含轴对称初始缺陷的具有正交各向异性表层的夹层圆柱壳的非线性屈曲

夹层圆柱壳具有很高的结构效能。在许多工程结构中被广泛采用。本文研究分析了含有轴对称初始缺陷的夹层圆柱壳在轴压下的非线性屈曲问题。该夹层壳具有正交各向异性表层和各向同性可承剪的夹心．利用Stein的前屈曲一致理论得出了前屈曲挠度随轴向载荷及缺陷参数的变化情况，运用Galerkin法导出了屈曲控制方程，并进行了数值计算，得到了屈曲载荷、缺陷幅值、缺陷波数、夹心模量等参量之间的关系．结果表明与壳体实际屈曲模态相同的初始缺陷具有很大的危害性，可以通过增加壳体表层的轴向弹性模量或优化夹心的有关参数等途径来提高屈曲载荷，改善壳体屈曲性能。     

基于弧长法的受压球壳稳定性分析

对受压球壳进行特征值屈曲分析,得到了前6阶屈曲模态及线性屈曲临界载荷;采用弧长法进行非线性有限元分析,对理想球壳施加初始扰动,通过2次扰动值折半的方法求得引起结构屈曲的最小扰动值,追踪到了屈曲分支点和全过程载荷-位移路线。基于前6阶屈曲模态位移,在受压球壳中分别引入2.5mm和1mm两种缺陷值,分析缺陷对球壳屈曲特性的影响。结果表明:取壳厚的0.5%即0.05mm时,得最小扰动值,近似模型与完善结构极值载荷的差值为0.93%;球壳是缺陷敏感性结构,缺陷的幅值和分布都对其极限载荷有影响,缺陷幅值与厚度比为0.1时,缺陷球壳承载力相对理想结构下降了约11%,缺陷幅值与厚度比为0.25时,承载力相对下降了约30%,说明提高球壳稳定性需要提高球壳加工精度。     

薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法

针对薄壁圆筒壳结构轴压屈曲载荷的缺陷敏感性以及真实几何缺陷的不确定性,提出一种基于实测缺陷数据和极大熵原理的初始缺陷建模与屈曲载荷预测方法。首先,将初始几何缺陷视为二维随机场,并利用实测缺陷数据和Karhunen-Loève展开法将初始缺陷的随机场建模转化为随机向量的建模;其次,利用极大熵方法确定随机向量的概率分布;最后,基于所构建的初始缺陷随机模型,利用MCMC抽样方法和确定性屈曲分析方法,进行随机屈曲分析并给出基于可靠度的屈曲载荷折减因子。数值算例表明,与直接假设随机场相关结构的方法相比,本文方法的结果是对薄壁圆筒壳屈曲载荷的一个更无偏估计。     

Effect of multiple localized geometric imperfections on stability of thin axisymmetric cylindrical shells under axial compression

Stability of imperfect elastic cylindrical shells which are subjected to uniform axial compression is analyzed by using the finite element method. Multiple interacting localized axisymmetric initial geometric imperfections, having either triangular or wavelet shapes, were considered. The effect of a single localized geometric imperfection was analyzed in order to assess the most adverse configuration in terms of shell aspect ratios. Then two or three geometric imperfections of a given shape and which were uniformly distributed along the shell length were introduced to quantify their global effect on the shell buckling strength. It was shown that with two or three interacting geometric imperfections further reduction of the buckling load is obtained. In the ranges of parameters that were investigated, the imperfection wavelength was found to be the major factor influencing shell stability; it is followed by the imperfection amplitude, then by the interval distance separating the localized imperfections. In a wide range of parameters this last factor was recognized to have almost no effect on buckling stresses.     

安全壳中钢衬壳热屈曲问题理论与实验研究(I)———理论分析部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题把铆固之间的钢衬壳视为钢衬板的特殊缺陷形式，利用Ｋｏｉｔｅｒ初始后屈曲理论分析了完善和具有初始缺陷钢衬壳的弹性热后屈曲性态给出了用挠度－温度载荷表示的钢衬壳的后屈曲平衡路径表达式和屈曲临界载荷表达式具体分析了三种钢衬壳模型：四点铆固钢衬壳、四边固支钢衬壳和五点铆固钢衬壳给出了钢衬的初始缺陷、锚钉间距、钢衬厚度等参数对钢衬热屈曲载荷的影响结果对安全壳中钢衬壳的设计有很好的参考价值     

初始几何缺陷对网壳截面优化结果影响研究

单层网壳结构是缺陷敏感结构,初始几何缺陷不同对"网壳截面优化结果"有显著影响,该文研究了网壳杆件截面取值与缺陷分布、结构极限承载力之间的关系.结果表明:经截面优化设计的网壳结构最不利应力最早并且一直出现在初始几何缺陷较大处;优化寻优结果与初始几何缺陷分布有直接关系,增大缺陷较大处杆件截面能显著提高结构承载力;由于缺陷随机分布,经截面优化设计的网壳结构须校核其在不同缺陷下的稳定承载力以确保结构安全.     

Influence of extra terms on asymptotic analysis of imperfection sensitivity of toroidal shell segment with random imperfection

The bifurcation of a toroidal shell segment with initial imperfection which are subjected to lateral or hydrostatic pressure is studied under the assumption that the initial imperfection are Gaussian random stress-free displacement whose mean and autocorrelation function are given. We use a perturbation scheme developed by Amazigo [Amazigo, J.C., 1971. Buckling of stochastically imperfect columns on nonlinear elastic foundation. Quart. Appl. Math. 403–491]. A simple approximate asymptotic expression is obtained for the bifurcation load for small magnitudes of the imperfection. The result is compared with results obtained earlier under secondary bifurcation analysis for the imperfections in the shape of the buckling mode and the results in the literature, which shows some significant differences as a result of inclusion of extra terms in the buckling equation.     

Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections

The effect of local geometric imperfections on the buckling and postbuckling of composite laminated cylindrical shells subjected to combined axial compression and uniform temperature loading was investigated. The two cases of compressive postbuckling of initially heated shells and of thermal postbuckling of initially compressed shells are considered. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometric imperfection of the shell. The analysis uses a singular perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of cross-ply laminated cylindrical shells with or without initial local imperfections, from which results for isotropic cylindrical shells follow as a limiting case. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.     

Imperfection sensitivity of laminated conical shells

The sensitivity of laminated conical shells to imperfection is considered, via the initial post-buckling analysis, on the basis of three different shell theories: Donnell’s, Sanders’, and Timoshenko’s. Unlike isotropic conical shells or laminated cylindrical shells, in the case of laminated conical shells the thickness and the material properties vary with the shell coordinates, which complicates the problem considerably. The main objective of the study is to investigate the influence of the variation of the stiffness coefficients on the buckling behavior and on the imperfection sensitivity of laminated conical shells. It is felt that by finding the various parameters that influence the shell’s imperfection sensitivity, it is possible to improve the behavior of the whole structure.A special Level-1 computer code ISOLCS (Imperfection Sensitivity of Laminated Conical Shells) had been developed. ISOLCS calculates the classical buckling load and the imperfection sensitivity via Koiter’s theory of laminated conical shells with consideration to the variation of the material properties in the shell’s coordinates. The range of validity of the Level-1 predictions by ISOLCS is verified by the Level-3 code STAGS-A.     

Creep buckling and postbuckling of circular cylindrical shells under axial compression

An infinitely long, axially compressed, circular cylindrical shell with an imperfection in the shape of the axisymmetric classical buckling mode, undergoing steady or non-steady creep, is analyzed. The axisymmetric problem is solved incrementally using nonlinear shell equations The ratio of the applied stress to the classical buckling stress determines if the shell will collapse axisymmetrically or if it will bifurcate into a nonaxisymmetric mode, and whether or not bifurcation will result in instantaneous collapse. The bifurcation problem is formulated exactly and the initial postbuckling behavior is investigated via an asymptotic elastic analysis, based on Koiter's general theory Numerical results are compared with available experimental data.     

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.     

Multimode Interaction in Axially Stiffened Cylindrical Shells

ABSTRACT

A number of studies show that nonlinear interaction between a shortwave local panel buckling mode and a longwave overall shell buckling mode usually causes strong imperfection sensitivity in stiffened shells. Interaction is particularly strong for simultaneous or nearly simultaneous modes. Mode interaction between two overall buckling modes, as well as interaction between two overall and one local mode, has received much less attention. The present study indicates that for certain imperfection combinations, such mode interactions are important. On the other hand, in most cases, interaction between one overall mode and one local mode governs.     

基于模态缺陷的受压球壳屈曲特性研究

针对受压球壳非线性屈曲过程,对含初始缺陷受压球壳的稳定性进行研究。根据EN1993-1-6（2007）规范,给出不同制造等级壳体的等效缺陷值计算方法;基于线性特征值分析的模态构型给出初始缺陷的分布。利用非线性有限元弧长法对球壳受压失稳过程进行数值模拟,得到屈曲前后球壳变形情况及全过程载荷-位移曲线。计算一致缺陷模态法和N阶缺陷模态法对应的球壳屈曲临界载荷,结果表明,受压球壳对缺陷较敏感,承载能力随缺陷值增大而降低;一致缺陷模态法计算便捷,在工程应用上具有合理性,N阶缺陷模态法考虑高阶模态缺陷构型,结果更加全面,可以为工程中缺陷结构稳定性设计提供参考。     

On the Buckling of Axially Compressed Thin Cylindrical Shells

ABSTRACT

A simple general method for the evaluation of the effect of shape imperfections on the buckling of thin shells is briefly presented. This method is applied to the axially compressed thin cylindrical shell resulting in an efficient numerical procedure for the computation of its buckling strength. The procedure is applicable to any sufficiently smooth imperfection pattern and has given results in good agreement with the available experimental data.     

Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments

A postbuckling analysis is presented for a shear deformable functionally graded cylindrical shell of finite length subjected to combined axial and radial loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect cylindrical shells with two constituent materials subjected to combined axial and radial mechanical loads and under different sets of thermal environments. The results reveal that the temperature field and volume fraction distribution have a significant effect on the postbuckling behavior, but they have a small effect on the imperfection sensitivity of the functionally graded shell.     

Stresses around elliptic holes in circular cylindrical shells

The stress state around an elliptic hole in a circular cylindrical shell under axial loads is measured. The test cylinders which are made of aluminum are loaded both in tension and compression. Stress-concentration factors around the hole for different eccentricities of the ellipse and different curvature parameters are evaluated. Stress-concentration factors away from the edge of the hole are also determined. The results obtained are compared with theoretical results available in the literature. The effect of bending on the stress concentration as related to the eccentricity of the elliptic hole and to the curvature parameters of the shell is discussed. The results from tension test and those from compression test are also compared, and the sensitivity of the shell to any imperfection and possible local buckling at the hole in the case of compression test are demonstrated.     

Experimental investigation of the buckling of shallow spherical shells

In the present paper, the buckling behavior of clamped thin shallow spherical shells under external pressure is studied. Seventy-nine plastic shells formed by thermovacuum process were tested. The distributions of initial geometrical imperfections and vertical displacements were minutely measured with a differential transformer. It was possible to control the symmetrical initial geometrical imperfection of each specimen.Results indicate that the buckling phenomena of shallow spherical shells vary greatly with the symmetrical initial imperfection parameter η. In the case of the geometrical parameter λ larger than 5.5, the amplitude of the asymmetrical displacement component with the bifurcation buckling wave calculated by Huang becomes large immediately before buckling. The validity of Huang's theory for an initially perfect shell is experimentally demonstrated.     

Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration

This paper considers the dynamic stability of a harmonically base-excited cylindrical shell carrying a top mass. Based on Donnell’s nonlinear shell theory, a semi-analytical model is derived which exactly satisfies the (in-plane) boundary conditions. This model is numerically validated through a comparison with static and modal analysis results obtained using finite element modelling. The steady-state nonlinear dynamics of the base-excited cylindrical shell with top mass are examined using both numerical continuation of periodic solutions and standard numerical time integration. In these dynamic analyses the cylindrical shell is preloaded by the weight of the top mass. This preloading results in a single unbuckled stable static equilibrium state. A critical value for the amplitude of the harmonic base-excitation is determined. Above this critical value, the shell may exhibit a non-stationary beating type of response with severe out-of-plane deformations. However, depending on the considered imperfection and circumferential wave number, also other types of post-critical behaviour are observed. Similar as for the static buckling case, the critical value highly depends on the initial imperfections present in the shell.     

Post-buckling dynamic behavior of periodically supported imperfect shells

A circular cylindrical shell, periodically supported and subjected to step-loading in the form of lateral or hydrostatic pressure, is studied. Using the time-dependent von Kármán-Donnell equations, its imperfection sensitivity is examined and a simple asymptotic expression for the dynamic buckling load, valid for small imperfections, is obtained. There is a simple relation, independent of the imperfection, between the dynamic and static buckling loads.     

Theoretical and Experimental Results on the Post-Buckling of Ring-Stiffened Cylinders

ABSTRACT

The post-buckling behavior of ring-stiffened cylinders subjected to lateral pressure is studied theoretically and experimentally. The theoretical analysis uses the energy method and terms of up to and including fourth order of the buckling displacements are considered. The results of experiments on ten machined ring-stiffened cylinders subjected to lateral pressure and used to verify the theoretical analysis. The theory shows the post-buckling behavior to be stable-symmetric for both the shell and general instability modes. The experimental results are in reasonable agreement with the theory, although they indicate, in general, a lower post-buckling stiffness. For the range of parameters considered, no instability or imperfection sensitivity is found in either the theoretical or the experimental studies.