The tolerance averaging model of dynamic stability of thin plates with one-directional periodic structure

A dynamic stability of thin plates with one-directional periodic structure is investigated. An averaged non-asymptotic approach, called the tolerance averaging, is applied to derive governing equations of these plates. Obtained tolerance model equations of the Kirchhoff-type plate take into account the effect of the period lengths on the overall plate behaviour [Jędrysiak J. Dispersive models of thin periodic plates. Theory and applications. Sci. Bul. Łódź Tech. Univ., No. 872, series. Sci Trans 289, Łódź, 2001 [in Polish]]. It is shown that this effect plays a crucial role in some special cases of a dynamic stability of such plates.     

Critical load of a bilayered orthotropic elastic–plastic conical shell with the change of the shell basic surface location

The paper presents the derivation of stability equations and the comparison of critical loads for an orthotropic elastic–plastic conical shell with proper location of the shell basic surface. Prandtl–Reuss plastic flow theory is accepted in the analysis. To derive the stability equations the variational method was accepted and Ritz method was used to solve the equations. Numerical results were obtained by the use of a special iterative algorithm of the elastic–plastic analysis implemented on the PC.     

Vibration, buckling and dynamic stability of cracked cylindrical shells

The presence of cracks in a structure can considerably affect its behaviour. This paper presents a finite element study on the vibration, buckling and dynamic stability behaviour of a cracked cylindrical shell with fixed supports and subject to an in plane compressive/tensile periodic edge load. The effects of crack length and orientation are analysed. Under tension load, the results show that the frequency of the shell initially increases with the load, but then decreases as the load further increases leading to buckling due to tension load. The size and the orientation of the crack and the loading parameter can all have a significant effect on the dynamic stability behaviour of the shell under both compressive and tensile loading. The effects of these parameters are discussed in detail.     

Buckling and postbuckling of imperfect cylindrical shells under external pressure

A comprehensive nonlinear finite element elastic stability analysis was performed with the aim of explaining the effect of a deep single longitudinal initial dent on the load-carrying behaviour of an externally-pressurized cylindrical shell. The numerical results are compared with available test results and agree well, at least qualitatively. Imperfection sensitivity studies were carried out comparing the effect of the single dent with the effect of evenly distributed periodic initial imperfections. Imperfection sensitivity tends to vanish for increasing amplitudes of the idealized case of a single dent.     

Stability of orthotropic elastic–plastic open conical shells

The paper presents a derivation of the stability equation and the solution method of the problem for an orthotropic elastic–plastic open conical shell. The use is made of the constitutive relations of incremental plastic flow theory, elastic compressibility of the material, and Shanley concept of increasing load are taken into account in the consideration. A variation, strain energy method is used to derive the stability equation for bilayered open conical shell with nonuniform pre-critical stress distribution. The shell is free supported at the edges and the load acting the shell, in the form of longitudinal force and lateral pressure, is active one, i.e. unloading is not considered.     

Stability loss of thin-walled cylindrical tubes, subjected to longitudinal compressive forces and external corrosion

The paper is devoted to investigation of stability loss of thin-walled elastic circular cylindrical pipes subjected to simultaneous action of longitudinal compressive forces and uniform corrosion from outside. The pipe is treated as a thin closed elastic circular cylindrical shell which can be described within Kirchhoff–Love approximation. The critical time of stability loss of the pipe is found, using the upper critical load value for static stability loss of the pipe, not subjected to corrosion, and the law of corrosion rate. Numerical results were obtained for pipes, made from steel and aluminum with different initial wall thickness.     

预应力双层柱面网壳整体稳定性分析

双层柱面网壳结构是一种新型空间网壳结构,近几年得到快速发展,相关理论也更加成熟.但是预应力双层柱面网壳的研究却不多,理论计算分析也不完善,尤其对其稳定性的研究更是少之又少.利用有限元法,考虑不同矢跨比、荷载分布及预应力水平对预应力双层柱面网壳稳定性的影响,并与对应的双层柱面网壳结构进行对比,分析预应力作用下网壳的稳定特性.     

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.     

Experimental analysis of the influence of imposed displacements at the base of a cooling tower on its buckling stability

The results of an experimental investigation into the effect of displacements of the base of a model cooling tower on its buckling stability are presented. The displacement of the cooling tower base was imposed according to the formula: u_v = Δ_vcos 2β, where Δ_v represents the amplitude of the vertical displacements and β is the circumferential coordinate. An additional axisymmetric load was applied to the upper ring and the shell. The results were compared with findings for a shell without any base deformations. These investigations showed an insignificant influence of the imposed displacements at the tower base on its stability. Recommendations for design practice concerning the influence of base displacements on the cooling tower shell stability are included.     

华能大厦单层柱面网壳的设计及分析

以某低矢跨比的单层柱面网壳分析与设计为例,分析该网壳在各种荷载作用下的受力特点;讨论网壳支承刚度对网壳的受力影响;介绍网壳的设计和节点构造方法;并着重研究网壳的整体稳定性。得出：低矢跨比单层柱面网壳的整体稳定对支承刚度和初始几何缺陷较敏感;考虑塑性影响后,低矢跨比柱面网壳的稳定承载力相对弹性稳定承载力有大幅度降低;不同...     

天津某贝壳形单层网壳整体稳定分析

对天津于家堡站房贝壳形单层网壳进行了全面的整体稳定分析。首先进行线性稳定性分析,预测结构屈曲荷载的上限;然后,运用非线性有限元方法,考虑几何非线性以及初始缺陷的影响,全面分析网壳在各个工况荷载下的稳定性能,得到较准确的结果。     

The effect of geometric imperfections on the vibrations of anisotropic cylindrical shells

Analytical–numerical models to analyse the flexural vibration behaviour of anisotropic cylindrical shells are presented. The two models (denoted as Level-1 and Level-2 Analysis) have different levels of complexity and can be used to study the influence of important parameters, such as geometric imperfections, static loading, and boundary conditions. A specific anisotropic shell is used in the calculations in this paper. The influence of the imperfection shape and amplitude on the natural frequency is investigated for this shell via both the Level-1 and the Level-2 Analysis. Imperfections with the shape of the “lowest vibration mode” give a decrease of the natural frequency with increasing imperfection amplitude. The results of the Level-2 Analysis for the effect of imperfections on the natural frequency are in reasonable agreement with Finite Element calculations.     

Stress state and elastic buckling of a thin-walled beam with monosymmetrical open cross-section

The subject of this study is a simple thin-walled beam carrying a uniformly distributed transverse load. Strength and stability problems of the beam are resolved on the ground of Vlasov’s theory. Local stability is described according to the theory of thin plates and shells. The results of analytical solution are verified with the use of finite element method. Discrete model of the beam is built on the bases of shell elements SHELL4 of the COSMOS/M system. The results of both methods are compared using diagrams.     

Critical state of an axially compressed cylindrical panel with three edges simply supported and one edge free

The subject of the paper is a circular cylindrical panel with three edges simply supported and one edge free. The structure is axially compressed by a load uniformly distributed at both ends. The system of stability equations of shallow cylindrical shell was solved, assuming the deflection function and the force function—the Airy function which were formulated with respect to the boundary conditions. The system of stability equations was reduced to one regular differential equation of eighth degree. The results of numerical investigations (FEM) and buckling models are presented in the figures. The results of analytical and numerical investigation are compared in the paper.     

Recent advances in local–global FE analysis of shells of revolution

A local–global finite element technique, suitable for the analysis of shells of revolution with localized non-axisymmetric effects such as cracks, cutouts and column supports, is presented. Both material and geometrical nonlinearities are considered. The model combines, in a single analysis, rotational shell elements, general shell elements, and column elements. Rotational shell elements are employed in the axisymmetric portion of the shell, where the nonaxisymmetric behaviour in loading and deformation is accounted for by including appropriate Fourier harmonics. In the local zone, where deviations from axisymmetry are contained, a general isoparametric shell element is employed. Continuity of displacements between the rotational and general shell elements is achieved either by a layer of transitional elements or by a direct coordinate transformation. If the shell is supported on a discrete system of columns , a standard 3-D beam element with six degrees-of-freedom per node is deployed. This local–global approach has been applied to a wide variety of shell problems.     

索撑双向网格型单层柱面网壳稳定性研究

双向网格型单层柱面网壳结构不仅外型美观、各构件布置规则,而且质量轻、采光好。但是随着网壳跨度越来越大,整体稳定性问题也日益突出,因此制约了此类网壳结构在实际工程中的应用。为此,针对双向网格型单层柱面网壳结构,提出了一种新型布索方案,即在双向网格面内布置斜拉索提高结构的面内刚度,在双向网格面外通过撑杆布置横、纵拉索提高结构的面外刚度。首先通过对不同跨度网壳结构的弹塑性分析验证拉索的布置效果,并考虑各种参数变化对结构稳定性的影响,论证了此类网壳结构的合理性和实用性。其次,结合模型的静力试验研究了此类索撑柱面网壳结构的稳定性,论证了拉索布置的合理性。结果表明,采用撑杆和拉索的交错布置后,网壳结构的受力更加合理,其承载能力有了大幅度提高。此类索撑网壳结构为缺陷不敏感结构,但是撑杆长度对结构承载能力的影响很大,对于不同跨度的网壳结构,撑杆的最佳长度有所不同,实际工程中要确保撑杆具有最佳长度。     

考虑杆件屈曲的网壳结构的稳定性

为了了解杆件屈曲对网壳结构稳定性的影响,关键问题就是如何区分网壳结构中的杆件屈曲并得出其辨别方法。以一个Kiewitt-8型球面网壳为实例,研究杆件屈曲的特性和传播规律。同时,应用有限元分析软件ANSYS对一个球状网壳结构模型的测试结果进行分析和比较,得出对杆件屈曲的判定结果和其对结构的影响。判定结果与试验数据完全吻合。从杆件屈曲方面考虑,对材料非线性,初始几何缺陷以及杆件型号对杆件和网壳结构稳定性的影响进行研究。结果显示,所采用的方法可以有效地判定网壳结构的杆件屈曲问题;杆件屈曲和其扩散会直接影响到整个结构的稳定性。     

Stability of reticulated shells considering member buckling

In order to understand the influence of member buckling on the stability of reticulated shells, a key problem of how to distinguish the member buckling for reticulated shell structures was pointed out, and judgment methods of member buckling were obtained. Using a Kiewitt-8 dome as an example, the buckling characteristic and propagation rule of member buckling were studied. Meanwhile, a reticulated dome model tested was analyzed and compared by using the finite element software ANSYS. Judgment results of member buckling and the influence of member buckling on the structure were obtained. The judgment results accorded well with the test. Then taking the member buckling into consideration, the effect of material nonlinearity, initial geometrical imperfections, and member size on the stability of the members and the reticulated shell structures were investigated. The results show that the methods adopted can judge the member buckling for reticulated shell structures effectively; the member buckling and its propagation can affect the stability of the structure directly.     

大庆石油会展中心椭球形单层网壳稳定分析

本文对大庆石油会展中心椭球形单层网壳进行了全面的整体稳定分析。首先进行了线性稳定性分析,预测结构屈曲荷载的上限;然后,运用非线性有限元方法,考虑几何和材料非线性以及初始缺陷的影响,全面分析了网壳在各个工况荷载下的稳定性能,得到较准确的结果。