Elastic arches with large elevation. Singularly perturbed problem of nonlinear elasticity

In this paper we examine the asymptotic expansion of a three-dimensional displacement field defined over a slender, bowlike domain whose shape corresponds to a thin arch. We show that it is possible to derive from the principles of virtual work two families of arch equations whose forms vary with the scale of external forces and the curvature of the arch. The first family of models, for relatively small curvatures, is described by singularly perturbed ordinary differential equations. The second family, when the curvature of the original arch is large, is described by two-dimensional partial differential equations whose form depends on the shape of the cross-section of the solid arch.     

冲击载荷下轻质夹芯拱最大刚度拓扑优化及动力响应

基于双向渐进结构优化方法（bi-directional evolutionary structural optimization,BESO）框架,将传统动态载荷优化法中的内外层迭代引入到ABAQUS-MATLAB平台集成优化中,改进动态载荷拓扑优化流程。对初速度为100 m/s的子弹冲击下的夹芯拱结构进行拓扑优化设计和动力学响应分析。优化后夹芯拱芯层的变形模式可分为3个对称的部分,跨中区域的中部和上部主要发生压缩变形,呈现类三角点阵桁架结构,边界区域上部发生拉伸变形,下部发生压缩变形,呈现C形型结构,跨中和边界之间的过渡区域以拉弯联合变形为主,呈现Y形结构。通过与两种等质量的拱结构对比,分析了3种结构在不同初速度的子弹冲击下结构的挠度以及芯层的能量吸收情况。结果表明:在相同的冲击速度下,优化后的结构挠度最小,芯层比吸能最高;当冲击速度较低时,优化后的结构的抗冲击性能优势并不明显;在所研究的冲击速度范围内,冲击速度越高,优化后结构的抗冲击性能越好。对比对称载荷与非对称载荷（冲击点偏移量为100%）下2种优化结构在不同载荷工况下的动态响应,结果表明:载荷工况不同,得到的最终优化结果也略有所不同,但在相同载荷下结构的响应相差较小,每种工况下得到的优化结果在相应工况下所展现的力学性能略优,但均明显优于传统结构。因此,在对称冲击载荷下优化所得的结构具有一定的普遍性。     

Explicit solutions for depressed masonry arches loaded until collapse—Part I: a one-dimensional nonlinear elastic model

In this paper the equilibrium problem for masonry arches is formulated in terms of a suitable set of nonlinear ordinary differential equations. We show that by making a small number of simple hypotheses it is possible to find the explicit expressions for the displacements and rotations of the cross-sections of an in-plane loaded masonry arch. To this end, the masonry arch is schematised as a curved, one-dimensional nonlinear elastic beam made of a material that is by hypothesis incapable of withstanding significant tensile stresses. In this first part of the two-part paper, the one-dimensional model and the explicit expressions for the displacements and rotations, obtained by integrating the set of differential equations, are presented. In particular, the formal expressions for displacement, stress and strain fields are illustrated in full detail for an explicit, albeit approximate, solution for a statically determinate depressed arch subjected to a uniform vertical load.     

设置反拱加固的拱结构力学性能研究

提出了一种设置反拱结构的拱桥加固方法,该方法是通过在主拱圈拱肋下方设置反拱,在反拱和拱肋之间用竖杆相连,并通过抗弯预埋件和抗剪锚栓把反拱的拱脚和拱肋连接,使反拱结构和原主拱圈共同形成结构受力体系。本文基于有限元参数分析方法,通过设置6个不同参数:拱的矢高f1、拱的拱轴系数m1、反拱的矢高f2、反拱的拱轴系数m2、反拱与待加固拱的等效半径比i、反拱纵向长度与待加固拱的总跨径的比值Kr,以考虑不同拱桥、反拱结构参数对原拱桥关键截面内力、跨中挠度及整体屈曲系数的影响。基于大量计算数据的参数拟合,分别获得跨中弯矩、跨中挠度、拱脚弯矩、拱脚推力、整体屈曲系数的拟合表达式。通过对拟合数据的分析,获得了反拱加固的拱桥结构力学特性的相关变化规律。最后对一个100m跨径拱桥进行加固计算分析,结果表明:本文提出的加固方法不但可以显著提高待加固桥梁的整体刚度与稳定性,而且可有效地降低主拱关键截面的内力。     

曲厚壳单元在斜板拱桥分析中的应用

介绍了利用曲厚壳单元对斜板拱桥进行空间受力分析,并将曲厚壳单元所得结果与采用实体单元分析的结果和模型实验所得结果进行了比较,证明利用曲厚壳单元来分析斜板拱桥是行之有效的。     

Three-Dimensional Shape Optimization of Arch Dams with Prescribed Shape Functions*, †

Development and application of shape optimization of double-curved arch dams are presented. A mathematical formulation of arch dam design is described, where design variables, objective function, and constraint functions are defined. The geometrical form of the arch dam and part of its load-carrying foundation are described by three-dimensional hyperelements. Design variables are identified as geometrical parameters of these hyperelements. For static analysis of the dam-foundation system, the finite element method is employed with eight node solid elements and an incompatible displacement function. Elements are automatically generated within the hyperelements in each design step. Four different load cases are considered to account for important design specifications. A complete static sensitivity analysis is performed and used in each design iteration. Partial derivatives of element stresses with respect to all design variables are computed within the finite element context. The optimization problem is solved by sequential linear programming. It is demonstrated that practical three-dimensional shape optimization is feasible and economical.     

The static and dynamic behavior of MEMS arch resonators near veering and the impact of initial shapes

We investigate experimentally and analytically the effect of initial shapes, arc and cosine wave, on the static and dynamic behavior of microelectromechanical systems (MEMS) arch resonators. We show that by carefully choosing the geometrical parameters and the initial shape of the arch, the veering phenomenon (avoided-crossing) among the first two symmetric modes can be strongly activated. To demonstrate this, we study electrothermally tuned and electrostatically driven initially curved MEMS resonators. Upon changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically the dynamic behavior of the arc beam for different electrostatic loads. The analytical study is based on a reduced order model of a nonlinear Euler–Bernoulli shallow arch beam model. The veering phenomenon is also confirmed through a finite-element multi-physics and nonlinear model.     

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。     

地震作用下高拱坝损伤开裂分析

采用应变率相关的砼非线性损伤模型模拟拱坝横缝,研究了砼非线性本构情况下整体拱坝与考虑分缝拱坝的应力响应和损伤开裂的特点与差别。对实际拱坝的地震响应分析表明,基于非线性砼模型的整体拱坝动力响应模型可以基本反映拱坝的实际应力分布情况。     

静风荷载作用下大跨度钢拱桥施工稳定性的参数研究

随着钢拱桥跨径的不断增大，钢拱桥在静风荷载作用下的施工稳定性问题已引起了人们的广泛重视。本文以上海在建的主跨550m的中承式钢拱桥为例，采用几何和材科非线性分析法详细分析了大跨度钢拱桥在两个不同施工阶段下的静风稳定性。结果表明，拱肋最初合拢状态是拱桥施工过程中最不利的状态。最后，详细探讨影响大跨度钢拱桥施工过程中静风稳定性的主要参数。     

含缝拱坝强震失效破坏振动台试验研究

为探究强震时含缝拱坝结构的承载能力及失效路径,在振动台上开展了一系列拱坝模型强震失效破坏试验.基于弹性力-重力准则设计试验,分别进行了不分缝、只有横缝、诱导缝与横缝联合作用这三种情况的振动台模型试验,试验中考虑了材料率相关性的影响,忽略了库水-拱坝相互作用.结果表明,强震作用时由于设缝处的抗拉能力较低,导致缝位置首先发...     

Non-linear in-plane analysis and buckling of pinned–fixed shallow arches subjected to a central concentrated load

This paper is concerned with an analytical study of the non-linear elastic in-plane behaviour and buckling of pinned–fixed shallow circular arches that are subjected to a central concentrated radial load. Because the boundary conditions provided by the pinned support and fixed support of a pinned–fixed arch are quite different from those of a pinned–pinned or a fixed–fixed arch, the non-linear behaviour of a pinned–fixed arch is more complicated than that of its pinned–pinned or fixed–fixed counterpart. Analytical solutions for the non-linear equilibrium path for shallow pinned–fixed circular arches are derived. The non-linear equilibrium path for a pinned–fixed arch may have one or three unstable equilibrium paths and may include two or four limit points. This is different from pinned–pinned and fixed–fixed arches that have only two limit points. The number of limit points in the non-linear equilibrium path of a pinned–fixed arch depends on the slenderness and the included angle of the arch. The switches in terms of an arch geometry parameter, which is introduced in the paper, are derived for distinguishing between arches with two limit points and those with four limit points and for distinguishing between a pinned–fixed arch and a beam curved in-elevation. It is also shown that a pinned–fixed arch under a central concentrated load can buckle in a limit point mode, but cannot buckle in a bifurcation mode. This contrasts with the buckling behaviour of pinned–pinned or fixed–fixed arches under a central concentrated load, which may buckle both in a bifurcation mode and in a limit point mode. An analytical solution for the limit point buckling load of shallow pinned–fixed circular arches is also derived. Comparisons with finite element results show that the analytical solutions can accurately predict the non-linear buckling and postbuckling behaviour of shallow pinned–fixed arches. Although the solutions are derived for shallow pinned–fixed arches, comparisons with the finite element results demonstrate that they can also provide reasonable predictions for the buckling load of deep pinned–fixed arches under a central concentrated load.     

固支浅圆拱受子弹撞击的实验研究

本文报导了铝合金固支浅圆拱在子弹撞击下动力响应的实验研究,试验中采用应变片测量并由高速摄影得到试件变形的瞬态记录。实验结果表明,此类浅拱的动力响应不存在失稳现象;但在某一撞击速度区间内,拱的中心位移增加较快,拱的响应前期轴力可以忽略不计,而在后期则必须考虑。     

圆宝山隧道炭质板岩大变形段初期支护结构受力特性研究

为了准确掌握丽香铁路圆宝山隧道炭质板岩大变形段初期支护结构受力特性,结合深埋炭质板岩隧道大变形特点,通过调查分析发现炭质板岩具有显著的各向异性特征,在地下水、高地应力及施工扰动等复杂因素作用下表现出显著的蠕变特性,从而导致隧道发生大变形。同时,对圆宝山隧道展开围岩变形及初期支护受力监测,监测结果表明,薄层炭质板岩段围岩的变形速率、变形量整体上较中厚层炭质板岩段围岩大,且达到稳定所需的时间更长;围岩压力与钢拱架应力基本呈从拱顶到拱脚减小的趋势,且围岩压力最大值出现在拱肩,而钢拱架应力最大值分布位置不固定,常见分布位置为两侧拱墙上下,这与钢拱架因发生扭曲而设置横支撑基本吻合;变更支护参数后,围岩的时效特性有明显改善,尤以薄层炭质板岩段围岩最为明显,同时围岩压力分布更加均匀,钢拱架出现拉应力现象不再集中。基于上述研究成果,选择I18型工字钢焊制钢架、设置间距为0.6m、喷射厚为27cm的C25混凝土作为初期支护,同时采用"弱爆破、短进尺"的掘进方式,以达到控制深埋炭质板岩隧道围岩变形的目的。     

基于图像的主动脉弓运动和变形参数自动跟踪测量方法

提出一种基于动物实验序列图像的自动跟踪方法,测量主动脉弓在体运动和变形。在测量的初始帧,手动选取测量窗口,采用像素灰度值的梯度算法对图像测量窗口内的边界进行自动识别,得到主动脉弓的真实边界,进而调整测量窗口至最佳位置。在后续帧中,自动跟踪最佳测量窗口的位置,测量主动脉弓不同部位动脉直径和中心点位置随时间的变化。通过对四只兔子的实验测量,结果发现:主动脉弓具有一定锥度,在弓部直径最大,且主动脉弓在体运动和变形周期与心动周期之间存在较强的相关性。结论与生理现象或已有实验结果一致,表明基于图像的自动跟踪方法在测量主动脉弓运动与变形时不仅可行,而且可靠。     

Research of air-cushion isolation effects on high arch dam reservoir

A three-dimensional (3D) finite element model of air-cushion isolated arch dam is presented with the nonlinear gas-liquid-solid multi-field dynamic coupling effect taken into account.In this model,the displacement formulation in Lagrange method,pressure formulation in Euler method,nonlinear contact model based on Coulomb friction law are applied to the air-cushion,reservoir and contraction joint domain,respectively.The dynamic response of Jinping I arch dam with a height of 305 m is analyzed using the seismic records of the Wenchuan Earthquake in 2008.Numerical results show that the air-cushion isolation reduces significantly the hydrodynamic pressure as well as the opening width for the contraction joints of high arch dam.     

基于离散-连续耦合方法的隧道压力拱特性研究

隧道压力拱问题一直是隧道工程研究的关键问题,目前常用的连续介质数值模拟方法对于隧道压力拱特性的微观研究有所欠缺,而擅长微观力学研究的离散元数值模拟方法对计算机存储空间和计算时间的要求太高。基于现有离散-连续耦合思路,通过力的传递实现离散-连续模型的耦合;研究了耦合算法中的平均应力计算方法、平均应力计算区域面积及耦合程序遍历颗粒方法;基于自行开发优化的离散-连续耦合程序,模拟了隧道开挖后的围岩受力特性,研究了隧道压力拱形成机理及压力拱特性;计算了埋深分别为10 m,14 m,18 m,22 m,26 m,30 m和34 m情况下的隧道开挖产生的压力拱应力集中等效区域,揭示了隧道压力拱随着隧道埋深的变化规律。研究结果表明,自行开发优化的离散-连续耦合程序能在保证计算精度的前提下,充分发挥离散元方法在微观力学研究方面的优势;隧道开挖后,开挖面周边范围出现层状压力环,但在拱顶和仰拱底附近区域的围岩压力环的环间接触力降低,围岩承载能力急剧降低,形成压力拱;随着隧道埋深的增加,隧道压力拱应力集中等效区域减小,隧道周边围岩的压力拱承载能力越来越大;但当隧道埋深达到一定界限后,隧道压力拱高度趋于稳定。     

Nonlinear dynamic behaviors of viscoelastic shallow arches

The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical in- tegration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch viscoelastic shallow arches may appear to have a are investigated. The results show that chaotic motion for certain conditions.     

The dynamic behavior of MEMS arch resonators actuated electrically

In this paper, we investigate the dynamic behavior of clamped-clamped micromachined arches when actuated by a small DC electrostatic load superimposed to an AC harmonic load. A Galerkin-based reduced-order model is derived and utilized to simulate the static behavior and the eigenvalue problem under the DC load actuation. The natural frequencies and mode shapes of the arch are calculated for various values of DC voltages and initial rises. In addition, the dynamic behavior of the arch under the actuation of a DC load superimposed to an AC harmonic load is investigated. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response of the arch due to DC and small AC loads. Results of the perturbation method are compared with those obtained by numerically integrating the reduced-order model equations. The non-linear resonance frequency and the effective non-linearity of the arch are calculated as a function of the initial rise and the DC and AC loads. The results show locally softening-type behavior for the resonance frequency for all DC and AC loads as well as the initial rise of the arch.     

Finite extensional deformation of a rigid plastic arch

The exact, nonlinear extensional theory of a rigid perfectly plastic arch is used to determine the complete load-deflection behavior of a clamped semicircular arch under the action of a vertical upward point load at the crown. A rate formulation of the problem is discussed. Solution of the rate problem at the yield-point state provides the basis for the construction of exact solutions for thin and for thick arches. Numerical results are presented in graphical form. These results consist of load-deflection curves for three thin arches and one thick arch. The plots together with formulas presented herein show that the slope of the load-deflection curve at the yield-point state is nonzero and positive for upward loading. This result deviates from the zero slope predicted by the usual methods of limit analysis in which geometry changes are neglected.