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.     

钢管混凝土纯压拱失稳临界荷载计算的等效柱法

在双重非线性有限元分析的基础上,进行了钢管混凝土纯压拱失稳临界荷载的简化计算方法——等效柱法的研究,提出了等效柱法中考虑矢跨比影响的稳定系数K₁ 以及考虑初始几何缺陷影响的折减系数K₂及其与现有规范相对应的计算公式。与有限元计算结果的对比表明,采用考虑矢跨比因素的稳定系数的等效柱法能较精确地估算钢管混凝土纯压拱的非线性失稳临界荷载,且计算精度受含钢率和钢材种类变化的影响较小。     

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。     

钢管混凝土拱稳定分析的三维退化层合曲梁单元

为计算钢管混凝土拱的屈曲荷载,本文在文[1]三维退化梁单元的基础上,采用等效数值积分法,构造,出120－20结点三维退化层合曲梁单元,并考虑几何非线性影响,给出用于层合梁或拱线弹性稳定性分析的有限元列式,最后,以绍兴轻纺大桥为工程背景,计算出轻纺大枯钢管混凝土拱面内及面外屈曲的稳定系数。     

火灾下圆钢管混凝土柱非线性有限元分析

首先提出合理的火灾下钢管混凝土拉、压材料数值热-力耦合本构模型及相应的计算方法;然后基于连续介质力学,推导火灾下U.L.列式虚功增量方程,采用非线性梁单元理论,给出火灾下钢管混凝土柱非线性有限元方程组的求解方法,编制非线性有限元程序NACFSTLF;最后对已有火灾下钢管混凝土柱的试验资料进行双重非线性有限元分析并考察钢管混凝土柱初始缺陷对其抗火性能的影响。分析结果表明:火灾下钢管混凝土柱的轴向变形-火灾时间曲线的计算结果基本上反映钢管混凝土柱的变形特性,而计算的耐火极限基本上是试验结果的上限;同时随着火灾下柱初始缺陷的增大,相同火灾时间下柱的跨中侧向挠度变形逐渐增大,耐火极限逐渐降低,而对柱的轴向变形影响相对较小。     

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。     

钢管初应力对钢管砼拱桥承载力影响非线性分析

基于非线性问题的平衡方程和空间梁单元非线性几何方程,推导了一般线弹性关系下计入初应力影响的空间梁单元显式切线刚度矩阵。针对钢管混凝土哑铃型截面的构造特点,提出了组合空间梁单元法,较好解决了哑铃型截面钢管初应力的计算与存储问题,并给出了承载力分析时单元划分的具体方法,编制了专用计算程序,计算结果与试验吻合良好。开展了不同钢管初应力系数、不同截面含钢率和不同跨径对钢管混凝土拱桥承载力的影响分析。结果表明,钢管初应力将使钢管混凝土拱桥的承载力降低,降低幅度与拱肋截面型式有关,承载力最大降低值可超过30%。最后给出了三种考虑钢管初应力影响的常用拱肋截面型式拱桥承载力影响系数实用计算公式。     

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。     

一种抛物线浅拱线性单元

为研究抛物线浅拱在复杂受力状态下的线性内力及位移,考虑拱的压弯耦合作用,基于力法和浅拱假定,对抛物线拱平衡方程、几何方程和物理方程进行了分析;求得了抛物线拱内力方程通解格式,构建了抛物线浅拱位移形函数。利用最小势能原理,构造了抛物线浅拱单元。算例表明,本文构造的抛物线浅拱单元计算的抛物线拱内力与理论解计算结果符合较好,在划分一个单元时最大相对误差仅为4.03%,可用于抛物线拱分析。     

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提出了一种采用有限元法计算钢管混凝土受剪时等效剪切模量的方法,并对该方法 的正确性进行了验证;在分析了各种因素对等效剪切模量影响的基础上,给出了圆形和方形 钢管混凝土受剪时等效剪切模量的简化计算公式;与其他得到钢管混凝土剪切模量的方法进 行比较,分析了结果不同的原因,表明对钢管混凝土采用有限元计算研究其等效剪切模量的 方法更为合理.     

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。     

Nonlinear dynamic buckling of pinned–fixed shallow arches under a sudden central concentrated load

The structural behavior of a shallow arch is highly nonlinear, and so when the amplitude of the oscillation of the arch produced by a suddenly-applied load is sufficiently large, the oscillation of the arch may reach a position on its unstable equilibrium paths that leads the arch to buckle dynamically. This paper uses an energy method to investigate the nonlinear elastic dynamic in-plane buckling of a pinned–fixed shallow circular arch under a central concentrated load that is applied suddenly and with an infinite duration. The principle of conservation of energy is used to establish the criterion for dynamic buckling of the arch, and the analytical solution for the dynamic buckling load is derived. Two methods are proposed to determine the dynamic buckling load. It is shown that under a suddenly-applied central load, a shallow pinned–fixed arch with a high modified slenderness (which is defined in the paper) has a lower dynamic buckling load and an upper dynamic buckling load, while an arch with a low modified slenderness has a unique dynamic buckling load.     

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.     

圆弧拱考虑一般缺陷的面内屈曲

研究了几何缺陷、荷载非均匀分布和支座沉陷对圆弧拱面内屈曲的影响.基于能量的变分原理推导了考虑缺陷的微分方程,得到了外荷载和轴力的关系式以及径向位移的表达式.从微分方程出发用摄动法对屈曲荷载的缺陷敏感性进行了分析,得到了屈曲荷载的近似表达式.结果表明近似解与精确解吻合良好;正对称屈曲荷载对正对称缺陷参数十分敏感;反对称缺陷参数对反对称屈曲荷载影响显著而正对称缺陷参数影响很小.     

薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法

针对薄壁圆筒壳结构轴压屈曲载荷的缺陷敏感性以及真实几何缺陷的不确定性,提出一种基于实测缺陷数据和极大熵原理的初始缺陷建模与屈曲载荷预测方法。首先,将初始几何缺陷视为二维随机场,并利用实测缺陷数据和Karhunen-Loève展开法将初始缺陷的随机场建模转化为随机向量的建模;其次,利用极大熵方法确定随机向量的概率分布;最后,基于所构建的初始缺陷随机模型,利用MCMC抽样方法和确定性屈曲分析方法,进行随机屈曲分析并给出基于可靠度的屈曲载荷折减因子。数值算例表明,与直接假设随机场相关结构的方法相比,本文方法的结果是对薄壁圆筒壳屈曲载荷的一个更无偏估计。     

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采用Ritz近似法建立客运专线下承式系杆拱桥侧向稳定承载力实用计算公式; 假定满足拱桥侧向弯扭边界条件的位移试函数, 建立系杆拱桥的主拱肋侧倾失稳结构势能的表达式,基于最小势能原理建立了下承式系杆拱桥侧倾失稳临界载荷实用计算公式. 采用该实用计算公式计算了某客运专线下承式系杆拱桥弹性侧向稳定承载力, 并与三维有限元屈曲计算结果进行比较, 结果表明: 该方法简单实用, 可准确地预测系杆拱桥侧倾临界载荷, 便于工程应用.     

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.     

Dynamic buckling of a shallow arch under shock loading considering the effects of the arch shape

In this paper, the influence of the initial curvature of thin shallow arches on the dynamic pulse buckling load is examined. Using numerical means and a multi-dof semi-analytical model, both quasi-static and non-linear transient dynamical analyzes are performed. The influence of various parameters, such as pulse duration, damping and, especially, the arch shape is illustrated. Moreover, the results are numerically validated through a comparison with results obtained using finite element modeling. The main results are firstly that the critical shock level can be significantly increased by optimizing the arch shape and secondly, that geometric imperfections have only a mild influence on these results. Furthermore, by comparing the sensitivities of the static and dynamic buckling loads with respect to the arch shape, non-trivial quantitative correspondences are found.     

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.