Post-buckling behavior of a point-supported cylindrical liner shell of concrete pressure vessels

Using W. T. Koiter's initial post-buckling theory, this paper deals with the critical load and post-buckling behavior of a point-supported cylindrical liner shell encased in a concrete pressure vessel while the liner shell is subjected to axial and lateral compressions. The reasonable spacing of anchors is given. The results show that the point-supported cylindrical liner shell has a relatively complicated post-buckling behavior. The behavior is subject to the change of anchor spacing in both axial and circumferential directions. When the ratio of the anchor spacing in the two directions satisfies a certain condition, the liner shell will carry the maximum load.     

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。     

Fracture mechanics of plates and shells applied to fail-safe analysis of fuselage Part II: Computational results

In this paper, the problem of the fracture of a fuselage stiffened by longitudinal longerons and circumferential frames is analyzed by means of the finite element method. Our research is motivated by the fail-safety design concept of fuselage for civil aircraft. In this study, the total energy release rate are evaluated for five types of basic loading, namely, axial extension, pure bending, twisting, transverse shearing, and radial expansion due to internal pressure. The crack is located either at the mid-point or near the end of the fuselage. It extends in two bays with the stiffener at its center. The stiffener which bisects the crack is assumed to be broken at the location of the crack. Computational results indicate that the total energy release rate G_t increases with the increasing crack length. However, when the crack tip approaches the stiffener, the value of G_t decreases as a result of the reinforcement from the stiffener. For a crack near the end of the fuselage, as a result of boundary effect, the value of G_t is larger in comparison with the case of the crack at the mid-point of the fuselage. We also find that the effect of geometrical nonlinearity can reduce the value of G_t for the fuselage under axial tension or pure bending. For the fractured fuselage under pure bending, shell buckling can occur at the concave side of the fuselage prior to crack growth. The maximum tensile stress in the stiffener in front of the crack tip is also investigated.     

Axially compressed buckling of pressured multiwall carbon nanotubes

This paper studies axially compressed buckling of an individual multiwall carbon nanotube subjected to an internal or external radial pressure. The emphasis is placed on new physical phenomena due to combined axial stress and radial pressure. According to the radius-to-thickness ratio, multiwall carbon nanotubes discussed here are classified into three types: thin, thick, and (almost) solid. The critical axial stress and the buckling mode are calculated for various radial pressures, with detailed comparison to the classic results of singlelayer elastic shells under combined loadings. It is shown that the buckling mode associated with the minimum axial stress is determined uniquely for multiwall carbon nanotubes under combined axial stress and radial pressure, while it is not unique under pure axial stress. In particular, a thin N-wall nanotube (defined by the radius-to-thickness ratio larger than 5) is shown to be approximately equivalent to a single layer elastic shell whose effective bending stiffness and thickness are N times the effective bending stiffness and thickness of singlewall carbon nanotubes. Based on this result, an approximate method is suggested to substitute a multiwall nanotube of many layers by a multilayer elastic shell of fewer layers with acceptable relative errors. Especially, the present results show that the predicted increase of the critical axial stress due to an internal radial pressure appears to be in qualitative agreement with some known results for filled singlewall carbon nanotubes obtained by molecular dynamics simulations.     

在径向载荷和轴向冲击联合作用下的圆柱壳塑性稳定性分析

对有径向载荷的圆柱壳，受轴向冲击时塑性失稳的临界速度进行理论分析。分析结果与实验值相吻合，并给出一般的规律，它也适用于无径向载荷的情况。     

圆柱壳在外压和轴向冲击联合作用下的稳定性实验研究

本文利用AMT铝合金三种不同厚度的圆柱壳,在常外压和不同轴向冲击载荷作用下的柱壳塑性动力屈曲问题。实验发现除了通常文献中提到的临界速度Vc1外,还有一个使柱壳发生较大变形而破坏时所对应的一个临界遵度Vc2。文章重点研究Vc2与轴向变形。柱壳厚度等之间关系以及柱壳屈曲形式。     

Experimental techniques employed for photoelastic analysis of cellular shells

The search for a shell construction superior to the usual ring-stiffened shells in strength and stability under external pressure with minimum weight has led to consideration of several other shell wall constructions.¹ The cellular-shell structure is one of the most promising designs of shells because of its ability to withstand high-pressure loading while maintaining a high degree of material efficiency. The analytical treatment of cellular shells has been undertaken only recently² and limited experimental study of these shells has been conducted. Thus, for obtaining reliable design formulas for the cellular-shell construction, these studies were undertaken. The cellular-shell construction may be visualized as two concentric thin cylinders spaced radially by a series of thin rings along their common longitudinal axis. The optimum wall thickness, rib thickness and rib spacing for a cellular shell of a given diameter and material which will result in the most efficient utilization of the material when the shell is placed under external pressure is the information required for shell design. The experimental techniques described in this paper have been employed to assist in the determination of the necessary design parameters.     

A genetic algorithm optimization of ring-stiffened cylindrical shells for axial and radial buckling loads

In this research, the general axial and radial buckling optimization of ring-stiffened cylindrical shells is implemented by the genetic algorithm (GA). The stiffened shell is subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. In addition, six design variables including shell thickness, number of stiffeners, stiffeners width and height, stiffeners eccentricity distribution order, and stiffeners spacing distribution order are considered. In analytical solution, the Ritz method is applied and stiffeners are treated as discrete elements. The effect of the weighting coefficients of the objective functions on the optimum solution is studied. The results show that optimized stiffening a cylindrical shell leads to a lower structural weight, higher natural frequencies, and larger axial and radial buckling loads, simultaneously. In addition, the upper and lower bounds of the design variables influence the optimum results considerably. It is also found that the distributions of eccentricity and spacing of the stiffeners influence the magnitudes of the axial and radial buckling loads considerably.     

高速碰撞下圆柱壳自由梁的穿孔特性

利用二级轻气炮加载,进行了球状2A12铝弹丸垂直撞击圆柱壳自由梁实验。并进行了弹丸速度、圆柱壳直径和壁厚等因素对穿孔直径影响的数值模拟,数值模拟结果和实验结果基本吻合。通过量纲分析和数值模拟结合,推导了穿孔直径与相关影响参数的经验关系式。研究结果表明：当圆柱壳直径和厚度不变时,高速撞击产生的穿孔直径在径向和轴向都随着弹丸速度增大而增大;当弹丸速度和圆柱壳厚度不变时,高速撞击产生的穿孔直径随着圆柱壳自由梁直径的增大而减小;当弹丸速度和圆柱壳直径不变时,穿孔直径随着圆柱壳厚度的增大而减小。

     

环向槽圆柱壳结构的参数分析和优化

基于有限元分析,以侧向爆炸冲击和轴向面力为载荷形式,对环向槽圆柱壳结构形式进行了大量的数值模拟计算,履行了参数分析,基于响应面法构造近似显式优化模型,采用MATLAB软件优化程序求解该模型,对各参数的组合进行了优化设计.     

Assessment of the stiffened panel performance in the OTEC seawater tank design: Parametric study and sensitivity analysis

Ocean thermal energy conversion (OTEC) is a process of generating electricity by exploiting the temperature difference between warm surface seawater and cold deep seawater. Due to the high static and dynamic pressures that are caused by seawater circulation, the stiffened panel that constitutes a seawater tank may undergo a reduction in ultimate strength. The current paper investigates the design of stiffening systems for OTEC seawater tanks by examining the effects of stiffening parameters such as stiffener sizes and span-over-bay ratio for the applied combined loadings of lateral and transverse pressure by fluid motion and axial compression due to global bending moment. The ultimate strength calculation was conducted by using the non-linear finite element method via the commercial software known as ABAQUS. The stress and deformation distribution due to pressure loads was computed in the first step and then brought to the second step, in which the axial compression was applied. The effects of pressure on the ultimate strength of the stiffener were investigated for representative stiffened panels, and the significance of the stiffener parameters was assessed by using the sensitivity analysis method. As a result, the ultimate strength was reduced by approximately 1.5% for the span-over-bay ratio of 3 and by 7% for the span-over-bay ratio of 6.     

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.     

Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material (FGM) coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable-coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.     

Experiments characterizing the interaction between two sprays of electrically charged liquid droplets

Experiments were conducted to characterize the interaction between two sprays of electrically charged ethanol droplets. The micrometer-size droplet sprays were generated electrohydrodynamically by applying a high positive voltage to two adjacent parallel needles that were located above a distant, electrically grounded funnel. The resultant droplet axial and lateral velocity components and diameter were measured as a function of needle spacing and applied voltage using a Phase Doppler Particle Analyzer. Data were acquired at two axial positions below the needles' tips, for two needle spacings, four applied voltages and at a single flow rate.The results revealed that an increase in applied voltage yielded an increase in the spray charge density. This produced an increase in both the axial and lateral droplet velocity components and a decrease in the droplet Sauter mean diameter and in its variation across the spray. An increase in needle spacing yielded a decrease in the axial velocity component. The lateral velocity component and the Sauter mean diameter, however, were not noticeably affected by this increase. Photographic data established a relationship between the lateral half-width of the spray and axial distance. This was used to identify a nondimensional similarity between the axial mean velocity component and lateral position. The results collectively support that appropriate variations in the applied voltage and needle spacing can yield more spatially uniform mean velocity component and Sauter mean diameter profiles. These variations bring about increased mixing between the two needles' sprays and, thus, an enhanced development of the combined droplet spray.     

Electromechanical responses and instability of electro-active polymer cylindrical shells

Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer (EAP) cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deformation of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.     

An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells

Using Donnell non-linear shallow shell equations in terms of the displacements and the potential flow theory, this work presents a qualitatively accurate low dimensional model to study the non-linear dynamic behavior and stability of a fluid-filled cylindrical shell under lateral pressure and axial loading. First, the reduced order model is derived taking into account the influence of the driven and companion modes. For this, a modal solution is obtained by a perturbation technique which satisfies exactly the in-plane equilibrium equations and all boundary, continuity, and symmetry conditions. Finally, the equation of motion in the transversal direction is discretized by the Galerkin method. The importance of each mode in the proposed modal expansion is studied using the proper orthogonal decomposition. The quality of the proposed model is corroborated by studying the convergence of frequency–amplitude relations, resonance curves, bifurcation diagrams, and time responses. The parametric analysis clarifies the influence of the lateral and axial loads on the non-linear vibrations and stability of the liquid-filled shell. Finally, the global response of the system is investigated in order to quantify the degree of safety of the shell in the presence of external perturbations through the use of bifurcation diagrams and basins of attraction. This allows one to evaluate the safety and dynamic integrity of the cylindrical shell in a dynamic environment.     

黄河水下三角洲硬壳层特征及其液化过程研究

为揭示黄河口水下三角洲硬壳层的土性特征和风浪作用下的液化破坏状况,选择典型研究区,在现场利用普氏贯入仪测试硬壳层的强度特征,原位取1m原状样进行室内土工试验;利用重锤锤击荷载板的方式模拟波浪对硬壳层的动力作用,通过孔压探头和普氏贯入仪实时监测土体内孔压和振动前后强度的变化;通过理论计算研究硬壳层在不同风浪等级下的液化深度。通过研究发现,（1）硬壳层土体基本上处于超固结状态,且超固结比随深度增加而减小,大王北和刁口地区硬壳层强度约是新滩和广利港的两倍,离河口近的地区强度的变异系数比远的地区要大;（2）根据孔压随振次的变化关系,现场土体在振动过程中,孔压的增长经历了4个阶段,即初始阶段、增长阶段、稳定阶段和衰减阶段,且表层土体达到液化,深层的未液化;（3）大王北硬壳层在6~10级风浪下的平均液化深度仅为7~11cm,新滩和广利港硬壳层在6~10级风浪作用下的液化深度达32~42cm。强度高的硬壳层液化深度小,低的液化深度大,这种液化深度的差异性造成了地貌上的凹凸不平。     

Nonlinear stability of truncated shallow conical sandwich shell with variable thickness

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卸荷条件下粉质粘土变形性状研究

通过室内应力控制的三轴试验研究卸荷条件下土体的应力-应变关系和孔隙水压力变化特征,得到变形模量的确定方法。研究表明:在初始偏压应力固结条件下,无论是轴向压力保持不变而侧向压力不断卸荷,还是轴向压力和侧向压力同时卸荷,其应力-应变关系均表现为较好的双曲线函数关系。而且,侧向固结压力愈大,强度值愈大。在卸荷过程中,随剪切应力的增大和剪切应变的发展,土样呈现剪胀趋势并在后期产生较大的负孔隙水压力。不排水条件下由于负孔隙水压力的存在,土样的表观强度略有增大。     

任意边界条件下环肋圆柱壳振动特性的建模与求解

边界条件对环肋圆柱壳的振动特性有重要影响.基于能量法,把环肋看作离散模型,构建了任意边界条件下加环肋圆柱壳的动力学模型.采用一种改进的傅里叶级数作为位移容许函数,通过瑞利里兹程序求解结构的拉格朗日方程,得到环肋圆柱壳的振动模态和频响特性.通过与实验和有限元(FEM)方法的计算结果进行对比,验证了论文方法的准确性,在此基础上分析了环肋偏心方式、截面尺寸、位置分布和边界弹簧刚度等参数对环肋圆柱壳振动特性的影响.