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     

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。     

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。     

基于双层平面索变形的车辐式张拉结构找形方法

建立了由上层索、下层索、飞柱组成的双层平面索结构,根据节点平衡推导了各索段拉力的计算公式;基于索拉力产生的平衡荷载与索拉力水平分量及索竖向变形之间的关系,推导了平面索在竖向荷载作用下变形计算的有限元列式;通过对平面索结构边界节点施加竖向位移,将上下索边节点移动到建筑要求的位置;当飞柱高度不同时,可通过飞柱的伸长或缩短达到设计要求的飞柱高度,最终实现车辐式张拉结构找形。本文还给出了找形后结构分析和索张拉控制所需的初应变计算公式以及考虑边界梁和柱子在索力下产生弹性变形的处理方法。通过对车辐式张拉结构工程实例进行找形计算,介绍了有限元法的计算过程;对找形后车辐式张拉结构进行了受力分析,将找形时结构荷载施加在找形后的结构上,结构最大竖向位移仅为0.72mm,验证了该找形方法的正确性。     

拉索穹顶结构非线性分析的混合有限元增量法

拉索穹顶结构是由受压桅杆和拉索组成的新型柔性大跨度空间组合结构,几何上表现为极强的非线性特性,计算困难,本文应用有限元法,结合拉索穹顶结构特征,假定拉索和桅杆的受力满足虎克宣定律,建立了可以直接考虑拉索垂度影响的两节点索单元模型,并与两节点直杆单元相结合,基于修正的拉格朗日描述方法和虚功原理建立了拉索穹顶结构非线性分析的混合有限元增量方程。采用荷载增量法与Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法相结合的求解     

风场中长单索结构流固耦合效应的动力学分析

本文介绍了长单索结构的风致振动现象及传统单索动力计算方法,分析了进行流固耦合计算的必要性.详细阐述了流固耦合的基本理论和方法,并介绍了有限元软件ANSYS的流固耦合计算流程.根据两种工况下的流固耦合算例分析,给出了长单索结构跨中节点的位移、应力以及索表面风压等物理量的时程曲线,通过对不同工况以及不同流场模型的模拟和分析比较,探讨了基于流固耦合分析的长单索结构风致振动响应的特点,对长单索结构的风致振动分析和设计具有参考意义.     

单层平面索网幕墙结构的风振响应分析及实用抗风设计方法

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其具有柔性大、质量轻、阻尼小、自振频率低的特点,属风敏感结构。由于单索幕墙具有较高的几何非线性,本文采用基于随机振动理论的模态叠加频域方法进行了单索幕墙结构的风振响应分析。将模态叠加频域方法的计算结果和非线性时程分析方法的精确计算结果进行了比较,证明了该方法的准确性。并且本文通过分析各阶模态对单索幕墙结构风振响应的贡献,得到脉动风荷载下结构的振动以第一阶模态为主的结论。根据该结论本文采用频域方法推导了单索幕墙结构的位移均方差和索内力均方差的实用计算公式,同时考虑单索幕墙的结构特点提出了基于结构响应的单索幕墙结构实用抗风设计方法。     

弦支穹顶结构动力分析

基于局部分析法并且在以预应力作为自平衡的初始内力情况下对弦支穹顶结构的动力特性进行了初步分析。局部分析法采用将索杆体系和上部单层网壳分开的思想,使弦支穹顶结构的初始预应力分布的确定得到简化。随着上部网壳结构的整体刚度的降低,预应力对体系的自振特性的影响逐渐增大。该体系的低阶振型大多为竖向振动振型。由时程分析的结果可见竖向常遇地震作用下索杆内力上下变化的幅度并不大（不超过7％）。竖向常遇地震作用下结构响应由内环、中环到外环逐渐减弱。常遇水平地震作用下体系索杆内力上下变化的幅度更小。相比竖向常遇地震作用下的索杆内力的变化要小的多。同时,常遇水平或竖向地震作用下线性和非线性时程分析差别不大。     

METHOD OF THE LINEAR ELASTIC BAR CALCAULATION UNDER SMALL DEFORMATION CONDITIONS

先用几何图解法对一简单线弹性杆系变形作分析计算,发现功能原理更可行有效. 方法是假设用一个和载荷P 相垂直的力H（虚拟力）先作用于杆系,根据功能原理导出在载荷P 作用下的位移计算公式. 并把这一方法推广到多个杆件组成的弹性杆系（桁架）中,并建立相应计算公式. 可望实现计算机编程,大大简化这一类问题的工程计算.     

PREDICTIONS OF EFFECTIVE OUT-PLANE SHEAR MODULUS AND SIZE EFFECT OF HEXAGONAL HONEYCOMB

给出了预测六边形蜂窝材料等效剪切模量及其尺寸效应的圆筒扭转力学模型和扭转能量法,建立了等效面外剪切模量G₁₃相对于材料体分比ν、周向单胞数n、圆筒半径r和单胞层数参数m变化的解析表达式;同时将扭转能量法、有限元数值模拟计算和G-A经典细观力学方法进行了比较,从理论上揭示并验证了尺寸效应的存在性. 结果表明,当蜂窝体胞尺寸相对结构尺寸无穷小时,预测结果趋近于细观力学方法的结果. 此外,利用周期性蜂窝材料的结构对称特性,使用体胞子结构有限元计算模型进行等效面外剪切模量及其尺寸效应的预测,在不影响计算结果的前提下极大地提高了计算效率.     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.     

Rarefactive solitary waves in two-phase fluid flow of compacting media

Rarefactive solitary wave solutions of a third order nonlinear partial differential equation derived by Scott and Stevenson (Geophys. Res. Lett. 11, 1161–1164 (1984)) to describe the one-dimensional migration of melt under the action of gravity through the Earth's mantle are investigated. The partial differential equation contains two parameters, n and m, which are the exponents in power laws relating, respectively, the permeability of the medium and the bulk and shear viscosities of the solid matrix to the voidage. It is proved that, for any value of m, rarefactive solitary wave solutions satisfying certain physically reasonable boundary conditions always exist ifn>1 but do not exist if 0n1. It is also proved that the speed of the solitary wave is an increasing function of the amplitude of the wave. Six new exact rarefactive solitary wave solutions, four of which are expressed in terms of elementary functions and two in terms of elliptic integrals, are derived for six sets of values of n and m. The large amplitude approximation is considered and the results of Scott and Stevenson for n>2, m=0 and n>1, m=1 are extended to n>1 and all m0. It is shown that, for sufficiently large amplitude, larger amplitude solitary waves are broader in width if 0m1 and are narrower in width if m>1.     

An extended study of the hydrodynamics of gravity-driven film flow of power-law fluids

A new similarity transformation has been devised for extensive studies of accelerating non-Newtonian film flow. The partial differential equations governing the hydrodynamics of the flow of a power-law fluid down along an inclined plane surface are transformed into a set of two ordinary differential equations by means of the dimensionless velocity component approach. Although the analysis is applicable for any angle of inclination (0<π/2), the resulting one-parameter problem involves only the power-law index n. Nevertheless, physically essential quantities, like the velocity components and the skin-friction coefficient, do depend on and relevant relationships are deduced between the vertical and inclined cases. Accurate numerical similarity solutions are provided for n in the range from 0.1 to 2.0. The present method enables solutions to be obtained also for highly pseudo-plastic films, i.e. for n below 0.5. The mass flow rate entrained into the momentum boundary layer from the inviscid freestream is expressed in terms of a dimensionless mass flux parameter Φ, which depends on the dimensionless boundary layer thickness and the velocity components at the edge of the viscous boundary layer. Φ, which is thus an integral part of the similarity solution, turns out to decrease monotonically with n. This parameter is of particular relevance in the determination of the streamwise position at which the entire freestream has been entrained and viscous stresses prevail all the way to the free surface of the film. A short-cut method to facilitate rapid and yet accurate estimates of the mass flux parameter is developed to this end.     

Droplet combustion experiments in varying forced convection using microgravity environment

A new microscopic model of the interaction between droplet flames and fine vortex tubes which compose a coherent structure of turbulence was developed. Three non-dimensional numbers were introduced to extend the length scale and time scale so as to be suitable for microgravity experiments using droplets of combustion of about 1 mm in diameter. An experimental apparatus for combustion of a single droplet and that of an array of two droplets in varying airflow was developed, and experiments were performed in microgravity and normal gravity at pressures up to 2.0 MPa for n-nonane and ethanol as fuels. Variations of the instantaneous burning rate constant, K_i, in response to the varying flow velocity was successfully observed. At high pressure, the effects of droplet Reynolds number Re on K_i was clearly seen, while the effects of natural convection, which increases K_i with Re, was seen in normal gravity even in the forced airflows. As for the experiments on combustion of an array of two droplets, K_i reduction of the downstream droplet became weak when the flow direction was varied. However, the K_i reduction of the downstream droplet for flow direction variations was clearly seen for n-nonane droplets but almost not for ethanol droplets. The interaction mechanism between upstream and downstream droplets is considered to result from the elimination of oxidizer supply to the downstream droplet, indicating strong interaction effects of n-nonane droplets for a stoichiometric oxygen-fuel ratio of n-nonane (i.e., 14.0) greater than that of ethanol (i.e., 3.0).     

Radiation and laminar forced convection of non-Newtonian fluid in a circular tube

Interaction of radiation with thermally developing laminar forced convection of power-law, non-Newtonian, absorbing, emitting, isotropically scattering, gray fluid through an isothermal circular tube with a black boundary is investigated. The energy equation is solved by an implicit finite-difference scheme, while the radiation part of the problem is solved by the collocation method. Results are presented for the effects of conduction-to-radiation parameter, single scattering albedo, optical thickness and the inlet temperature on the local Nusselt number along the tube for the case of power-law index n=1/3, 1 and 3, where the case n=1 corresponds to the Newtonian fluid.     

First order piecewise linear systems with random parametric excitation

The Fokker-Planck equation is used to develop a general method for finding the spectral density and other properties of first order systems governed by stochastic differential equations of the form

dx/dt + f(x)[1 + m(t)] = n(t)

, where f(x) is piecewise linear and m(t) and n(t) represent stationary Gaussian white noise. The method is similar to one used by the authors to deal with the case m(t) = 0, but is complicated by the possible existence of irregular (singular) points of the Fokker-Planck equation. Graphical results for some special cases are presented.     

On rubber disks under rotation or axisymmetric stretching

The governing equations for a class of axisymmetric problems under large elastic deformation, concerned with a circular rubber disk with body force as well as non-uniform initial thickness, are formulated in terms of two coupled first-order ordinary differential equations with explicit derivatives. The following two problems subjected to different boundary conditions are solved: (a) Rotating disks with uniform initial thickness (b) Circular disks with non-uniform initial thickness under axisymmetric stretching at the outer boundary. In problem (b), the rubber disk whose initial thickness contour is h₀ = crⁿ (where c and n are any constants), or whose final thickness is a constant, is considered. Highly elastic materials with a Mooney strain-energy function are used for numerical calculations.     

Periodic motions of coupled simple pendulums with periodic disturbances

Several theorems on the existence of oscillatory, rotary, and mixed periodic motions of n, coupled simple pendulums are proved. These theorems are very general and include subharmonic and ultraharmonic type solutions as well as harmonic type solutions and cover cases of large coupling and disturbances as well as small. The results are also extended to include more general systems of nonlinear oscillators.     

Creep transition in torsion

Stresses for a circular cylinder of compressible material subjected to torsion are derived in closed form for steady state creep. It is shown that the asymptotic solution through stress leads from elastic state to plastic and then to creep and through stress difference leads to the creep state. The effect of compressibility is presented graphically. The results indicate that the value of maximum shear stress for a cylinder of compressible material is greater than that for an incompressible material and increases with the increase in a measure index n. For an incompressible material, as a particular case, the results obtained are the same as given by Marin [9].     

Boundary layer flow at a three-dimensional stagnation point in power-law non-Newtonian fluids

Similarity solutions for the three-dimensional flow and heat transfer of a power-law fluid near a stagnation point of an isothermal surface are presented. The results of the numerical integrations are given in tables and shown on graphs for some different values of the power-law index n, geometric parameter c, and the Prandtl number Pr. Whenever possible, these results are compared with available analytical solutions and found to be highly accurate.