多自应力模态索穹顶结构的几何构造分析

索穹顶结构是发展和推广Fuller张拉整体结构思想后唯一实现的一种新型大跨空间结构,它的几何构造分析是一项非常重要的工作。本文在对一般空间杆件体系的分类、自应力模态和机构位移模态研究的基础上,从索穹顶结构特有的杆件拓扑关系入手,提出了单位整体可行预应力这一新概念,并最终解决了多自应力模态下该体系稳定性判定问题;通过对若干类型索穹顶结构的几何构造分析,得出了一些对结构设计有用的结论。     

Finite element based form-finding algorithm for tensegrity structures

This paper presents a novel form-finding algorithm for tensegrity structures that is based on the finite element method. The required data for the form-finding is the topology of the structure, undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The form-finding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two- and three-dimensional examples are presented that demonstrate the excellent performance of the proposed algorithm.     

索穹顶结构的找力分析方法--不平衡力迭代法

索穹顶的刚度和承载能力都是通过施加预应力来获取的,预应力设计是对索穹顶进行任何其它分析的基础,所以它的找力分析(Force finding)是一项很重要的工作。本文提出一种找力分析方法———不平衡力迭代法,它可以克服整体可行预应力法的一些不足:即使在索穹顶构件分组发生错误时仍可找到满足已知形状的预应力分布,并且该方法具有良好的稳定性和运算效率,算例表明不平衡力迭代法非常适合大型复杂索穹顶结构的找力分析。     

基于非线性有限元的索穹顶施工模拟分析

索穹顶结构的成形和施工模拟分析是该体系的基础问题。由于包含着刚体位移的分析使得跟踪难度相当大。本文采用了基于非线性有限元的施工过程分析 ,适应性强、分析精度高 ,避免了刚体位移假定。从而使得索穹顶体系的成形过程、受荷状态的全过程分析方法获得了统一。通过与试验模型对比分析表明本文方法操作简单且分析精度较高 ,分析的结果能够很好地指导施工     

A necessary condition for stability of kinematically indeterminate pin-jointed structures with symmetry

Stability conditions are the key to transform kinematically indeterminate structures into prestressed structures or deployable structures. From the viewpoint of symmetry, a necessary condition is presented for the stability of symmetric pin-jointed structures with kinematic indeterminacy. The condition is derived from the positive definiteness of the quadratic form of the tangent stiffness matrix. Numerical examples verify that the proposed necessary stability condition is in accord with the conventional theory of structural rigidity, and is considered to be more comprehensible. It is robust and easy to implement. Results show that a symmetric prestressed structure is guaranteed to possess integral prestress modes, if the necessary condition is satisfied. Further, a pin-jointed structure with fully symmetric mechanism modes is proved to be unstable, if it does not satisfy the condition.     

张拉结构非线性分析的五节点等参单元

本文针对张拉结构的特点，提出了一种五节点等参数单元有限元模型，采用四次多项式作为位移插值函数及单元初始形状函数，并假定索是理想柔性的且满足虎克定律，基于修正的Ｌａｇｒａｎｇｉａｎ坐标描述法，建立了非线性有限元基本方程和切线刚度矩阵，利用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法进行了实例计算。结果表明：本文方法精度极高，可供大跨度索网，索穹顶，拉线塔等张拉结构分析，设计时采用。     

端点位移激励下斜拉索非线性振动计算方法研究Investigation on computing method of nonlinear vibration of the stayed cable with displacement excitation at the end point

考虑拉索不同阶模态大幅振动之间的耦合效应,根据拉索的振动理论,详细地推导了单根拉索在端点位移激励下发生大幅振动时的非线性振动方程。根据某实际斜拉桥拉索参数,讨论了不同垂跨比对拉索振动特性的影响。使用四阶Runge-Kutta法求解拉索的非线性振动方程,通过对比有限元模型的非线性动力时程积分数值计算结果,验证了理论模型的可靠性与适用性。     

Non-linear interactions in the flexible multi-body dynamics of cable-supported bridge cross-sections

An elastic section model is proposed to analyze some characteristic issues of the cable-supported bridge dynamics through an equivalent planar multi-body system. The quadratic non-linearities of the four-degree-of-freedom model essentially describe the geometric coupling which may strongly characterize the dynamic interactions of the bridge deck and a pair of identical suspension cables (hangers or stays). The linear modal solution shows that the flexural and torsional modes of the deck (global modes) typically co-exist with symmetric or anti-symmetric modes of the cables (local modes). The combinations of parameters which realize remarkable 2:1:1 internal resonance conditions among one of the global modes (with higher natural frequency) and two local modes (with lower and close natural frequencies) are obtained by virtue of a multiparameter perturbation method. The non-linear response of the resonant systems shows that the global deck motion – directly forced at primary resonance by an external harmonic load – can parametrically excite the local cable motion, when the deck vibration amplitude overcomes the critical value at which a period-doubling bifurcation occurs. The relevant effects of both viscous damping and internal detuning on the instability boundaries are parametrically investigated. All the internal resonance conditions as well as the critical vibration amplitudes are expressed as an explicit, though asymptotically approximate, function of the structural parameters.     

Analysis of prestressed mechanisms

A new theory is presented for the matrix analysis of prestressed structural mechanisms made from pin-jointed bars. The response of a prestressed mechanism to any external action is decomposed into two almost separate parts, which correspond to extensional and inextensional modes. A matrix algorithm which treats these two modes separately is developed and tested. It is shown that the equilibrium requirements for the assembly, in its initial configuration as well as in deformed configurations which are obtained through infinitesimal inextensional displacements, can be fully described by a square equilibrium matrix. It is also shown that any set of extensional nodal displacements has to satisfy some equilibrium conditions as well as standard compatibility equations, and that the resulting system of linear equations defines a square kinematic matrix. Theoretical as well as experimental evidence supporting this approach is given in the paper ; two simple experiments which were of crucial importance in arriving at the equilibrium conditions on the extensional displacements are described.The interaction between the two modes of action of a prestressed mechanism is discussed, together with a rapidly converging iterative procedure to handle it. A study of the non-linear effect by which the self-stress level in a statically indeterminate assembly rapidly increases if an inextensional mode is excited, supported by further experimental results, concludes the paper. This work is relevant to the analysis of most cable systems, pneumatic domes, fabric roofs, and “Tensegrity” frameworks.     

端点位移激励下斜拉索非线性振动计算方法研究

考虑拉索不同阶模态大幅振动之间的耦合效应,根据拉索的振动理论,详细地推导了单根拉索在端点位移激励下发生大幅振动时的非线性振动方程。根据某实际斜拉桥拉索参数,讨论了不同垂跨比对拉索振动特性的影响。使用四阶Runge-Kutta法求解拉索的非线性振动方程,通过对比有限元模型的非线性动力时程积分数值计算结果,验证了理论模型的可靠性与适用性。     

A steady laminar flow of a suspension in a channel

A two dimensional model of a steady flow of a suspension in an inclined channel is developed and studied with the aid of an integral method. The model explains the existence of two operational modes in such a channel, predicted earlier by Probstein et al. (1977).     

Parametric aeroelastic modeling based on component modal synthesis and stability analysis for horizontally folding wing with hinge joints

To investigate the aeroelastic stability of a folding wing effectively, a parametric aeroelastic analysis approach is proposed. First, the fixed interface component modal synthesis is used to derive the structural dynamic equation for a folding wing, in which the elastic connection is considered. The unsteady aerodynamic model is established by the doublet lattice method (DLM), and the aeroelastic model is achieved from integration of the DLM with the component modal analysis. The generalized aerodynamic influence coefficient matrix is established by modes kept and constraint modes of each component. The aeroelastic stability of a folding wing is investigated based on the Gram matrix in control theory. The effectiveness of the proposed method is verified via comparison with traditional flutter eigenvalue analysis for both extended and folded configurations. The proposed method identifies coupled modes and improves computational efficiency when compared to classical aeroelastic stability analysis methods, such as the p–k method.     

Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed.The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method.The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems.The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation.A bilinear controller by using the direct method of Lyapunov is introduced.The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.     

损伤拉索的等效弹性模量及其参数分析

损伤拉索会出现线形松弛、应力水平降低的情况,必然会影响拉索的等效弹性模量。本文首先引入损伤程度、位置及范围3个参数,用以描述拉索损伤形态的特征,建立损伤拉索索力和线形计算公式,采用数值方法计算了损伤拉索弦向等效弹性模量精确数值,并和经典的等效弹性模量公式的计算结果进行了比较分析,分析了考虑损伤时两种不同计算方法结果的误差。计算表明,对于500m弦向长度以内的损伤拉索,拉索的弦向长度Lc越大,倾角越小,等效弹性模量的损失越大,并且应用割线模量公式计算的误差也越大,当Lc=500m时,损伤拉索相对误差值在2.5%~4.5%之间。弦向应变越小,等效弹性模量损失越大,弦向应变在[0.001,0.004]内,应用割线模量公式计算的相对误差小于3.5%。损伤程度及损伤范围对引用等效弹性模量公式的误差影响较大,倾角对等效弹模公式相对误差的影响也不容忽视。弦向长度、弦向应变、倾角和损伤程度参数都是通过改变拉索的松弛程度进而影响等效弹性模量的数值以及公式的误差。     

Super-Harmonic and Internal Resonances of a Suspended Cable with Nearly Commensurable Natural Frequencies

In this paper, super-harmonic and internal resonance characteristics ofa viscously damped cable with nearly commensurable natural frequenciesare investigated by use of a novel method. The proposed frequency-domainsolution method is based on the combined use of a three-dimensionalnonlinear finite element approach and the incremental harmonic balancetechnique. It is an accurate algorithm in the sense that it accommodatesmulti-harmonic components and no mode-based model reduction is utilizedin the solution process. The alternating frequency/amplitude-controlledalgorithm enables complete solution to the frequency-response curvesincluding unstable branches, sub- and super-harmonic resonance andinternal resonance. A suspended cable paradigm under internal resonancecondition is studied using the proposed method. Nonlinear response andmodal interaction characteristics of the cable at different frequencyregions are identified from analysis of response profiles and harmoniccomponent features. The super-harmonic and internal resonance responsesare respectively characterized based on the harmonic distribution. Underan in-plane harmonic excitation, the two-to-one internal resonancebetween the in-plane and out-of-plane modes and the super-harmonicresonance around the second symmetric in-plane mode are revealed. Strongnonlinear interaction among different modes in the parameter spaceranging from primary resonance to super-harmonic resonance is observed.     

Solution of a mixed dynamic problem on the displacements given on the boundary of a half-plane lying on the surface of an isotropic homogeneous elastic half-space

We consider the problem on the motion of an isotropic elastic body occupying the half-space z ≥ 0 on whose boundary, along the half-plane x ≥ 0, the horizontal components of displacement are given, while the remaining part of the boundary is stress-free. We seek the solution by the method of integral Laplace transforms with respect to time t and Fourier transforms with respect to the coordinates x, y; the problem is reduced to a system of Wiener-Hopf equations, which can be solved by the methods of singular-integral equations and circulants. We invert the integral transforms and reduce the solution to the Smirnov-Sobolev form. We calculate the tangential stress intensity coefficients near the boundary z = 0, x = 0, |y| < ∞ of the half-plane. The circulant method for solving the Wiener-Hopf system was proposed in [1]. A static problem similar to that considered in the present paper was solved earlier. The Hilbert problem was reduced to a system of Fredholm integral equations in [2]. In the present paper, we solve the above problem by reducing the solution to quadratures and a quasiregular system of Fredholm integral equations. We give a numerical solution of the Fredholm equations and calculate the integrals for the tangential stress intensity coefficients.     

爆破开挖扰动下锚固节理岩质边坡位移突变特征与能量机理

针对白鹤滩水电站左岸坝基河谷底部边坡岩体爆破开挖,采用现场岩体位移监测、锚索轴力监测及数值模拟的手段,研究了爆破开挖扰动下锚固节理岩质边坡的位移突变特征及其能量机理。研究结果表明:对于深切河谷底部高地应力边坡岩体爆破开挖,爆炸荷载挤压及地应力作用下,岩体所积聚的应变能快速释放,导致了节理岩质边坡的位移突变,突变位移包括节理张开位移和岩体回弹位移两部分;地应力水平越高、岩体弹性模量越低,总的突变位移量越大;预应力锚索主要通过抑制节理张开位移来控制边坡岩体的位移突变,锚索预应力等级越高,其吸能和释能速率越高,对节理岩体位移突变的控制效果越好,当锚索的预应力等级高到一定程度后,节理岩体的突变位移不再随锚索预应力等级的升高而显著减小。     

预应力混凝土简支梁桥锚下有效预应力分析

为了确定预应力混凝土简支梁桥在施工张拉与运营养护全寿命过程中结构锚固端锚下有效预应力值,基于梁挠曲变形理论与简支梁受力特性,推导出简支梁桥锚下有效预应力计算公式,并提出了一种预应力混凝土简支梁桥下有效预应力简便检测方法.以某40 m预制简支T梁桥为依托工程,通过对不同工况下简支梁桥跨中挠度值与锚固端有效预应力值进行测量,计算了不同工况下简支梁桥锚下有效预应力值,并与实测值进行了比较.研究结果表明:本文所提简支梁桥锚下有效预应力计算公式能较准确预测锚固端有效预应力值,依托工程简支梁桥锚下有效预应力公式计算值与实测值相对误差最大仅为4.83%,计算精度满足工程需求;所提出的预应力混凝土简支梁桥锚下有效预应力简便检测方法可为桥梁全寿命预测提供指导与借鉴.     

Dynamics of a prestressed stiff layer on an elastic half space: filtering and band gap characteristics of periodic structural models derived from long-wave asymptotics

Anti-plane and plane-strain, time-harmonic, small-amplitude vibrations of an elastic layer on an elastic half space are considered, superimposed upon a state of finite, uniform stress and strain. A (compressible) elastic material is considered, orthotropic with orthotropy axes aligned parallel and orthogonal both to the layer and the prestress principal directions. A non-uniform mass density is assumed in the layer. A formal long-wave asymptotic solution is derived under the assumptions of high contrast between the stiffnesses of the layer and the half space and between certain prestress components and the current elastic shear modulus.It is shown that (i) the layer asymptotically behaves as a beam subject to transversal and axial vibrations; (ii) the response of the half space can be found in a closed-form, under the assumption of plane wave motion (which becomes consistent when the density of the layer is uniform), otherwise it is represented by a hypersingular integral equation; (iii) if the nonlocality introduced by the hypersingular integral equation is restricted to an influence area of finite extent, the integral can be analytically approximated, so that a Winkler-type spring model representing the half space is rigorously derived. For uniform density of the layer, the constants defining the spring model are given as functions of the prestress and anisotropy parameters of the half space; and, finally, (iv) the asymptotic solution provides new analytical expressions for incremental displacement of the layer, which, compared to the exact numerical solution (also included), are shown to perform quite well, even for values of parameters much beyond the limits imposed by the asymptotic analysis.The asymptotic analysis allows us to explore, for the first time, dynamic properties of a periodic layer bonded to an elastic half space and subject to a uniform prestress state. We find that the system exhibits band gaps (ranges of forbidden frequencies) and that the prestress can be used as a parameter tuning the filtering properties of the structure, an effect which may have important consequences in the design of resonant devices.     

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

This paper describes the development and application of a general domain integral method to obtain J-values along crack fronts in three-dimensional configurations of isotropic, functionally graded materials (FGMs). The present work considers mode-I, linear-elastic response of cracked specimens subjected to thermomechanical loading, although the domain integral formulation accommodates elastic–plastic behavior in FGMs. Finite element solutions and domain integral J-values for a two-dimensional edge crack show good agreement with available analytical solutions for both tension loading and temperature gradients. A displacement correlation technique provides pointwise stress-intensity values along semi-elliptical surface cracks in FGMs for comparison with values derived from the proposed domain integral. Numerical implementation and mesh refinement issues to maintain path independent J-values are explored. The paper concludes with a parametric study that provides a set of stress-intensity factors for semi-elliptical surface cracks covering a practical range of crack sizes, aspect ratios and material property gradations under tension, bending and spatially-varying temperature loads.