱肋极限承载力研究

为了研究哑铃型钢管混凝土拱肋的力学性能,基于统一强度理论和等效梁柱法,考虑中间主应力和材料拉压比的影响,推导了其极限承载力的新公式。采用梁单元建立哑铃型钢管混凝土拱肋的有限元模型,对其受力全过程进行双重非线性分析。将理论分析结果和数值计算结果与相关文献的试验结果进行比较,吻合良好,验证了本文理论分析方法和有限元计算方法的正确性。采用有限元方法,对荷载工况、长细比、矢跨比、截面形式和腹腔混凝土等参数的影响特性进行分析,研究结果表明,荷载工况对哑铃型钢管混凝土拱肋的极限承载力影响显著,荷载越对称、均匀,拱肋的极限承载力越高,竖向变形越小;拱肋的极限承载力随长细比的增大而显著降低,随矢跨比的增大先提高后略有降低;截面形式对拱肋的强度和刚度均有较大影响,而腹腔混凝土对其强度和刚度几乎没有影响。     

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一定长度的薄壁构件在纵向或横向荷载作用下，未达到材料极限破坏前就有 可能发生弹性弯扭屈曲失稳的问题. 分析了工字型截面悬臂钢梁的此类问题，应用平衡 法和能量法导出构件在轴向和横向荷载作用下的弹性弯扭屈曲微分方程，利用里兹法求其临 界载荷，并确定截面固定时的极限特征长度.     

中柱失效时组合框架压拱效应力学模型分析

钢-混凝土组合梁在正弯矩下的转动中心通常要高于其在负弯矩作用下的转动中心,因此在中柱失效工况下,组合框架中存在压拱效应．针对两榀分别采用了焊接连接和平齐式端板连接的钢-混凝土组合框架进行了拆除中柱的试验研究,记录并详细分析了压拱效应．分析结果表明,无论采取何种梁柱节点形式,组合框架中均存在压拱效应;常规压杆模型无法准确描述压拱效应的效果．提出了一种考虑钢梁下翼缘及部分腹板受拉的桁架弹簧模型,并对该模型的竖向荷载-位移公式和水平位移-竖向位移公式进行了推导,公式结果与试验结果吻合良好．本文提出的桁架弹簧模型及相应变形公式可以很好地预测压拱效应对于整体结构承载力和变形的贡献,为抗连续倒塌工况下组合框架的设计提供了参考．     

两铰弹性圆拱的动力屈曲

1 引言稳定性准则在系统稳定分析中占有极其重要的地位.对于保守系统而言,Budiansky-Roth 准则,或称运动方程法,是目前动力稳定数值分析中普遍采用的方法.对于弹性结构,若荷载参数的微小变化,引起响应幅值的巨大变化,则称结构丧失动力稳定性,即结构在Liapunov 意义上丧失稳定性.本文采用此准则判别弹性圆拱在均布突加阶跃荷载作用下的动力稳定性.     

Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

In this paper an integral equation solution to the linear and geometrically nonlinear problem of non-uniform in-plane shallow arches under a central concentrated force is presented. Arches exhibit advantageous behavior over straight beams due to their curvature which increases the overall stiffness of the structure. They can span large areas by resolving forces into mainly compressive stresses and, in turn confining tensile stresses to acceptable limits. Most arches are designed to operate linearly under service loads. However, their slenderness nature makes them susceptible to large deformations especially when the external loads increase beyond the service point. Loss of stability may occur, known also as snap-through buckling, with catastrophic consequences for the structure. Linear analysis cannot predict this type of instability and a geometrically nonlinear analysis is needed to describe efficiently the response of the arch. The aim of this work is to cope with the linear and geometrically nonlinear problem of non-uniform shallow arches under a central concentrated force. The governing equations of the problem are comprised of two nonlinear coupled partial differential equations in terms of the axial (tangential) and transverse (normal) displacements. Moreover, as the cross-sectional properties of the arch vary along its axis, the resulting coupled differential equations have variable coefficients and are solved using a robust integral equation numerical method in conjunction with the arc-length method. The latter method allows following the nonlinear equilibrium path and overcoming bifurcation and limit (turning) points, which usually appear in the nonlinear response of curved structures like shallow arches and shells. Several arches are analyzed not only to validate our proposed model, but also to investigate the nonlinear response of in-plane thin shallow arches.     

In-plane stability of arches

Classical buckling theory is mostly used to investigate the in-plane stability of arches, which assumes that the pre-buckling behaviour is linear and that the effects of pre-buckling deformations on buckling can be ignored. However, the behaviour of shallow arches becomes non-linear and the deformations are substantial prior to buckling, so that their effects on the buckling of shallow arches need to be considered. Classical buckling theory which does not consider these effects cannot correctly predict the in-plane buckling load of shallow arches. This paper investigates the in-plane buckling of circular arches with an arbitrary cross-section and subjected to a radial load uniformly distributed around the arch axis. An energy method is used to establish both non-linear equilibrium equations and buckling equilibrium equations for shallow arches. Analytical solutions for the in-plane buckling loads of shallow arches subjected to this loading regime are obtained. Approximations to the symmetric buckling of shallow arches and formulae for the in-plane anti-symmetric bifurcation buckling load of non-shallow arches are proposed, and criteria that define shallow and non-shallow arches are also stated. Comparisons with finite element results demonstrate that the solutions and indeed approximations are accurate, and that classical buckling theory can correctly predict the in-plane anti-symmetric bifurcation buckling load of non-shallow arches, but overestimates the in-plane anti-symmetric bifurcation buckling load of shallow arches significantly.     

Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.     

Long-term non-linear behaviour and buckling of shallow concrete-filled steel tubular arches

This paper presents a theoretical analysis for the long-term non-linear elastic in-plane behaviour and buckling of shallow concrete-filled steel tubular (CFST) arches. It is known that an elastic shallow arch does not buckle under a load that is lower than the critical loads for its bifurcation or limit point buckling because its buckling equilibrium configuration cannot be achieved, and the arch is in a stable equilibrium state although its structural response may be quite non-linear under the load. However, for a CFST arch under a sustained load, the visco-elastic effects of creep and shrinkage of the concrete core produce significant long-term increases in the deformations and bending moments and subsequently lead to a time-dependent change of its equilibrium configuration. Accordingly, the bifurcation point and limit point of the time-dependent equilibrium path and the corresponding buckling loads of CFST arches also change with time. When the changing time-dependent bifurcation or limit point buckling load of a CFST arch becomes equal to the sustained load, the arch may buckle in a bifurcation mode or in a limit point mode in the time domain. A virtual work method is used in the paper to investigate bifurcation and limit point buckling of shallow circular CFST arches that are subjected to a sustained uniform radial load. The algebraically tractable age-adjusted effective modulus method is used to model the time-dependent behaviour of the concrete core, based on which solutions for the prebuckling structural life time corresponding to non-linear bifurcation and limit point buckling are derived.     

Nonlinear analysis and buckling of elastically supported circular shallow arches

Arches are often supported elastically by other structural members. This paper investigates the in-plane nonlinear elastic behaviour and stability of elastically supported shallow circular arches that are subjected to a radial load uniformly distributed around the arch axis. Analytical solutions for the nonlinear behaviour and for the nonlinear buckling load are obtained for shallow arches with equal or unequal elastic supports. It is found that the flexibility of the elastic supports and the shallowness of the arch play important roles in the nonlinear structural response of the arch. The limiting shallownesses that distinguish between the buckling modes are obtained and the relationship of the limiting shallowness with the flexibility of the elastic supports is established, and the critical flexibility of the elastic radial supports is derived. An arch with equal elastic radial supports whose flexibility is larger than the critical value becomes an elastically supported beam curved in elevation, while an arch with one rigid and one elastic radial support whose flexibility is larger than the critical value still behaves as an arch when its shallowness is higher than a limiting shallowness. Comparisons with finite element results demonstrate that the analytical solutions and the values of the critical flexibility of the elastic supports and the limiting shallowness of the arch are valid.     

几何缺陷浅拱的动力稳定性分析

研究了几何缺陷对粘弹性铰支浅拱动力稳定性能的影响。从达朗贝尔原理和欧拉-贝努利假定出发推导了粘弹性铰支浅拱在正弦分布突加荷载作用下的动力学控制方程,并采用Galerkin截断法得到了可用龙格-库塔法求解的无量纲化非线性微分方程组。同时引入能有效追踪结构动力后屈曲路径的广义位移控制法,对含几何缺陷浅拱的响应曲线进行几何、材料双重非线性有限元分析。用这两种方法分析了前三阶谐波缺陷对浅拱动力稳定性能的影响,其中动力临界荷载由B-R准则判定。主要结论有:材料粘弹性使浅拱动力临界荷载增大且结构响应曲线与弹性情况差别很大;二阶谐波缺陷影响显著,它使动力临界荷载明显下降且使得浅拱粘弹性动力临界荷载可能低于弹性动力临界荷载。     

In-plane buckling of prismatic funicular arches with shear deformations

The in-plane buckling behavior of funicular arches is investigated numerically in this paper. A finite strain Timoshenko beam-type formulation that incorporates shear deformations is developed for generic funicular arches. The elastic constitutive relationships for the internal beam actions are based on a hyperelastic constitutive model, and the funicular arch equilibrium equations are derived. The problems of a submerged arch under hydrostatic pressure, a parabolic arch under gravity load and a catenary arch loaded by overburden are investigated. Buckling solutions are derived for the parabolic and catenary arch. Subsequent investigation addresses the effects of axial deformation prior to buckling and shear deformation during buckling. An approximate buckling solution is then obtained based on the maximum axial force in the arch. The obtained buckling solutions are compared with the numerical solutions of Dinnik (Stability of arches, 1946) [1] and the finite element package ANSYS. The effects of shear deformation are also evaluated.     

Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load

This paper investigates the non-linear in-plane buckling of pin-ended shallow circular arches with elastic end rotational restraints under a central concentrated load. A virtual work method is used to establish both the non-linear equilibrium equations and the buckling equilibrium equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling loads are obtained. It is found that the effects of the stiffness of the end rotational restraints on the buckling loads, and on the buckling and postbuckling behaviour of arches, are significant. The buckling loads increase with an increase of the stiffness of the rotational restraints. The values of the arch slenderness that delineate its snap-through and bifurcation buckling modes, and that define the conditions of buckling and of no buckling for the arch, increase with an increase of the stiffness of the rotational end restraints.