Dynamics of cable truss via polynomial shape functions

A model for the in-plane dynamic behaviour of a biconcave cable structure, subject to large static deformations and potentially slack harnesses is proposed, based on polynomial shape functions, in line with the classical Ritz method. The model provides a semi-analytical approach to the calculation of natural frequencies and modal shapes of the structure. The proposed formulation leads to an eigenvalue problem, based on a reduced number of degrees of freedom compared with equivalent FEM solutions, providing the basis for fast and accurate sensitivity analysis. The behaviour of the deformed structure is analysed in detail to understand the non-linear effects of non-symmetric mass and load distribution and slack harnesses on natural frequencies and corresponding modal shapes. Results confirm the relevance of the non-linear effects, due to the statically loaded configuration, on the linear vibrations of the structure, in particular evidencing the influence of the slackening of harnesses on modal shapes. Results are compared to analytical models, where available (single sagged cable), and to FEM solutions (for cable trusses with non-uniform mass and load distribution and potentially slack harnesses), providing good agreement.

     

予应力钢桁架刚度反演分析的摄动迭代法

基于文（１）所建立的拉索式予应力钢桁架基本计算,根据矩阵摄动原理进一步给出了以竖向为位移为约束反演确定任意布索张拉予应力钢桁架单元刚度和的索刚度的摄动迭代公式。算例表明,该方法具有较高的精度,可满足工程设计需要。     

随机拉索刚度预应力空间钢桁架随机内力摄动分析

基于已建立的拉索式平面预应力钢桁架基本理论 ,考虑到拉索刚度的随机性 ,得到了拉索式空间预应力钢桁架随机内力摄动分析的一般公式及敏度分析式 ,给出了空间预应力钢桁架随机内力统计特性计算表达式。为进一步进行空间预应力钢桁架可靠性分析奠定了一定的理论基础。最后针对工程中常见的三角形立体钢桁架 ,给出了算例     

大准铁路黄河特大桥钢桁梁静载试验

大准铁路黄河特大桥钢桁梁为 96 132 96m三跨连续式、无竖杆刚性桁梁柔性拱组合系结构。运营十年后进行了静载试验,并将测试结果与数值计算进行了对比。钢桁梁在中 -活载和恒载作用下,轴向总应力最大的杆件为A17E18,其总应力为 142. 083MPa。在中 -活载作用下,边跨中和中跨中的挠度,分别为 76. 23mm和 63. 94mm,其挠跨比分别为 1 /1259和 1 /2064。由此可以看出该桥承载力和竖向刚度符合设计标准,满足使用要求,且承载力和竖向刚度安全储备较大。上下游两片主桁受力均匀性较好。测试方法和结果可供类似工程参考。     

随机边界弹性约束空间预应力钢桁架随机内力摄动分析

本文在文献[2]-[4]的基础上,进一步建立了具有任意弹性约束的拉索式空间预应力钢桁架计算模型,其中所有弹性约束均由一组弹簧模拟,在此基础上考虑到边界弹性约束刚度的随机性,进一步建立了拉索式预应力空间钢桁架随机内力摄动分析的计算公式,并针对三角形立体钢桁架进行了分析,为预应力立体钢桁架的可靠性研究奠定了一定的理论基础。     

横观各向同性弹性半空间地基上正交异性矩形中厚板弯曲解析解

对横观各向同性体通解进行双重傅里叶变换,获得了直角坐标系下横观各向同性弹性半空间地基受任意竖向荷载作用下的位移积分变换解;在此基础上建立了板与地基的变形协调方程,并与三个广义位移变量描述的弹性地基上四边自由正交各向异性矩形中厚板的弯曲控制方程相结合,用三角级数法,得出横观各向同性弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用的弯曲解析解。相关算例分析表明,本文方法是有效的。     

Large deflections of cantilever beams of non-linear elastic material under a combined loading

Large deflection of cantilever beams made of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. Governing equation was derived by using the shearing force formulation instead of the bending moment formulation because in the case of large deflected member, the shearing force formulation possesses some computational advantages over the bending moment formulation. Since the problem involves both geometrical and material non-linearities, the governing equation is complicated non-linear differential equation, which would in general require numerical solutions to determine the large deflection for a given loading. Numerical solution was obtained by using Butcher's fifth order Runge-Kutta method and are presented in a tabulated form.     

横观各向同性弹性半空间地基上四边自由各向异性矩形薄板弯曲解析解

选用更具广泛性的横观各向同性弹性半空间地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解．将异性薄板的弯曲控制方程,与基于横观各向同性弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后用三角级数法,得出横观各向同性弹性半空间地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及内力的解析表达式．该解析解克服了数值法的弊端,取消了对地基反力的假设,板的内力及地基反力求解更切实际．算例结果与文献结果吻合良好,证明本文方法的可行性．     

预应力钢桁架结构分析中的摩擦滑移索单元

为精确模拟预应力钢桁架中连续长索在支撑点的滑动,本文创建了一种考虑摩擦力影响的新单元。被称为摩擦滑移索单元的新单元有三个节点,中间节点为支撑点。本文首先利用弹性悬链线的解析解,建立了弹性悬链线单元,并推导了单元两端点的张拉刚度。摩擦滑移索单元由两个弹性悬链线单元组合而成,根据支撑点处索的滑动方向、索力差、滑动摩擦力和滑移刚度调整两索段的原长,使支撑点两侧的索力满足给定的摩擦关系。算例验证了新单元算法的正确性和高效性,对设计的预应力钢桁架的分析,显示了张拉过程中及使用荷载作用下新单元在结构分析中的应用。新单元可直接用于常规的有限元分析,研究在工作状态或施工中存在连续长索滑移的索结构。     

Large displacement analysis of elastic pyramidal trusses

The paper examines the equilibrium stability problem for a simple class of elastic space trusses in the shape of a regular pyramid. Joints located at the vertices of the base polygon are fixed while the joint at the apex is subjected to a proportionally increasing load acting in either the vertical direction, in the horizontal plane, or along a generic oblique direction. Exact closed-form solutions are derived for each load condition under the common hypotheses of linear material law, small or moderate axial deformation in bars and large nodal displacements. Despite their seeming simplicity, these mechanical systems exhibit a wide variety of post-critical responses, not exhausted by the classical snapping and bifurcation phenomena. In addition to regular primary and secondary branches, the equilibrium paths may include neutral branches, namely branches entirely composed of bifurcation or limit points. Besides their immediate theoretical interest, these branches are particularly difficult to handle by the standard numerical procedures of non-linear analysis, so the given solutions may represent severe benchmark tests.     

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

Non-linear studies of orthotropic shallow spherical shells on elastic foundation

Governing non-linear integro-differential equations for cylindrically orthotropic shallow spherical shells resting on linear Winkler-Pasternak elastic foundations, undergoing moderately large deformations are presented. Three problems, namely, non-linear static deflection response, non-linear dynamic deflection response and dynamic snap-through buckling of orthotropic shells have been investigated. The influences of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply- supported immovable edge conditions accurately. Orthotropy, foundation interaction and material damping play significant roles in improving the load carrying capacity of the shell structures.     

一种连续索滑移的处理方法

目的是建立一种快速简便的拉索滑移问题的有限元计算方法。采用基于弹性悬链线精确解的两节点悬链线单元模拟索结构中的拉索，利用求解非线性方程组的延拓法，再配以常用的牛顿法，建立了快速的给定索原长情况下的拉索刚度计算方法。此法对于一般的给定初值，能很快逼近真实解，从而扩大了解的收敛范围，更重要的是与牛顿法相比更加高效。进而采用二分法建立了索结构中拉索滑移问题处理的算法，编制了相应的程序段，并通过算例证明了其正确性。本文的拉索滑移处理方法可用于索结构的设计与施工。     

S型功能梯度扁球壳非线性屈曲的渐近分析

本文利用渐近迭代法获得了边界弹性支撑的功能梯度扁球壳的非线性屈曲问题的理论解．假设材料组分体积分数沿壳体厚度方向呈sigmoid幂函数变化,边界上考虑一般的弹性支撑约束．基于经典的薄壳理论和几何非线性关系,导出了S型功能梯度扁球壳的非线性屈曲问题的控制方程．采用渐近迭代法通过两次迭代得到了无量纲挠度和均布荷载之间的非线性特征关系．通过与已有有限元方法和其他数值方法的结果对比,验证了本文解的有效性和高精度．同时,通过计算阐述了缺陷因子、材料参数、边界约束系数及特征几何参数对壳体临界屈曲荷载的影响．     

Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the von K′arm′an geometrical nonlinearity,the Stein and McE lman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material,and dimensional parameters on dynamic responses of shells are considered.     

弹性支承多次张拉预应力钢桁架刚度反演摄动分析

本文基于文献「１」所建立的拉索式预应力钢桁架基本理论,通过引入组合单元和刚度变化因子,利用矩阵摄动原理建立了以结点竖向位移为约束,以确定弹性支承多次张拉预应力钢桁架各类单元刚度为目标的反演摄动迭代方程。算例表明,该方法具有较高的逼近精度,可满足工程设计需要。     

THE COMPUTATIONAL METHOD FOR STABILITY OF TRUSSES WITH SMALL DEFORMATION

基于桁架结构稳定性计算的经典理论,分析了利用特征值理论开展桁架结构屈曲分析的计算方法,以及利用欧拉临界载荷屈曲理论,采取杆件撤除的静力求解确定桁架结构稳定临界载荷的计算方法. 通过理论研究和相关算例分析,论证了利用特征值理论和临界载荷屈曲理论相结合的方法,判断小变形桁架结构的失稳模态,求解桁架结构稳定临界载荷的确定性.     

On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach

This paper presents the extension of a flexibility-based large increment method (LIM) for the case of cyclic loading. In the last few years, LIM has been successfully tested for solving a range of non-linear structural problems involving elastoplastic material models under monotonic loading. In these analyses, the force-based LIM algorithm provided robust solutions and significant computational savings compared to the displacement-based finite element approach by using fewer elements and integration points. Although in cyclic analysis a step-by-step solution procedure has to be adopted to account for the plastic history, LIM will still have many advantages over the traditional finite element method. Before going into the basic idea of this extension, a brief discussion regarding LIM governing equations is presented followed by the proposed solution procedure. Next, the formulation is specified for the treatment of the elastic perfectly plastic beam element. The local stage for the beam behavior is discussed in detail and the required improvement for the LIM methodology is described. Illustrative truss and beam examples are presented for different non-linear material models. The results are compared with those obtained from a standard displacement method and again highlight the potential benefits of the proposed flexibility-based approach.     

Homoclinic bifurcation and chaos attractor in elastic two-bar truss

In this paper, we present a dynamic bifurcation analysis of the non-linear Duffing's equation on a simple elastic structure. The structure is a two-bar elastic truss with a damper, and possesses geometrical non-linear stiffness. We consider the dynamic instability of its structure based on Duffing's oscillation, which shows bifurcation behavior of the homoclinic orbit. We could numerically forecast the trajectory near the invariant saddle point of homoclinic bifurcation on this model, and we found that it is possible to solve dynamic bifurcation and strange attractors (chaos) on this non-linear structure. On this truss, we could investigate the dynamic stability of the strange attractor using Lyapunov exponents under the frequency and/or the amplitude parameter of periodic load.