含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法

提出了一种分析含内埋矩形脱层正交各向异性圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。     

基于混合变量的脱层壳屈曲分析

提出一种分析脱层圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于一阶剪切理论，通过定义广义位移变量和对应的广义力变量，建立壳的改进的混合变量能量泛函；然后引入条形单元，对混合变量在环向进行离散，从而导出超级壳单元的混合变量能量泛函，由变分原理得到控制方程，采用传递函数方法得到其形式解；最后，将含环向贯穿脱层的复合材料层合壳作为超级壳单元的组合体，得到脱层壳的屈曲方程。给出了脱层大小和深度以及脱层壳边界条件对屈曲载荷的影响。     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

中厚夹层圆柱扁壳的屈曲分析

基于一阶剪切变形中厚圆柱壳理论,考虑夹心层的面内刚度,根据中厚夹层圆柱扁壳的几何方程、本构关系、平衡方程,建立了中厚夹层圆柱扁壳小挠度屈曲的微分方程;应用广义傅里叶级数解法,得到了四边简支条件下中厚夹层圆柱扁壳屈曲的临界荷载表达式。该表达式可以退化为硬夹心夹层板的表达式,表明本文推导过程的正确性。本文还讨论了夹心层的弹性模量和泊松比以及中厚夹心圆柱扁壳的长宽比和厚度对扁壳屈曲荷载的影响。结果表明:临界荷载与夹心层的弹性模量和泊松比成正比,与扁壳的长宽比和厚度成反比。     

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。     

阶跃扭矩作用下弹性圆柱壳冲击屈曲

本文首先基于Koiter初始后屈曲理论和Thompson离散坐标方法,给出了受扭圆柱壳的缺陷敏感性分析及冲击扭转屈曲渐近分析,并指出它对应于对称失稳的情形。然后通过求解受扭圆柱壳的非线性动力学方程,指出在阶跃扭矩作用下的后屈曲阶段,壳体的振动幅值剧增,周期变大。     

脱层梁屈曲的高阶剪切理论

脱层的存在将会大大降低层合结构的屈曲载荷。该文将含任意位置脱层的两端固支梁分成多段子层,用厚度的三次多项式模拟脱层梁屈曲时子层的轴向位移,利用变分原理和欧拉方程导出了脱层梁的屈曲方程和定解条件,并用状态空间方法进行求解。通过与一阶剪切理论和经典理论的比较,指出了它们各自的适用范围;考虑了脱层梁三种不同的屈曲模态。分析了脱层长度、深度、位置和材料的铺层方向对脱层梁屈曲载荷的影响;最后给出了多处简单脱层的屈曲分析。     

阻尼约束的圆柱壳在轴向冲击载荷作用下的屈曲分析

建立并求解了受径向阻尼约束圆柱壳的径向位移控制方程,考虑边界条件及相容条件,得到了应力波传播及反射过程中圆柱壳的动力屈曲分叉条件。通过计算得到了应力波传播及反射过程中屈曲临界载荷与应力波传播时间、径向阻尼的关系,以及有阻尼约束和无阻尼约束条件下圆柱壳的屈曲模态。数值计算结果表明:阻尼约束圆柱壳发生轴对称和非轴对称屈曲情况下,临界载荷关于应力波传播时间、径向阻尼的趋势一致;临界载荷随波传播时间的增加逐渐降低并趋于平缓;径向阻尼使圆柱壳的抗动力屈曲能力增强,且应力波反射后圆柱壳从低阶轴向屈曲到高阶轴向屈曲比反射前更容易;径向加阻尼约束后圆柱壳的屈曲模态形状与不加阻尼约束时保持一致。     

三维编织复合材料圆柱壳在外压作用下的屈曲分析

提出一种三维四向编织复合材料圆柱壳的细观力学模型,宏观上基于Reddy高阶剪切变形理论和广义Kármán型方程,采用奇异摄动法求解在固支边界条件下三维四向编织复合材料圆柱壳在外压作用下的屈曲和后屈曲.分析中同时考虑非线性前屈曲、大挠度和初始几何缺陷的影响.讨论了纤维体积含量、壳体几何参数等因素对圆柱壳屈曲行为的影响.     

变角度纤维复合材料圆柱壳的轴压屈曲

变角度纤维复合材料的纤维方向角可沿铺层面内连续变化,因此相应结构的性能具有更高的设计灵活性和更大的优化空间．本文假设纤维方向角沿圆柱壳的轴向呈正弦函数变化,对变角度纤维复合材料圆柱壳在两端简支边界条件下的轴压屈曲问题进行研究．基于Donnell经典壳体理论,推导变角度纤维复合材料圆柱壳的前屈曲控制方程并运用伽辽金法进行求解,然后采用瑞利里兹法求解屈曲问题．通过和现有文献及有限元数值结果的对比,验证了本文模型的收敛性和正确性,通过数值算例分析了纤维起始角和终止角的变化对圆柱壳的屈曲临界荷载的影响．本文的研究结果可为变角度纤维复合材料圆柱壳的分析和设计提供一定的参考．     

Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties

Thermal postbuckling analysis is presented for graphene-reinforced composite (GRC) laminated cylindrical shells under a uniform temperature field. The GRC layers are arranged in a functionally graded (FG) graphene reinforcement pattern by varying the graphene volume fraction in each GRC layer. The GRCs possess temperature dependent and anisotropic material properties and the extended Halpin–Tsai model is employed to evaluate the GRC material properties. The governing equations are based on a higher order shear deformation shell theory and include the von Kármán-type kinematic nonlinearity and the thermal effects. A singular perturbation method in conjunction with a two-step perturbation approach is applied to determine the thermal postbuckling equilibrium path for a GRC shell with or without geometric imperfection. An iterative scheme is developed to obtain numerical thermal buckling temperatures and thermal postbuckling load–deflection curves for the shells. The results reveal that the FG-X piece-wise FG graphene distribution can enhance the thermal postbuckling capacity of the shells when the shells are subjected to a uniform temperature loading.

     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

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Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.The English text was polished by Yunming Chen.     

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.     

Delamination growth of laminated composite cylindrical shells

The local buckling may occur in delaminated cylindrical shells under axial compression. This often causes delamination growth and structure failure. Based on the variational principle of moving boundary, in this paper, the postbuckling governing equations for the laminated cylindrical shells are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of delamination sizes and depths, the boundary conditions, the material properties and the laminate stacking sequences on delamination growth are discussed.     

Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical shell subjected to torsion 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. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation theory with a von Kármán–Donnell-type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, FGM cylindrical shells under different sets of thermal fields. The results reveal that the volume fraction distribution of FGMs has a significant effect on the buckling load and postbuckling behavior of FGM cylindrical shells subjected to torsion. They also confirm that the torsional postbuckling equilibrium path is weakly unstable and the shell structure is virtually imperfection–insensitive.     

安全壳中钢衬壳热屈曲问题理论与实验研究(Ⅱ)──实验部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题,但实验研究方面的文章发表得不多文中以200兆瓦核电站安全壳中钢衬壳为研究对象,采用局部1：1模型,测得了钢衬壳热屈曲温度和应变载荷,给出了钢衬壳屈曲和初始后屈曲过程中挠度和温度关系、以及膜应变和温度关系,实验测得钢衬壳具有局域屈曲的现象,实验屈曲载荷与理论结果符合较好     

A boundary layer theory for the buckling of thin cylindrical shells under external pressure

Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref. [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.     

Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium

This paper presents a study on the postbuckling response of a functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to internal pressure in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless elastic foundation of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large.     

Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators

A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Kármán–Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. 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 hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.