圆柱壳开孔的应力集中──非圆孔问题的一般解

本文从Donnell型圆柱壳的基本方程出发,利用复变函数方法和保角映射技术,对圆柱壳开非圆形孔的问题进行了研究.首先给出了逼近具有非圆形孔的圆柱壳开孔问题一般解的完备函数序列,构造出了问题的一般解;其次利用有关圆柱壳开小孔的假设概念,给出了圆柱壳开非圆孔时边界条件的一般表达式.进而利用正交函数展开的方法,将待解的问题归结为一组无穷代数方程组的求解问题,并进行直接求解.在本文最后,对圆柱壳开圆孔.椭圆孔附近的应力集中问题进行了数值计算,给出了分析结果.     

厚壁圆柱壳开孔应力集中问题的复变函数解法

本文基于考虑横向剪切变形影响的厚壳理论建立了求解圆柱壳开孔应力集中问题的复变函数方法，得到了此种问题的一般解和满足任意形开孔边界条件的表达式·该应力集中问题可以简化为求解无穷代数方程组的问题·用复变函数方法可以规范地求解应力集中问题·文中给出了圆柱壳开小圆孔和椭圆孔时应力集中系数的数值结果·     

一类非线性发展方程组的定解问题

将不可压缩的广义neo-Hookean材料组成的超弹性圆柱壳径向对称运动的数学模型归结为一类非线性发展方程组的初边值问题.利用材料的不可压缩条件和边界条件求得了描述圆柱壳内表面径向运动的二阶非线性常微分方程.给出了微分方程的周期解(即圆柱壳的内表面产生非线性周期振动)的存在条件,讨论了材料参数和结构参数对方程的周期解的影响,并给出了相应的数值模拟.     

复合材料叠层圆柱壳的非线性动力稳定性理论

用Hamilton原理建立了复合材料叠层圆柱壳非线性动力稳定性理论的一般性基本方程,其中包含了非线性大挠度,横向剪切,纵向惯性力等因素。用变分法获得基本方程的解。分析表明:叠层圆柱壳在动载荷下会发生参数共振而进入动力不稳定区域而导致动力失稳。计算了几种典型复合材料圆柱壳:即T300/5208石墨环氧,E-玻璃环氧和ARALL圆柱壳。结果表明:这些因素对于各种复合材料圆柱壳的动力稳定性具有程度不同的重要影响,所以研究叠层圆柱壳动力稳定性时,考虑这些因素是重要的。     

受轴向压缩圆柱壳塑性屈曲的内时分析

采用内时塑性本构方程的增量和全量表达式分析了受轴向压缩圆柱壳的塑性屈曲，得到了塑性屈曲临界应力与圆柱壳特征尺寸间的关系。对ＡＭＦ和铝合金圆柱壳塑性屈曲进行了分析，与实验结果的比较表明：除对于ＡＭＦ圆柱壳由内时塑性本构方程的全量表达式给出了较经典塑性理论全量分析略为保守的结果外，在其它杨合下，内时分析均给出了较经典塑性理论更符合实验数据的结果。     

弹性介质中受轴向冲击载荷作用的圆柱壳的屈曲临界载荷计算分析

建立并求解了弹性介质中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.通过计算得到了不同时间段屈曲临界载荷与应力波波阵面到达圆柱壳的位置、弹性介质的刚度、壳体未嵌入弹性介质部分的长度与总长之比的关系.数值计算结果表明,弹性介质中的圆柱壳发生轴对称屈曲和非轴对称屈曲趋势一致;嵌入弹性介质部分越深、弹性介质刚度越大圆柱壳越难屈曲;屈曲临界载荷随着弹性介质刚度的增大经历了增长缓慢、增长迅速以及增长较慢3个阶段;应力波反射前波阵面通过分界面后,屈曲仅发生在应力波传播区域,反射波波阵面通过分界面前,临界载荷较小时屈曲先发生在反射端部,随着轴向阶数增大,屈曲覆盖整个圆柱壳区域,反射波波阵面通过分界面后,壳体发生的屈曲始终覆盖整个圆柱壳区域.     

复杂载荷下加筋圆柱壳非线性冲击屈曲研究

将加筋圆柱壳离散成为由圆柱壳和加强筋组成的壳体-肋骨系统,假设环向加筋与壳体在接触处刚性连接,由Hamilton变分原理推导出加筋圆柱壳结构的运动方程,以研究加筋圆柱壳在水下冲击载荷和静水压力以及动水压力组成的复杂载荷联合作用下的非线性屈曲行为。借助增量数值(在时域采用4阶Runge-Kutta方法)的方法来分析了加筋圆柱壳的非线性屈曲行为,经过算例分析验证了材料因素和初始缺陷对结构屈曲的重要影响。     

轴压加筋圆柱壳Koiter-边界层奇异摄动法

将Koiter理论和奇异摄动理论中的边界层法相结合,处理加筋圆柱壳无因次化非线性边界层型Karman－Donnell方程由分支点和边界层导致的双重奇异性,提出轴压加筋圆柱壳Koiter-边界层奇异摄动法.对AS－2壳分析表明,本方法具有很好的计算效率和计算精度,与数值解相比更能揭示其内在的影响规律.     

环肋加劲圆柱壳在静水压力作用下的初始后屈曲分析

本文用Koiter理论分析环肋加劲圆柱壳在静水压力作用下的后屈曲性能.前屈曲状态采用与边界条件一致的非线性有矩方程,本征值问题的解用伽辽金方法求出,得到的临界载荷与经典线性解作了比较.具体计算了三种不同环肋参数的外肋加劲圆柱壳.结果表明,肋的强弱不仅显著影响临界载荷值,同时也改变了柱壳的缺陷敏感度.     

静水压力下压电弹性圆柱振动的主动控制

对静水压力下压电弹性层合壳的振动控制进行了研究。首先利用Hamiltion原理推导出压电弹性层合壳的非线性动力基本方程，进一步得到了静水压力作用下封闭压电弹性层合壳的动力方程。对两端简支条件下的压电弹性圆柱壳的振动问题进行了求解，并基于速度反馈控制法得到了带压电感测层／激励层的层合圆柱壳的主动控制模型，相应的数值结果表明在载荷的情况下，压电层上施加合适大小，方向的电压可以改变圆柱壳的静变形。对于系统的动力响应问题，速度反馈的增益越大，越能抑制系统在共振区的振动，验证了该控制模型抑制结构振动的有效性。     

Influence of geometric parameters on the stress concentration in an elastoplastic cylindrical shell

The elastoplastic stress-strain state of cylindrical shells weakened by a curvilinear (circular) hole is investigated. Numerical results are given for shells with a reinforced hole under the action of an internal pressure of specified intensity. The influence of the geometric parameters of the shell on the stress distribution in the concentration zone is investigated in the elastic and inelastic stages of deformation. The variation in flexure along the hole contour is given for linear and nonlinear problems, and the distribution of the maximum stress-concentration coefficients is also given for various geometric parameters.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 100–103, 1988.     

On a method of studying the stress state of orthotropic shells and plates weakened by a hole with cracks extending to its edge

On the basis of the Timoshenko kinematic hypothesis for shells we give a formulation of the problem of studying the stress-strain state of orthotropic plates and shells weakened by a combined stress concentrator (a hole with two symmetric cracks extending to its edge). We propose a method of solving such problems on the basis of the finite-element method. To simulate the singularity of the stresses and displacements in a neighborhood of the tip of a crack we apply special finite elements with degenerate faces and nodes displaced by 1/4 the length of an edge. The stress intensity factors are found in terms of the displacements of the nodes of such elements. We give the results of computation of the concentration coefficients and the stress intensity factors for spherical and cylindrical shells loaded by internal pressure and for a cylindrical shell and a plate under the action of a distending load with various concentrators: a circular hole, an isolated crack, and a combined concentrator. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 48–54.     

开孔浅球壳的非线性动力响应及其动力稳定

本文建立了具轴对称变形、考虑横向剪切影响的浅球壳的非线性运动方程:对周边弹性支承开孔浅球壳的非线性静、动力响应及动力稳定问题进行了探讨.在解题方法上,对位移函数在空间上采用正交配点法离散.在时间上采用平均加速度法(Newmark-β法)离散.变求解一组非线性微分方程为求解一组线性代数方程.文中给出了不同情况下的若干数值结果,且与有关文献的结果作了比较.     

多夹层板壳的非线性理论及应用（Ⅲ）：扁壳的弯曲和稳定

本文根据文[1]获得的多夹层扁壳非线性基本方程，求解了各种载荷及边界条件下矩形底面多夹层扁壳的非线性弯曲问题，多夹层板、扁柱亮在轴向压力作用下的稳定问题，以及一般形状的扁壳在边界作用力下的变形．     

New variational-asymptotic formulations for 3-D stress analyses of laminated composite shells with a circular hole

A new approach for three-dimensional stress analyses in composite cylindrical shells is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. Classical assumptions have been justified and new approximations have been established. These formulations are directed especially towards, new high integrity mixed-hybrid finite element schemes. The expository examples chosen are of cross-ply and angle-ply laminated shells. The circumferential location of the delamination failure initiation, for angle-ply laminates containing a circular hole, is within a sector located symmetrically around the perpendicular direction to the applied load.     

Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

圆柱壳小开孔理论解在工程实践中的应用

完全从一个新的角度,重新研究圆柱壳小开孔的理论解,指出了它与圆柱壳大开孔理论解之间的某一种特殊的内在联系。利用这种联系,重新估计了小开孔理论解在工程实践中的应用范围,为如何利用圆柱壳小开孔理论,提供了一种设想。对圆柱壳小开孔理论在工程实践中的应用重新做出了一个评价。     

Approximation of a circular cylindrical shell by Clough-Johnson flat plate finite elements

Summary In this paper, we study the approximation of a right circular cylindrical shell by a nonconforming method using Clough-Johnson flat plate finite elements. Compatibility conditions which have to be satisfied by the degrees of freedom at every node of the triangulation are given. Then, we prove that convergence is insured for shallow shells when using particular families of triangulations which are practically easy to implement. Finally, we propose a new approximation method by flat plate finite elements which assures the convergence for any kind of circular cylindrical shell.     

Application of the method of partitioning the state of stress to the analysis of thermoelastic shells : PMM vol. 40, n 6, 1976, pp. 1085–1092

By using an asymptotic approach [1], the method of partitioning the state of stress is extended to thermoelastic shells. It is examined in detail in [2] forun-heated shells subjected to the effect of external forces, and consists of representing the total state of stress of the shell as the sum of those simpler states of stress for each of which the simplest methods for their construction can be given.Partitioning of the state of stress was performed in [3] for shells with a constant temperature over the thickness. It was noted in [4] in an analysis of a circular cylindrical shell by bending theory that integrals extended over the whole middle surface, which describe the fundamental state of stress, and integrals which damp out with distance from the edges and represent edge effects are contained in the general solution. In a number of papers, [5] for example, partitioning is performed on the basis of graphic physical representations for simple examples of analyzing circular cylindrical shells.A general approach to the analysis of rigid thermoelastic shells by the partitioning method is described below.