Dynamic stiffness analysis of toroidal shells

The free vibration of a toroidal shell is studied using the dynamic stiffness method. The dynamic stiffness method eliminates both spatial discretization error and mesh generation. Moreover, with a finite number of degrees of freedom, the dynamic stiffness method can predict an infinite number of natural frequencies. The dynamic behavior of the toroidal shell is modeled by DMV (Donnell-Mushtari-Vlasov) linear thin shell theory in the present paper. However, the procedure can be adapted to be used with any other linear thin shell theory without difficulty. Since a close form solution of toroidal shell using DMV theory is not (yet) possible, in order to obtain the desired dynamic stiffness matrix, a finite number of Fourier's series terms are taken in the circumferential direction and the unknown longitudinal displacements are then solved from the reduced governing equations exactly. The solution obtained from the dynamic stiffness method can be regarded as semi-analytical due to the Fourier approximation. With the dynamic stiffness matrices in hands, a toroidal shell with different boundary conditions and connections (to other toroidal shells) can be analyzed. This paper presents the procedure and assumption made in order to obtain the dynamic stiffness matrix of a toroidal shell in harmonic oscillation. Also some numerical examples will be given and discussed.     

Numerical solution of curved pipes submitted to in-plane loading conditions

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.     

泡沫填充的薄壁圆柱壳体轴向压碎的分析模型

由于填充轻型泡沫的薄壁钢管有良好的耗能能力而被广泛地应用于工程中。当结构轴心受压时,钢管与泡沫芯之间的作用对吸收能量起到关键作用。已有理论研究的大部分对象为完全填充的钢管。本文提出了一个理论模型,用于分析部分填充的钢管的轴向对称压碎性能。采用改进的模型分析壳体,并考虑了泡沫芯的作用。由能量平衡原理得到极限压力的平均值。建议公式得到的结果与先前文献中的结果吻合。参数分析用于研究泡沫芯稳定时期的压力值(σf),以及填充的比例和壳体的径厚比对结构轴向受压性能的影响。为薄壁结构的吸能性能方面的设计提供指导。     

组合空腹梁的静力特性研究

提出了一种新的组合空腹板结构形式,它由下层交叉钢肋、上层混凝土板及连接上下层并使之共同工作的钢管或钢管混凝土剪力键组合而成。为研究该类结构的静力特性,对组合空腹板的组成单元——组合空腹梁进行了足尺模型试验,侧重研究组合空腹梁下层钢肋、上层混凝土板的内力分布规律;对组合空腹板建立了基于空间梁单元与壳单元的混合元计算模型、空间壳单元计算模型两种有限元分析方法,对试验模型进行了理论分析。将试验数据、两种有限元计算方法的计算结果进行了比较。研究结果表明,组合空腹梁的内力分布均匀,能较好地发挥材料强度,具有刚度大、整体性好的特点;对简支组合空腹梁,其下层钢肋处于拉-弯、上层混凝土板处于压-弯的受力状态,弯曲应力在总应力中占了较大的比例;研究结果同时也验证了理论分析的可靠性。     

双层双曲线网壳结构冷却塔温度应力的研究

把双层双曲线网壳结构竖向应用于冷却塔的筒壁 ,在网壳的周围挂金属面板 ,筒壁放在底部环梁上 ,形成了上面为网壳结构 ,下面为钢筋混凝土结构的新型结构。考虑双层双曲线网壳结构冷却塔由于均匀温度场变化 ,导致筒壁内外的温差 ,产生温度应力。并且结合边界约束条件的影响来探讨该结构的温度应力。分析了冷却塔杆件在均匀温度场变化下 ,由于不能自由地热胀冷缩 ,而产生了温度应力 ,同时给出了分析方法。并且根据有限元理论 ,用VisualBasic编制了温度应力分析程序。针对具体的工程实例探讨温度应力在边界的法线方向 ,约束条件分别为固定、弹性、放松三种情况下杆件温度应力的变化规律 ,给出了一些对网壳结构冷却塔设计有参考价值的结论和建议     

Vibration analysis of toroidal panels using the differential quadrature method

The free vibration characteristics of linear elastic toroidal shell panels are determined. A solution based on the Mushtari–Vlasov–Donnell shell equations is developed using the Differential Quadrature Method. The work represents the first application of this method to problems in shell theory with variable coefficients in the governing equations. Numerical results are calculated using the method, and these are compared with results found using a Fourier series and a finite element solution.     

Investigation of pointed domes—I. Theory

A theoretical method of shell analysis has been utilized and, with the help of certain innovations, the study of pointed domes subjected to pointed loading is presented in this paper.To derive an analytical expression for the pointed dome, the general theory of shell of revolution is used to take into account the effect of membrane and bending stress field. Additionally the general classical approach of analytical multi-shell analysis is utilized to obtain the solution.This solution is applied to a pointed dome with a given dimension and the membrane stress field was calculated. The results thus obtained give a good approximation of the internal force field in the central portion of the dome. However this is not true near the lower boundary and near the kinked vertex of the dome.The values of internal meridional bending moment and meridional shear have also been calculated. These indicate that the bending field diminishes in magnitude as we move away from the kinked region.     

波纹板隧道支护结构分析方法与承载特征

波纹板结构相比钢筋混凝土结构其力学、耐久性能更好,且施工工期更短.将其应用于隧道支护领域具有重要的理论意义和工程价值.本文通过有限元数值模拟,建立梁、壳两种单元组合成的波纹板结构模型,并对不同荷载模式下的承载力进行了计算.研究表明:梁、壳单元模型应力、位移相差不大;波纹板结构在以竖向荷载为主导时,隧道拱顶位置受力及沉降...     

含中心裂纹薄壁型钢的又一组应力强度因子解

首先根据无限大中心裂纹板在Ⅰ型荷载作用下应力分布的全场解析解,构建薄壁杆件在均匀拉伸时沿裂纹所在截面的正应力的分布模型;然后利用平衡条件确定无量纲应力强度因子Y(ξ)获得含中心裂纹拉伸薄壁型钢的又一组无量纲应力强度因子Y(ξ)的近似解析解。与现有的数值结果比较表明,该方法不仅简单实用,而且结果可靠。文中给出的几种常见薄壁杆件含Ⅰ型中心裂纹时的无量纲应力强度因子的近似简单解析表达式,既适用于焊接组合薄壁杆件,也适用于冷弯薄壁杆件。     

Free vibration analysis of a toroidal shell

The free vibration of a toroidal shell (curved pipe) is studied using DMV (Donnell-Mushtari-Vlasov) thin shell theory, Fourier's series and Galerkin's method. Some behaviors of the vibration of cylindrical shell, as a special case of toroidal shell, are discussed. Also, a 90-degree-bend curved pipe is studied numerically. Results obtained by the present method are compared to those obtained by finite element and other methods. DMV linear thin shell theory is employed for simplicity. However, the method applies to any other shell theories without difficulties.     

Comparison of elastic solutions for three-point bending of curved pipes

In this paper the linear elastic shell theory problem of the three-point bending of a curved pipe is considered. Such a loading arises in the industrial pipe ram bending process. Summaries are given for solutions to this problem based on the Mushtari-Vlasov-Donnel (MVD) and Sanders linear shell theories. Numerical results for displacements and stresses are obtained using the two shell theories, and these are compared with results from the finite element method (FEM). The present study gives practical information about the behavior of curved pipes subjected to ram bending. As well it provides information about the solution characteristics of thin-shell theories in toroidal coordinates.     

Natural frequencies and mode shapes of an orthotropic thin shell of revolution

A method is developed to determine the free vibration characteristics of an orthotropic thin shell of revolution of arbitrary meridian. A solution is given within the context of the Sanders–Budiansky shell theory and using the differential quadrature method (DQM). Numerical examples for frequencies and mode shapes are given for a complete toroidal shell. Both completely free shells, and shells with circumferential line supports are considered. Close agreement is observed in comparisons with previously published results and with results obtained using the finite element method. The paper ends with a set of appropriate conclusions.     

An analytical model for axial crushing of a thin-walled cylindrical shell with a hollow foam core

A thin-walled tube filled with light-weighted foam has wide engineering applications because of its excellent energy absorption capacity. When the structure is axially crushed, the interaction between the tube and foam core plays an important role in its energy absorption performance. Previous theoretical studies so far have largely been concerned with fully in-filled tubes. In this paper, a theoretical model is proposed to predict the axi-symmetric crushing behaviour of such structures but with a partial infill. Using a modified model for shell and considering the volume reduction for the foam core, the mean crushing force is predicted by the energy balance. The proposed formula agrees well with previous results reported in literature. A parametric study is carried out to examine the contribution of foam core plateau stress (σ_f), amount of filling and shell's radius-to-thickness ratio (R/h) on the axial crushing behaviour of the structure. This study can give valuable design guidelines in using thin-walled structures as an energy absorber.     

无粘结预应力技术在大直径圆柱壳中的应用和试验分析

通过工程实例,介绍无粘结预应力混凝土技术在大直径圆柱壳中的应用。利用轴对称圆柱壳有矩理论进行结构分析、设计,并在施工现场进行了一系列应力、应变和变形测试。结果证明,理论分析结果与现场测试结果吻合极好。工程实例表明,无粘结预应力混凝土技术应用于大直径圆柱壳可有效地控制裂缝产生,获得可观的经济效益和社会效益,有广泛的应用前景。最后,对设计理论提出了建议。     

板肋加劲板整体稳定数值模拟与受力机理研究

分别采用梁单元与板壳单元建立同时考虑初始几何缺陷和焊接残余应力的受压板肋加劲板整体稳定分析有限元模型,并以相应试验结果进行验证,得到梁与板壳单元模拟受压板肋加劲板整体稳定的异同。采用经验证的数值模拟方法,对不同弯曲失稳方向板肋加劲板的受力机理进行了研究。结果表明:采用板壳单元可以较好还原板肋加劲板整体稳定受力性能,板壳有限元模型与试验试件的承载力最大相对误差为4.2%,平均相对误差为1.48%; 梁单元模型与长(中长)柱试验试件的承载力最大相对误差为5.4%,平均相对误差为1.92%,与短柱试件的承载力相对误差虽仅为0.7%,但由于不能考虑板件发生的塑性失稳,其应力-位移曲线拟合情况相对较差; 不同弯曲失稳方向板肋加劲板整体稳定构件的破坏特征不同,其中对于板肋侧弯曲的板肋加劲板整体稳定构件,被加劲板边缘部分受压达到材料屈服强度且板肋边缘受拉达到屈服强度时,构件整体达到其承载极限; 对于被加劲板侧弯曲的板肋加劲板整体稳定构件,当板肋边缘部分受压达到材料屈服强度时,构件整体达到其承载极限; 对于实际工程中组成钢箱梁顶板的板肋加劲板,制作时应避免朝向板肋侧的变形。     

预应力网壳-拉杆拱组合结构预应力全过程分析与监测

以长江防洪模型试验大厅为工程背景,介绍了一种新型大跨空间结构体系:预应力网壳-拉杆拱组合结构。结合该工程的结构特点,采用提出的"迭代求解法"确定了索的初始形变,并利用"顺序分析法"进行预应力施工全过程模拟得到各水平拉索和竖向吊杆的张拉控制力,最后将预应力施工的现场监测结果与理论分析结果进行对比,验证了理论分析的准确性。     

结构性黄土排水柱孔扩张问题弹塑性解析

为研究黄土地区原位测试、沉桩扩孔以及劈裂注浆等岩土工程问题,基于结构性黄土修正剑桥模型,在严格遵循平均有效应力与偏应力定义前提下,针对排水柱孔扩张问题导出严密解.在孔周弹性区采用小变形理论求得土体应力与位移解析解,在孔周塑性区采用大变形理论,并借助中间变量将圆孔扩张问题转化为基于拉格朗日描述的一阶常微分方程组的初值问题...     

理论t-z法在双桩相互影响系数计算中的应用

以弹性半空间Mindlin应力解和理论t-z法为基础 ,建立了单桩和考虑相互影响的双桩在荷载作用下的数值分析模式。以此为基础可以建立考虑相互影响的群桩共同作用。计算结果表明 ,该方法具有理论清晰、计算简单、结果合理的优点     

组合空腹板架结构研究与应用

钢-混凝土组合空腹板架是一种新的组合结构形式,本文详细介绍和总结了该类结构的构造、理论分析方法、试验研究及工程应用情况。理论分析方面,总结了离散化的有限元法及连续化的拟板法两类分析计算方法,并给出了算例对比。研究表明,基于梁单元、壳单元的混合有限元模型可以满足工程设计精度的需要,同时计算和数据处理工作量较小。试验研究方面,介绍了针对该类结构所做的四项试验,其中既有结构模型试验,也有结构原位试验;既有结构静力试验,也有结构动力特性测试试验以及节点低周反复加载的拟静力试验研究。试验结果证明了此类结构的安全性,也验证了理论分析的可靠性,同时为结构形式的完善和工程设计提供指导。组合空腹板架结构已在多项工程中应用,具有代表性的有两项,其一,为跨度19.5m的大荷载楼盖结构;其二,为跨度33m的楼盖结构,两项工程均已使用多年,效果良好。     

拱形支护结构的内力、变形计算

针对工程上采用的拱形支护体系,利用壳体理论建立其微分方程,进而计算出支护结构的内力和变形,由于考虑了此种支护结构的空间特性,故这种方法更加符合它的实际受力情况,同时,结合工程实例对拱形支护结构进行了分析。