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。     

充满液体的封闭圆柱壳受轴压时屈曲过程的实验研究

报导了对充满水的金属圆柱薄壳在轴向压缩时屈曲性能的实验结果。实验观察表明，充满液体的金属圆柱壳在轴压作用下的屈曲模态呈轴对称型，液体的内压与外部轴压随轴向缩短的变化趋势大致相同。由于壳内液体的存在，同内空的圆柱壳相比只是临界载荷略有提高，屈曲后承载能力并无显著降低，且对初始几何缺陷表现得远不象内空柱壳那样敏感。     

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。     

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法

利用随机场对圆柱薄壳结构的初始几何缺陷进行建模，并据此建立了一种用于含初始几何缺陷轴压圆柱薄壳屈曲分析的随机分析方法。首先，指出已有将圆柱薄壳初始几何缺陷表征为二维高斯随机场的方法会导致与实际不相符的初始几何缺陷，如圆柱周长显著增大或缩小的几何缺陷。其次，提出一种考虑周长不变约束的随机场建模方法，以剔除与实际不相符的随机几何缺陷。最后，基于所建立的初始几何缺陷随机场模型，利用非干涉多项式混沌展开法进行圆柱薄壳的随机屈曲分析，给出临界屈曲载荷的概率分布。数值试验结果表明，基于随机场理论的初始几何缺陷建模方法可有效刻画几何缺陷对结构承载能力的影响，而提出的约束随机场建模方法又能有效减小结果的分散性。     

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。     

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。     

圆柱壳的非线性动力屈曲分析

本文研究在轴向冲击作用下，具有初始几何缺陷的圆柱壳的非线性弹性动力屈曲问题。由于冲击过程中作用时间极短，应力波的影响变得相当重要，同时认为圆柱壳经历大挠度变形。分析中不仅考虑圆柱壳的径向惯性力，而且也考虑轴向惯性力和几何非线性的影响。假设圆柱壳中位移和薄膜力可分成轴对称分量和非轴对称分量之和，并引入应力函数表示非轴对称内力，对平衡方程应用伽辽金方法，将导出的和冲击物体的质量对动屈曲性能的影响很大。     

辛方法和弹性圆柱壳在内外压和轴向冲击下的动态屈曲

针对有内压或外压的弹性圆柱壳在轴向冲击载荷耦合作用下的动态屈曲问题,构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法。该方法直接得到非轴对称的屈曲模态。数值结果给出了圆柱壳问题的临界载荷和屈曲模态以及一些规律。     

复杂载荷作用下圆柱壳的弹塑性动力屈曲研究

对复杂载荷作用下圆柱壳的弹塑性动力屈曲问题进行了研究。基于Hamilton变分原理导出圆柱壳的运动方程 ,本构关系采用增量理论 ,借助增量数值算法求解动力方程组。结果表明 ,均匀径向外压对圆柱壳的轴向冲击的过程或冲击性态有较大的影响 ,并讨论了径向压力与轴向冲击载荷的幅值对结构临界动力屈曲载荷和临界动力失效载荷的影响。     

复合圆柱壳冲击压缩数值模拟及稳定性研究

针对复合圆柱壳在炸药爆轰作用下的动力学响应及在此过程中伴随的失稳问题,研究了其制造工艺中可能出现的缺陷以及圆柱壳中铜线螺旋角和直径对复合圆柱壳稳定性产生的影响。采用SPH-FEM耦合算法,建立了复合圆柱壳二维细节模型,并提出了一种基于圆柱壳内壁粒子速度历史的失稳判据,计算了在不同参数条件下复合圆柱壳的失稳时间及对应的压缩率,对影响复合圆柱壳稳定性的因素进行了评估。分析结果表明,在复合圆柱壳制备过程中存在的折返层缺陷和铜线直径对复合圆柱壳的稳定性有较大影响,而螺旋角度对其稳定性影响不大。     

电活性聚合物圆柱壳静态与动态电压下的响应及稳定性

摘要：在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场。这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏。本文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题。采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程。给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏。同时,也讨论了厚度和边界条件对临界电压的影响。圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动。给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性。采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏。最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论。     

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．     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Dynamic stability of viscoelastic circular cylindrical shells taking into account shear deformation and rotatory inertia

The present work discusses the problem of dynamic stability of a viscoelas- tic circular cylindrical shell,according to revised Timoshenko theory,with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement.Pro- ceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For a wide range of vari- ation of physical mechanical and geometrical parameters,the dynamic behavior of the shell is studied.The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown.Results obtained using different theories are compared.     

Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account

We consider nonlinear vibration and dynamic stability problems for a viscoelastic circular cylindrical shell according to the refined Timoshenko theory, which takes into account the shear strain and the inertia of rotation, in a geometrically nonlinear setting. The problem data are reduced to systems of nonlinear integro-differential equations with singular relaxation kernels, which can be solved by the Bubnov-Galerkin method combined with a numerical method based on quadrature formulas. We study the numerical convergence of the Bubnov-Galerkin method. We analyze the shell dynamic behavior in a wide range of physical-mechanical and geometric parameters. We demonstrate the influence of the viscoelastic properties of the material on the nonlinear vibrations and dynamic stability of a circular cylindrical shell. We also compare the results obtained according to different theories.     

Studies of nonlinear deformation and stability of stiffened oval cylindrical shells under combined loading by bending moment and boundary transverse force

The finite-element statement of stability problems for stiffened oval cylindrical shells is presented with the moments and the nonlinearity of their subcritical stress-strain state taken into account. Explicit expressions for the displacements of elements of noncircular cylindrical shells as solids are obtained by integration of the equations derived by equating the linear deformation components with zero. These expressions are used to construct the shape functions of the effective quadrangular finite element of natural curvature, and an efficient algorithm for studying the shell nonlinear deformation and stability is developed. The stability of stiffened oval cylindrical shells is studied in the case of combined loading by a boundary transverse force and a bending moment. The influence of the shell ovality and the deformation nonlinearity on the shell stability is investigated.     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

激光辐照下圆柱壳结构的稳定性分析

针对航天工程中常用的承受轴压作用的薄壁圆柱壳,分别采用解析方法与特征值屈曲有限元方法分析了圆柱壳结构在均匀轴压作用下的稳定性能,得到了屈曲承载力.并进行了对比,验证了有限元模型的合理性.采用线性屈曲特征值有限元方法分析了强激光辐照作用下圆柱壳的稳定性能,分析表明激光辐照导致壳体局部温度上升并由此带来材料参数的改变,是因为激光辐照在壳体中引起了热应力与热应变,使轴压圆柱壳的屈曲承载力明显降低.论文还着重对加筋圆柱壳结构的稳定性进行了研究,数值分析结果表明,加筋能有效提高圆柱壳结构的抗压承载力,激光辐照作用下,加筋对轴压作用下圆柱壳的屈曲承载力的提高作用更为明显.     

Maximum stability formulas for reinforced cylindrical shells under external pressure

The problem of determining the reinforcement structure that maximizes the stability of a cylindrical shell subjected to external pressure was formulated in [1], where a numerical solution was obtained for a particular class of structures on the basis of a formula for the stability limit of a hinged anisotropic circular cylindrical shell of medium length in the membrane state. In the present article the stability limit is determined more accurately, without any constraint on the length of the shell, and the optimization is carried out over a broader class of structures.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 5, pp. 159–167, September–October, 1977.