A Review of External Pressure Testing Techniques for Shells including a Novel Volume-Control Method

A review of conventional testing methods for applying external hydrostatic pressure to buckling-critical shells is presented. A new “volume-control” pressure testing method, aimed at preventing catastrophic specimen failures and improving control of specimen deformation near the critical load, is also introduced. The implementation of conventional and volume-control systems in an experimental program involving the destructive pressure testing of ring-stiffened cylinders is described. The volume control method was found to improve control of the specimen deformations, especially near the critical load, and catastrophic failures observed while using a conventional setup were avoided. The quasi-static tracking of post-collapse load-deformation relationships for snap-through buckling behaviour was possible while using a volume-control system, but precise control of dynamic shell deformations during buckling was not achieved for specimens failing with large buckling lobes. Expressions for estimating the available control over specimen deformations for pressure testing systems are presented.     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.     

薄壁加筋肋圆柱壳稳定性分析的参数化研究

针对在轴向载荷作用下的正置、正交网格形式的薄壁加筋肋圆柱壳结构，利用有限元程序，对薄壁加筋肋圆柱壳稳定性分析进行了参数化研究，得到了进行结构优化设计的准则，对于给定的设计载荷，当结构参数位于某一个局部失稳与整体失稳的临界区域时，结构的重量最轻。提出了基于有限元分析进行结构优化设计的策略，利用优化策略，获得了一薄壁加筋肋圆柱壳结构的优化设计结果，同时给出了粘合刚度简化模型与有限元计算结果的比较。     

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。     

Nonlinear stability of truncated shallow conical sandwich shell with variable thickness

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Buckling of spherical sandwich shells

An experimental investigation was carried out to determine the critical buckling loads of several shallow spherical sandwich shells. A cold-forming process simultaneously using pressure and vacuum was employed to manufacture the nearly perfect spherical facing layers from 5052 aluminum-alloy sheets of 0.006 and of 0.008-in. thicknesses. Eight shallow spherical-shell specimens of 20-in. base diameter and of 20 and 30-in. radii with 1/8 and 1/4-in. thickness of “Flexcore” have been tested in a 300-psi autoclave specifically designed for these experiments. The pressure on shells was developed by the differential pressure between the inner and the outer chambers separated by the shell being tested. When the inner chamber was maintained at atmospheric pressure and gas pressure was applied in the outer chamber, the testing procedure was termed “soft.” Alternatively, the inner chamber would be filled with fluid with the outer chamber remaining filled with gas. By initially pressurizing both chambers equally, a load on the shell could be developed by the differential pressure due to controlled bleeding of the fluid inside the inner chamber, while the gas in the outer chamber was maintained at the initial pressure. This is an accurate volume-control experiment and this testing procedure was termed “hard.” In the latter case, it was possible to monitor the displacements of the shell for each load increment with a nest of clip gages of an unique design. It was found that there is no substantial difference in the buckling loads between the hard and “soft” systems. All shells buckled in the plastic range. A reasonably good correlation is obtained with a linear theory using the double modulus for the sandwich segments.     

前屈曲应力状态对组合加肋旋转壳失稳临界压力影响的探讨

推导了包含前屈曲弯矩和横剪力的旋转壳弹性稳定性基本方程.运用Riccati传递矩阵法对组合加肋旋转壳算例进行了稳定性分析,并与假设前屈曲状态为薄膜应力状态计算出的失稳临界压力进行了比较.结果表明,前屈曲弯矩和横剪力对组合加肋旋转壳失稳临界压力的影响较小,随着壳板厚度和肋骨尺寸的增大及肋骨间距的缩短,影响略有增大.因而,分析组合加肋旋转壳弹性稳定性时,前屈曲状态采用薄膜应力状态的假设是合理的.     

Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love’s First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly.     

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.     

Buckling of yeast modeled as viscoelastic shells with transverse shearing

Yeast cells can be regarded as micron-sized and liquid-filled cylindrical shells. Owing to the rigid cell walls, yeast cells can bear compressive forces produced during the biotechnological process chain. However, when the compressive forces applied on the yeast go beyond a critical value, mechanical buckling will occur. Since the buckling of the yeast can change the networks in its cellular control, the experimental research of the buckling of the yeast has received considerable attention recently. In this paper, we apply a viscoelastic shell model to study the buckling of the yeast. Meanwhile, the turgor pressure in the yeast due to the internal liquid is taken into account as well. The governing equations are based on the first-order shear deformation theory. The critical axial compressive force in the phase space is obtained by the Laplace transformation, and the Bellman numerical inversion method is then applied to the analytical result to obtain the corresponding numerical results in the physical phase. The concepts of instantaneous critical buckling force, durable critical buckling force, and delay buckling are set up in this paper. And the effects of the transverse shear deformation and the turgor pressure on the buckling phenomena are also given. The numerical results show that the transverse shearing effect will decrease the instantaneous critical buckling force and the durable critical buckling force, while the turgor pressure will increase both of them.     

考虑制作缺陷的变角度纤维复合材料层合板的屈曲

假设纤维方向角沿层合板的长度方向线性变化,研究含丝束重叠、间隙等制作缺陷的变角度纤维复合材料层合板的屈曲问题.采用ABAQUS有限元软件建立层合板的有限元模型,选用S4壳单元计算四边简支层合板在两端压缩荷载作用下的屈曲临界荷载及屈曲模态,并进行详细的参数分析.研究结果表明:当起始角相同时,含或不含制作缺陷的层合板的屈曲...     

Experimental and theoretical studies on buckling of thin-walled MHS compressed between two rigid plates

This paper presents the theoretical and experiment results of buckling behavior of thin-walled metallic hollow sphere (MHS) compressed between two rigid plates. The first critical buckling load of MHS has been derived. It is shown that the critical load is related to the radius, thickness of the sphere shell, the elastic modulus, and Poisson’s Ratio of the material. Two hemispheres are welded to make the MHS with three different angles of welding-line. The quasi-static compressive experiment of the MHS has been carried out, and the load-deformation curves are obtained. To match theoretical and experimental results, a modified equation is presented. Then a good agreement between the theoretical and the experimental results is obtained.     

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear

The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.     

NEW STRUCTURAL DESIGN OF SPHERICAL PRESSURE HULL FOR DEEP-SEA SUBMERSIBLES:A MULTILAYER AND PRESSURE REDISTRIBUTION APPROACH

耐压壳是深海潜水器中最关键的结构,直接关系到潜水器安全性和总体性能.本文对当今的单层耐压壳结构设计进行了评述,并设计了一种基于分层/分压的新型耐压壳结构,该结构借鉴了自然界的两种深潜动物的结构：抹香鲸分层结构和鹦鹉螺隔片分割螺壳亚结构.综合了这两种结构特性的双层壳结构能够有效提高抗压能力,从而提升深潜能力.与以往单层球壳的耐压壳结构相比,该结构不仅提高了强度,也提高了抗屈曲能力.同时,该结构还兼具大容积、高可靠性、以及避免超厚壳制备上的难点等特征,使得深海潜水器的综合性能得到显著提高.新结构中的桁架将圆壳分割为若干个柱壳亚结构,本文针对此亚结构严格推导了桁架增强壳体抗屈曲的公式.从实验数据中总结出来的泰勒水池公式是目前广泛使用的潜水器壳体设计依据,新推导的公式与之相比只有6%的差别,这使得新型结构设计有了更坚实的理论基础.     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题,研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型,考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关,导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下,外压屈曲临界压力的数值结果,并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示,对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。     

Reinforcement minimization of cylindrical shells

In the search for the absolute minimum amount of reinforcement to be provided in a structure to support predefined loading, most attention has been given to problems for which the relationship between unit cost of material and stress relationships is simple—usually linear. Such an assumption is convenient and reasonably realistic when reinforcement percentages are low. However, for higher reinforcement percentages, and when, as in the case of cylindrical shells, there occur axial as well as radial loads, a more refined analysis procedure is desirable. This paper considers the optimal (absolute minimum reinforcement) strength design of closed cylindrical shells subject to uniform pressure and having rigid ends. Two cases are considered: the shell wall rigidly connected to the ends, and the shell wall hinged at the ends. For convenience, only internal pressure loading is considered in detail, although, using the theory given, results for external pressure cases can readily be obtained. It is assumed that buckling is not a critical factor in the design and that serviceability criteria can be met independently.     

复合材料襟翼壁板屈曲失稳行为的栅线投影实验研究

本文利用栅线投影测量方法研究了蜂窝夹层板、工字型及T型加筋板三种不同结构形式复合材料襟翼壁板在压缩载荷下的屈曲失稳行为,得到了不同形式结构件屈曲的全场离面位移分布规律,分析了各自的屈曲失稳模式.研究结果表明,栅线投影测量方法在大尺度复合材料结构失稳变形测试中具有可行性;在相同面板尺寸条件下,工字型加筋复合材料襟翼壁板屈曲临界载荷最大,承载能力最强.本文结果可为飞机复合材料结构设计提供实验依据.     

金属圆柱壳受大质量低速冲击的屈曲变形

对钢质和铜质金属圆柱壳的轴向冲击动力响应进行了实验研究,记录了两种不同材料圆柱壳在大质量低速冲击下的冲击力时程曲线,得到其屈曲模态。采用高速摄像及模拟技术给出了钢质圆柱壳渐进屈曲的全过程,为理解钢质圆柱壳的屈曲机理提供了直观的结果。黄铜质圆柱壳在大质量低速冲击下, 出现整个壳面滿布屈曲波纹的塑性动力屈曲现象,说明高速冲击不是产生塑性动力屈曲的充要条件。像铜这样具有高密度的韧性材料,在大质量低速冲击下,会在轴向产生持续的压缩塑性流作用而出现塑性动力屈曲现象。