Dynamic instability of three-layered cylindrical shells containing an FGM interlayer

In this study, the dynamic instability of three-layered cylindrical shells containing a functionally graded (FG) interlayer subjected to static and time dependent periodic axial compressive loads are investigated. The governing relations, modified Donnell type dynamic stability and deformation compatibility equations are derived. The governing equations are reduced Mathieu–Hill equation by using Galerkin׳s method and the expressions for boundaries of unstable regions of three-layered cylindrical shell with an FG interlayer are found. Finally, the effects of variations of volume fractions of FG interlayer and shell characteristics on the magnitudes of boundaries of unstable regions are studied numerically.     

球面网壳结构在强震下的失效机理

研究了球面网壳结构在地震等动力荷载作用下两种可能的失效机理 :由于几何非线性起主要作用导致的动力失稳和由于塑性变形过度发展导致的强度破坏。提出了统一的基于响应分析的关于网壳结构失效机理的理论框架。对单层球面网壳在简谐荷载和地震荷载作用下的失效机理进行了较系统的分析 ,提出了具体的动力失稳和强度破坏判别准则 ,求得了相应的极限荷载。取得的结果具有良好的规律性 ,验证了所提出的理论框架的合理性和实用性     

Optimal design of shells against buckling under overall bending and external pressure

In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by an external pressure and lateral forces causing overall bending moment (which varies along the axis of a shell) and the appropriate shearing force. We look for the shape of meridian as well as the thickness of a shell, which ensure the maximal critical value of the loading parameter. As the equality constraints, the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied.     

Elasto-plastic instability of single-layer reticulated shells under dynamic actions

This paper addresses the issue on dynamic collapse mechanism of single-layer reticulated shells subjected to harmonic load, sudden load and seismic load. The method for failure mechanism has reviewed the relationship between the response of the reticulated shell and the peak acceleration of dynamic action. Besides, the steel damage accumulation is considered in the method by compiling a user subroutine based on the computing program ABAQUS. An example is introduced to describe dynamic instability collapse resulting from geometric nonlinearity of the shell and the other example is presented to describe strength failure resulting from excessive development of plastic deformation, for it is discovered that the structure is not only to be prone to instability collapse in dynamic action. According to the responses of the single-layer reticulated shell under dynamic loads, this study discusses the relationship between the failure model and the corresponding dynamic load parameters. Then, the method for distinguishing failure modes is proposed based on the fuzzy synthetic evaluation theory and the structural responses of sufficient samples at the failure state. The technique feasible to be used to distinguish different failure modes of single-layer reticulated shells under different dynamic loads is validated.     

联方型单层球面网壳的地震响应

以40 m跨度的联方型单层球面网壳为分析对象,并以位移准则作为动力稳定性判别方法,分析了该网壳受地震作用下的动力响应,得到了联方型网壳结构达到失稳临界峰值后,继续施加荷载,网壳结构位移不会突增,不会因达到失稳临界值而突然倒塌的结论。     

Buckling and dynamic instability analysis of stiffened shell panels

The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.     

Bending and stretching actions in shallow domes. Part 1. Analytical derivations

In this two-part set of articles the response of shallow axisymmetric shells with circular plan is investigated with the aid of the two-surface shell theory. Such an approach has the unique advantage of elucidating, both qualitatively, and quantitatively, the complex—and key—interaction of bending and stretching actions in such shells in a simple and direct manner. Although discussion centres upon a shallow paraboloid of revolution, the general features emerging from the study are, obviously, relevant for the generic family of shallow domes (e.g. spherical) covering the various limiting cases of support around their circumference.This first paper begins with a two-surface exposition of the set of equations describing the behaviour of the shell. Next, analytical bending solutions to the specific practical problem wherein the shell is subjected to uniformly distributed vertical loading (corresponding, say, to its self-weight) are presented; and this is followed by the working out of closed-form expressions for the distributions of bending and stretching effects in theshell under consideration.     

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.     

大跨度网壳结构强震失效机理研究

随着大跨度网壳结构近些年在重大工程中的大量应用,该结构在强震作用下的失效机理问题也逐渐突出,为空间结构学者所关注。在总结了近些年大跨度网壳结构强震失效机理领域的研究进展基础之上,介绍了适用于网壳结构强震失效机理分析的基于荷载域全程响应的分析方法,以及在该方法中引入材料损伤累积的研究过程;定义了网壳结构在强震作用下的两类失效模式,即由几何非线性引起的动力失稳和由过度塑性损伤导致的动力强度破坏;论述了基于模糊数学中模糊综合判断理论的判别网壳结构强震失效模式的方法;在此基础上,对网壳结构动力损伤模型的建立也进行了阐述,并对网壳结构在强震下失效极限的确定方法进行了总结。图5表3参20     

Recent advances on postbuckling analyses of thin-walled structures: Beams, frames and cylindrical shells

The lateral postbuckling response of thin-walled structures such as bars and frames with members having steel rolled shapes as well as circular cylindrical shells under axial compression is thoroughly reconsidered. More specifically via a simple and very efficient technique it is found that beams with rolled shapes (symmetric or non symmetric) under uniform bending and axial compression exhibit a stable lateral-torsional secondary path with limited margins of postbuckling strength. New findings for the static and dynamic stability of frames with crooked steel members-due to the presence of residual stresses-are also reported. It is comprehensively established that the coupling effect due to initial crookedness and loading eccentricity may have a beneficial effect on the load-carrying capacity of the frames. Moreover, simple mechanical models are proposed for simulating the buckling mechanism of axially compressed circular cylindrical shells. Very recently Bodner and Rubin proposed an 1-DOF mechanical model whose buckling parameters correlated to those of the shells by using an empirical formula based on experimentally observed shell buckling loads. In the present analysis a new 2-DOF model for the static and dynamic buckling of axially compressed circular cylindrical shells, which can include mode coupling, is presented.     

Bending analysis of a truncated conical shell subjected to asymmetric load

Bending analysis of a truncated conical shell of revolution subjected to asymmetrical bending has been undertaken by using an approximate theory similar to the Donnell's theory for cylindrical shells. A method of solution suggested by Budiansky and Radkowski⁹ has been used in this study. Numerical results obtained from this solution have been compared with those obtained from the literature. The results of bending theory have also been compared with that of membrane theory and it is shown for the type of loading considered here that membrane theory is valid over a large portion of the shell.     

角钢梁在静态和突发性动态荷载下的非线性不稳定性

介绍了纯弯曲载荷作用下角钢梁的扁屈性能。使用能量法对角钢梁弱轴在纯弯曲载荷下静态与动态的不稳定性推导出一种解析解。结果显示,角钢在受瞬间压力的作用时,其弯矩达到静态临界弯矩的71%时,即发生失稳;但是其在动力状态下纵向弯曲和屈曲的变形临界值是静力状态下的2倍。     

Nonlinear instability of angle section beams subjected to static and dynamic sudden step loads

This paper presents a study on the flattening behaviour of angle section beams subjected to pure bending. Analytical solutions for both static and dynamic instabilities of angle section beams subjected to pure bending about its weak axis are derived using energy methods. The results show that the dynamic instability of angle section beams under the action of a sudden step moment occurs at a moment about 71% of the corresponding critical static moment, but the deformations of the longitudinal curvature and flattening at the critical dynamic state are almost twice of those corresponding to the static instability case.     

外压作用下偏心加劲功能梯度圆柱壳的非线性屈曲和后屈曲分析

通过解析法研究外压作用下功能梯度加劲薄圆柱壳的非线性屈曲和后屈曲性能。通过其在内部的偏心环和纵梁对壳体进行加固,假定壳体和加固件的材料性能在厚度方向为连续梯度。根据VonKarman理论中的刚度法和传统的壳理论推导出基本关系和平衡方程,可更准确地选择三种关于挠曲的近似公式,且使用盖勒金法得出的显式表达式可以推测出临界荷载和后屈曲压力-挠曲曲线。数值结果显示了加固件能有效地增强壳体稳定性。     

三向球面空腹网壳稳定性分析

利用非线性有限元法对三向球面空腹网壳稳定性能进行了研究,采用了特征值屈曲分析和非线性屈曲分析两种方法来考查了三向球面空腹网壳的屈曲模态和失稳全过程。通过大规模的几何参数分析得到了不同矢跨比、网壳厚度和不同支承条件下的荷载—位移曲线和极限承载力。最后将三向球面空腹网壳与相同用钢量的单层网壳进行了对比。     

考虑杆件失稳影响的网壳结构稳定性研究

为了解和掌握杆件失稳对网壳稳定性的影响,指出判别网壳结构杆件失稳的关键问题并提出杆件失稳的判别方法。采用有限元软件ANSYS及自编的前后处理程序对已有网壳试验进行对比分析,得到模型结构的全过程响应、杆件失稳的判断结果和杆件失稳对结构的影响,分析结果符合已有试验结果。并以Kiewitt8型球面网壳为例,分析网壳结构杆件失稳特征及在网壳结构中的传播规律。同时,在考虑杆件稳定性的基础上,考察材料非线性、初始几何缺陷以及杆件挠曲二阶效应和挠曲失稳对杆件稳定性和网壳稳定性的影响规律。结果表明提出的方法可以有效地判断网壳结构杆件的稳定性,杆件失稳及其传播将直接影响结构稳定性。     

强震下单层柱面网壳损伤及失效机理研究

基于结构损伤理论,对单层柱面网壳在强震下的失效机理进行研究。单层柱面网壳在强震下不仅会发生动力失稳,也可能由于过度塑性发展导致动力强度破坏的模式。对于动力强度失效的研究,应当在分析中考虑材料损伤累积以及断裂效应的影响。为在有限元分析中包含这一影响因素,编制了基于通用有限元软件ABAQUS的用户材料子程序,具有较高的计算精度和较好的收敛性。应用其对单层柱面网壳在强震下的响应进行参数研究,并与基于理想弹塑性材料时的响应对比,讨论考虑材料损伤对网壳失效特征的影响。将单层柱面网壳在强震下失效时刻的多项特征响应进行统计分析,拟合了能够表征网壳损伤程度的损伤模型,建立单层柱面网壳在强震下的失效判别准则。针对实际工程抗震设计中采用损伤累积本构模型计算的困难,提出网壳结构失效极限的简化判别方法。     

Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.     

Thermal buckling of FGM shells resting on a two-parameter elastic foundation

This paper focuses on the thermal buckling analysis of FGM shells resting on the two-parameter elastic foundation. Material properties of the constituents are graded in the thickness direction according to the power-law distribution. The surrounding elastic medium is modeled as an elastic foundation of the Pasternak-type. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell subjected to thermal load and resting on a two-parameter elastic foundation have been derived. Critical temperature differences of FGM truncated conical shells with or without elastic foundations subjected to non-linearly distributed temperature across the thickness of the shells are obtained by solving eigenvalue problems. The appropriate formulas for FGM cylindrical shells with or without elastic foundations are found as a special case. In order to assure the accuracy of the present study, convergence properties of the critical temperature are examined in detail.     

Tragfähigkeitsminderung durch lokale Instabilität bei stählernen Zylindertanks mit Doppelmantel

Reduction of load bearing capacity by local instability of double‐shell steel tanks. The structure of a double‐shell steel tank creates specific risks for its local stability and load capacity. These risks form the subject of this paper. The following three issues have been discussed: Internal shell stability risk during hydrostatic test of the tank, deformation of the bottom in between the shells by heating of the storage liquids and difference in the settlement of the bottom under the internal tank shell and the external shell resulting from different loads acting on both these parts of the bottom.