悬链线斜靠式拱肋系侧倾失稳临界荷载

基于能量分析方法,推导了主拱肋和稳定拱肋拱轴线为悬链线的斜靠式拱肋系侧倾失稳临界荷载计算公式,并通过与有限元数值计算结果比较,证明了该计算公式的正确性,进一步验证了所提出的拱肋系侧倾失稳时横撑切向和径向力学模型的适用性,并将拱轴线为悬链线和圆弧曲线的斜靠式拱肋系的侧倾失稳临界荷载进行了比对分析,阐明了圆弧曲线代替悬链线斜靠式拱肋系侧倾失稳临界荷载的适用条件。研究结果表明:拱轴线的线型对斜靠式拱肋系的侧倾失稳临界荷载有一定的影响;当稳定拱肋倾角较小时,悬链线拱肋系的侧倾失稳临界荷载与圆弧曲线拱肋系的差异不超过5%;当矢跨比较小时,圆弧曲线拱肋系代替悬链线拱肋系的侧倾失稳临界荷载产生的误差在10%以下,但矢跨比较大时,二者的差异较大,不可等同。     

水平弹性支承圆弧钢拱的弹性屈曲分析

钢拱常支承于其他结构上.拱脚受到弹性约束并出现水平位移,弹性约束会显著影响拱的力学行为.该文得到了水平弹性支承拱在沿弦长均匀分布的面内竖向荷载作用下的内力及位移的解析解,构造了一个无量纲化柔度系数.利用这个参数,对线性解进行分析,提出了计算跨中轴力和拱脚支座位移的理论公式.根据跨中轴力大小,提出了在线性计算范围内划分拱...     

Buckling behavior of standing laminated Mindlin plates subjected to body force and vertical loading

In this article, an exact analytical solution for stability analysis of vertical moderately thick laminated rectangular plates subjected to selfweight and top load on the basis of the first-order shear deformation plate theory is presented. It is assumed that the symmetric laminated rectangular plate is composed of transversely isotropic layers. Employing an analytical approach, the coupled governing stability equations of the laminated plate are converted into two uncoupled partial differential equations in terms of transverse displacement and an auxiliary function. It is considered that the vertical sides of the laminated plate are simply supported. Using Levy-type solution, the decoupled equations are reduced to two ordinary differential equations. One of these equations has variable coefficients, for which an exact analytical solution is obtained in the form of power series method of Frobenius. After appropriate convergence study, the present analysis is validated by comparing the results with the existing data reported in the literature. Furthermore, the effects of aspect ratio, plate thickness, boundary conditions, weight of plate and top load on the stability of laminated rectangular plates are investigated and discussed in details. The presented formulations and results can be used as benchmark for future research studies.     

Minimum vertical load on masonry walls – a realistic view / Mindestauflast auf Mauerwerkswänden – eine realitätsnahe Betrachtung

To transfer bending moments in building components consisting of a material without tensile strength always requires a simultaneously acting normal force. Accordingly, masonry walls exposed to horizontal loads (e.g. wind) require a minimum vertical load, so that the resultant stress at the mid‐height of the wall remains the same within the cross‐section. As part of the A2 amendment to DIN EN 1996‐3/NA, this verification of walls subjected to low vertical loads, such as outer walls on the top floor exposed to high wind load was implemented in the National Annex. Part 3 of DIN EN 1996‐3 includes a similar standard regulation for verification of the minimum vertical load, which is based on an arch effect within the wall cross‐section. Based on this technical background and taking into account the main influencing parameters, a verification model is presented here which realistically describes the load‐bearing behaviour of unreinforced masonry walls subjected primarily to bending. Apart from the bending moments due to wind load, an initial eccentricity of the wall as well as second order effects due to wall deformations also have to be taken into account. In addition, a simple approximation equation is provided for the practical determination of the required minimum vertical load.     

高速移动荷载下弹性半空间饱和地基动应力响应

对承受高速移动荷载的饱和多孔地基动应力响应开展了解析理论研究。引入势函数,进行Helmholtz代换,通过傅里叶变换得到了承受矩形分布的竖向与水平向移动荷载的三维饱和地基动应力的基本函解,数值积分求解逆变换,进而得到移动荷载下饱和地基动应力响应的理论解。基于饱和多孔介质的动应力理论解,分析了移动荷载速度及频率的动应力响应,进一步分析了水平及竖向移动荷载耦合作用下饱和地基的动应力。理论分析表明,荷载速度及其频率诱发地基动应力水平的放大效应,动应力水平随荷载移动速度增大呈现指数型放大效应,移动速度接近剪切波速时动应力水平达到峰值,而荷载速度与频率引发的动应力放大效应随地基深度增大而增强。考虑水平动载的耦合效应,地基的动剪应力和水平向正应力水平显著增大,而竖向动正应力变化不大。     

活性粉末混凝土拱极限承载力试验研究

进行了两根活性粉末混凝土(RPC)模型拱的L/4处单点加载的面内受力全过程试验,建立了考虑材料与几何双重非线性的有限元模型,有限元计算结果与试验结果吻合良好。通过与普通混凝土(RC)模型拱的受力性能的比较,对RPC模型拱荷载-竖直位移曲线、裂缝开展情况、截面应变和结构破坏模式等方面进行了分析。试验与有限元计算结果表明,RPC拱受力过程和破坏模式与RC拱相似,分为弹性阶段、裂缝开展阶段和钢筋屈服阶段,最终因出现4个塑性铰形成机构而呈塑性破坏,其极限承载力也可用极限分析法进行简化计算。RPC拱由于其材料性能优越,使其受力性能优于RC拱,在同级荷载下RPC拱裂缝的宽度约为RC拱的25%~50%;而RPC拱的开裂荷载、钢筋屈服荷载和极限承载力均较RC拱有明显的提高。在极限承载力相同的条件下,RPC拱的截面积与自重可以减小到RC拱的67%左右,表明RPC可有效减轻结构自重,提高拱桥跨越能力。     

Combination of finite element analysis and analytical crack tip solution for mixed mode fracture

A finite element program was developed which combines the analytical crack tip solution with a conventional finite element analysis and evaluates various crack tip parameters as part of the solution. This program was used to analyze cracked specimens subjected to mixed mode loading. The importance of retaining the second term of the series expansion for local stress, a contribution which is independent of the distance from the crack tip, was demonstrated. It was first shown analytically that the presence of a load applied parallel to the crack reveals itself only through this constant second term, which vanishes only for specific loading conditions. The results of the numerical analysis demonstrate that the stress intensity factor K_I is independent of the load applied parallel to the crack only when this term is included in the analytical crack tip solutions. Failure to include the constant term has the effect that K_I varies with the horizontal load. The parameter K₁₁ is independent of this load in both cases. This indicatesonce again that it is this constant term which accounts solely and entirely for the presence of a load applied parallel to the crack.     

悬索桥主缆初始位形的悬链线方程精细迭代分析法

悬索桥非线性有限元法采用悬链线单元精度高,推导了基于自重约束方程,求解两种设计条件下主缆初始位形的悬链线精细迭代法公式,该方法能够计算主缆变形后自重荷载集度的变化。根据索鞍的受力特点,推导了不平衡索力与索鞍预偏量之间增量函数形式的显式刚度方程,导出了索鞍弧顶主缆曲线的无应力索长的精确计算公式。算例结果表明,方法精度高,计算稳定且收敛快。     

基础竖向多频参数激励下圆弧拱平面内动力失稳研究

地震波、冲击波、环境振动激励会通过地基基础传递到拱上,致使拱发生动力失稳失去承载能力。为深入研究拱在基础竖向激励下的动力稳定性,该文基于能量法,建立了基础竖向激励下圆弧拱平面内动力稳定能量方程,利用哈密顿原理得到了拱面内径向和切向振动的耦合控制方程,求解了圆弧拱平面内失稳前的动轴力与动弯矩解析解。引入拱轴线不可压缩假设,解决了圆弧拱平面内动力控制方程的解耦问题。利用伽辽金法建立了基础竖向多频激励下圆弧拱平面内二阶常微分动力稳定方程,运用多尺度法推导了基础竖向多频激励下圆弧拱平面内动力失稳的临界激励频率解析公式,得到了圆弧拱同时发生一阶反对称参数共振和二阶正对称共振失稳的动力不稳定域,并利用有限元数值分析验证了理论解析解的正确性。进一步分析了拱矢跨比、长细比和圆心角对动力不稳定域的影响。     

基于等效模型的索牵引并联机器人的刚度分析

现有索牵引并联机器人研究中,由于柔索长度较短大多将其处理成仅能受拉的直线索单元,没有考虑柔索垂度的影响,刚度分析过程与刚性支腿并联机器人相同.为考虑垂度影响,该文采用悬链线方程建立了大跨度柔索的静力学模型,推导出柔索的刚度矩阵.然后提出了一种刚度等效模型,将柔索等效为三根两两相互垂直的弹簧.于是便可将索牵引并联机器人等...     

深埋隧道轴线合理布置与衬砌结构稳定性研究

深埋隧道常处于构造应力状态,且水平应力分布并不均匀。采用数值模拟和模型试验方法,研究自重应力场、水平大主应力与洞线平行和垂直、不同围岩级别隧道轴线选择对围岩和衬砌结构稳定性影响。水平大主应力与洞轴平行时,围岩最不利位置发生在边墙;水平大主应力与洞轴垂直时,围岩最不利出现在拱顶。水平地应力使得二次衬砌受力特征发生很大改变,自重应力条件下,衬砌首先发生裂缝部位为拱顶,发生压弯破坏,建议加强衬砌拱顶内侧纵向配筋,提高正截面抗拉能力。当大主水平应力与轴线垂直时,关键控制部位为墙脚,出现压剪破坏,应增设墙脚箍筋,提高抗剪承载力。规范提出隧道轴线宜与水平大主应力方向一致原则,是有适用条件的。研究成果可为深埋隧道设计、施工提供参考。     

两端简支曲线梁面内位移精确解

应用虚功原理和曲线结构热胀变形规律,建立了在集中荷载和变温作用下两端简支曲线梁面内位移解析表达式。当曲率半径趋近于无穷大时,得到相应的直梁解,并与曲线梁有限元结果吻合较好,从而证明了该文解答的正确性。将单跨梁解答应用于多跨曲线桥的求解中,得出在变温和桥墩顶部摩擦力共同作用下多跨曲线桥面内位移解析解。建立实际曲线桥有限元仿真模型,通过仿真分析结果与解析解比较,说明了该文理论具有较好的工程应用性,可作为曲线桥结构研究和设计的理论依据。     

单柱失效下结构连续倒塌的动力响应分析

该文提出了一种基于三折线结构抗力形式和升压平台形荷载函数的非线性单自由度模型,并推导了该模型的解析解,用于分析由单柱移除引起的连续倒塌过程中的结构瞬态动力响应。该模型可以涵盖各类抗力形式,包括抗力软化及大变形条件下的悬链作用,并考虑了柱子移除时间对动力响应的影响。钢筋混凝土和钢结构的梁柱子结构的动力试验结果与非线性单自由度模型计算所得到的动力响应结果（例如跨中位移）的对比表明:此模型可以准确地预测结构倒塌过程中结构的动力响应,计算速度快,准确性高,便于应用。     

A frequency-domain approach for modelling transient elastodynamics using scaled boundary finite element method

This study develops a frequency-domain method for modelling general transient linear-elastic dynamic problems using the semi-analytical scaled boundary finite element method (SBFEM). This approach first uses the newly-developed analytical Frobenius solution to the governing equilibrium equation system in the frequency domain to calculate complex frequency-response functions (CFRFs). This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT of the CFRFs to obtain time histories of structural responses. A set of wave propagation and structural dynamics problems, subjected to various load forms such as Heaviside step load, triangular blast load and ramped wind load, are modelled using the new approach. Due to the semi-analytical nature of the SBFEM, each problem is successfully modelled using a very small number of degrees of freedom. The numerical results agree very well with the analytical solutions and the results from detailed finite element analyses.     

An analytical model to determine the ultimate load on masonry arch bridges.

This paper proposes an analytical elasto–plastic model to describe the behavior of arches. The modeling is carried out using the equations of (i) horizontal equilibrium, (ii) vertical equilibrium and (iii) equilibrium of moments. The latter equations of equilibrium are ordinary differential equations which can easily be solved by adding boundary conditions, imposing restrictions on the horizontal and vertical movement and on the rotation in the abutments of the arch. For masonry arches, including material properties allowing the occurrence of cracks and the subsequent formation of hinges is required. The latter theory has been implemented in a computer program (Matlab), offering numerical simulations. The software was used to illustrate two case-studies, i.e., the assessment of an arch loaded with a vertical point load and one with a horizontal point load.     

Non-singular term effect on the fracture quantities of a crack in a piezoelectric medium

The static problem of a crack in a piezoelectric plate subjected to biaxial loading at infinity is analyzed. The aim of this paper is to estimate the influence of non-singular terms originated by the load biaxiality on the stress fields and on the elastic and electric displacements in the vicinity of the crack tip. An analytical method for seeking the electro-elastic solution is proposed. The novel procedure involves a transformation of similarity induced by the fundamental matrix that enables to express the equations governing the problem in terms of complex potentials. The application of the boundary conditions leads then to the formulation of Hilbert problems whose solutions allow to obtain the generalized stress and displacement components. Numerical results and graphs are presented and discussed for various loading conditions. The non-singular solution is compared to the asymptotic one, generally considered in the literature when analyzing fracture problems. In particular, it is shown that the direction of incipient crack extension, sought through the maximum circumferential stress criterion, can be seen to deviate from the crack axis as the collinear load increases, although geometry and applied load are symmetric.     

钢筋混凝土梁-板子结构抗连续性倒塌性能研究

该文通过试验与有限元模拟研究边柱失效工况下钢筋混凝土（RC）梁-板子结构抗连续倒塌性能。在实验室通过对RC梁-板子结构缩尺模型开展pushdown试验研究梁-板子结构的破坏模态,并进一步讨论了梁-板子结构在倒塌过程中的荷载传递机理和抗力机制。试验结果表明:RC梁-板子结构在倒数第二个边柱失效下可以形成有效的梁机制、压拱机制、悬链线机制以及拉膜机制抵抗倒塌。在小变形阶段,楼板在负弯矩区作为梁翼缘可以显著提升RC梁抗弯承载力（T型梁作用）;在大变形阶段,楼板发展拉膜作用早于梁发展悬链线机制。此外,根据有限元软件LSDYNA开展的数值分析结果表明:楼板提升RC框架屈服承载力与极限承载力分别高达65%和61%。     

不对称跨度下钢框架梁柱子结构抗倒塌性能分析

将子结构引入结构抗倒塌分析是评估结构抗倒塌性能的一种快速有效方法。采用备用荷载路径法,选择钢框架梁柱子结构作为研究对象,建立了分析梁柱子结构抗倒塌能力的理论计算模型,研究了梁柱子结构由梁抗倒塌机制向悬链线抗倒塌机制转换的过程及机理。根据梁柱子结构内力变化将整个抗倒塌过程划分为4个阶段,推导了不对称跨度情形下梁柱子结构在不同阶段的承载力及挠度变形计算公式,分析了梁柱子结构由抗弯向拉弯转化并最终主要依靠拉力抵抗外载的全过程,并通过数值算例验证了理论计算公式,满足工程计算的精度要求。     

堆载-电渗联合作用下的一维非线性大变形固结理论

堆载-电渗联合作用下的软土地基加固属于大变形固结问题。该文在Esrig电渗固结理论的基础上,建立了拉格朗日坐标下以超静孔压作为变量的一维非线性大变形固结理论方程,推导出相应的超静孔压、沉降、平均固结度和孔隙比的解析公式,且通过了模型试验的验证。之后,采用该解分析了土体在堆载-电渗联合作用下的地基大变形固结特性,且与Esrig小变形固结解析解进行对比。结果表明:堆载-电渗联合作用下,考虑大变形的计算结果更符合工程实际,且此解可用于对大变形固结问题数值解法的验证。     

Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics

In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement.