湿热环境中复合材料层合圆柱薄壳的屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响.基于细观力学模型复合材料性能与湿度和温度变化有关.壳体控制方程基于经典层合壳理论,并包括湿热效应.壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径.分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响.数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为.讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响.     

湿热环境中复合材料层合圆柱薄壳屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响。基于细观力学模型复合材料性能与湿度和温度变化有关。壳体控制方程基于经典层合壳理论,并包括湿热效应。壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径。分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为。讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响。     

约束层阻尼圆柱壳的自由振动

给出了被动约束层阻尼圆柱壳(PCLD)的自由振动特性．波传播法被用来求解两端简支的PCLD圆柱壳的振动,而不是用有限元法、传递矩阵法和Rayleigh-Ritz法．基于Sanders薄壳理论,导出了PCLD正交各向异性圆柱壳的控制方程．数值结果表明当前的方法要比目前其它方法有效．讨论了粘弹性层和约束层的厚度,正交各向异性约束层的弹性模量比率和粘弹性层的复剪切模量对频率参数和损失因子的影响．     

带径向接管的圆柱壳端部受力矩作用时的薄壳理论解

给出可适用于大开孔率 ( ρ0 ≤ 0 .8)的带径向接管的圆柱壳受端部力矩作用时的薄壳理论解 .采用修正的Morley方程代替前人使用的Donnell扁壳方程 ,在主壳展开面极坐标 (α ,β)系中求解开孔圆柱壳齐次解 ,既保持了薄壳理论的精度量级 ,又不受开孔率的限制 ;利用Goldenveizer的位移函数圆柱壳方程 ,在支管展开面主坐标 ( ζ ,θ)系中求得非平齐端头支管的齐次解 .主壳与支管交界处的边界位移和边界力分别由 (α ,β)、( ζ ,θ)系转换到总体柱坐标 ( ρ,θ ,z)系后均为θ的周期函数 ,因而可分别展成Fourier级数 ,各谐的Fourier系数可利用数值积分获得 ,再由连续条件得到整体结构的薄壳理论解 .经前人的实验和三维有限元计算结果的检验 ,证明解是可靠的 .     

旋转薄壳自由振动中的转点问题及其奇异摄动解

在用渐近方法求解任意旋转薄壳(圆柱壳和球壳除外)自由振动的微分方程组时,在一定的参数范围内,存在转(向)点问题。其中,对于存在唯一简单转点的情况(此时,该转点具有枝点奇性),至今未获解决。本文解决了这一问题。文中仅讨论截顶旋转壳。此时,转点是唯一的奇点。最后,对于两端固定的任意旋转薄壳,给出了频率方程。     

圆柱薄壳在外压作用下屈曲的边界层理论

本文依据文[14]提供的圆柱薄壳屈曲的边界层理论,以挠度为摄动参数,采用奇异摄动方法,研究了固支圆柱薄壳在侧向外压和静水外压作用下的屈曲和后屈曲性态.本文同时考虑了初始几何缺陷的影响.计算结果与实验结果的比较表明二者是一致的.     

旋转壳的一般轴对称问题及积分方程分析*

本文得到了旋转弹性薄壳在一般荷载下轴对称问题的一种简化形式的复变量方程,该方程准确度在薄壳理论误差范围,并消除了经线极值奇点;给出了问题的Voltera积分方程表述及其数值解.     

被动约束层阻尼圆柱壳振动和阻尼分析的一种新矩阵方法

基于线弹性薄壳理论和线粘弹性理论,考虑粘弹性层的剪切耗能作用和各层间的相互作用力,导出了被动约束层阻尼层合圆柱壳在谐激励作用下的一阶常微分矩阵控制方程．然后,借助作者提出的齐次扩容精细积分技术建立了一种新的矩阵方法,并利用该方法研究了层合圆柱壳的振动特性和阻尼特性．该方法与已提出的以位移及其导数作为状态向量的传统传递矩阵法的根本区别在于,控制方程中的状态向量中包含了层合壳的全部位移和整合内力变量,因此,可以方便地适用于各种位移和内力边界条件以及部分环状覆盖约束层阻尼圆柱壳的动态分析．数值算例与解析解和有限元解的结果比较有力说明了该方法的正确性和有效性．     

非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解

该文基于笔者提出的辛叠加方法得到了经典解法难以直接获得的典型非Lévy型正交各向异性开口圆柱壳屈曲问题的解析解.首先，基于Donnell薄壳理论建立了正交各向异性开口圆柱壳屈曲问题的Hamilton体系控制方程，然后将非Lévy型边界下的原问题拆分为两个子问题，在Hamilton体系下利用分离变量和辛本征展开等数学手段对子问题进行求解，最后基于原问题边界条件，通过子问题解的叠加求得原问题的解析解.数值算例表明，辛叠加解析解与有限元数值解结果吻合良好.同时，定量研究了长度和厚度等参数对屈曲载荷的影响.相比于半逆解法等传统解析方法，辛叠加方法基于严格的数学推导，无需假定解的形式，可以获得更多类似问题的解析解.     

加肋圆柱壳在轴压作用下的屈曲和后屈曲

本文讨论完善和非完善的,纵向加肋和正交加肋圆柱壳在轴压作用下的屈曲和后屈曲性态.依据文[1]提供的圆柱薄壳屈曲的边界层理论及其分析方法,给出了加肋圆柱壳在轴压作用下的屈曲和后屈曲理论分析.本文同时讨论肋骨与壳板材料不同时对加肋圆柱壳屈曲和后屈曲性态的影响.     

Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment

Parametric resonance of a functionally graded (FG) cylindrical thin shell with periodic rotating angular speeds subjected to thermal environment is studied in this paper. Taking account of the temperature-dependent properties of the shell, the dynamic equations of a rotating FG cylindrical thin shell based upon Love's thin shell theory are built by Hamilton's principle. The multiple scales method is utilized to obtain the instability boundaries of the problem with the consideration of time-varying rotating angular speeds. It is shown that only the combination instability regions exist for a rotating FG cylindrical thin shell. Moreover, some numerical examples are employed to systematically analyze the effects of constant rotating angular speed, material heterogeneity and thermal effects on vibration characteristics, instability regions and critical rotating speeds of the shell. Of great interest in the process is the combined effect of constant rotating angular speed and temperature on instability regions.     

The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges

The problem of the existence of natural oscillations of a thin elastic orthotropic circular closed cylindrical shell with free and hinge-mounted ends and of an open cylindrical shell with free and hinge-mounted edges, when the two boundary generatrices are hinge-mounted is investigated. Dispersion equations and asymptotic formulae for finding the natural frequencies of possible vibration modes are obtained using the system of equations corresponding to the classical theory of orthotropic cylindrical shells. A mechanism is proposed by means of which the vibrations can be separated into possible types. Approximate values of the dimensionless characteristic of the natural frequency and the attenuation characteristic of the corresponding vibration modes are obtained using the examples of closed and open orthotropic cylindrical shells of different lengths.     

圆柱壳在径向冲击载荷作用下的弹性脉冲屈曲

当圆柱壳承受径向脉冲载荷时，如果其径厚比大于一特定值，圆柱壳将产生弹性动力屈曲．本文根据有关实验结果，假定变形模态，采用Ｌａｇｒａｎｇｅ方法分析了有限长薄圆柱壳（ａ／ｈ＝４８０）在余弦冲击载荷作用下的弹性脉冲动力屈曲．导出了动力屈曲方程组，借助数值方法求解方程，并与有关计算结果进行了比较．     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

The stressed state of a cylindrical shell with a circular neck loaded by internal pressure

We study the stressed state of a thin cylindrical shell with a circular neck loaded by a constant internal pressure. We start from the equations obtained using Reissner's variational principle applying expansions of the components of the stress tensor and the displacement vector with respect to the coordinates along the normal to the base surface of the shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

密封容器组合壳自由振动的精确解

给出了一类密封容器组合壳自由振动问题的精确解,基于Love经典薄壳理论,导出了具有任意经线形状的旋转壳体在轴对称振动时的基本方程,组合壳结构中球壳与柱壳的连接条件是通过连接处的变形连续性和内力平衡关系得出的。问题的数学模型被归结为常微分方程组在球壳和 壳两个区间上的特征值问题。振动模态函数是由Legendre和三角函数构造出来,并且得到了精确的频率方程。所有的计算都是在Maple程序下运行的,无论是精确的符号运算还是具有所需有效数学精度的数值计算,都表明该文所编译的Maple程序是简单而有效的。固有频率的数值结果同文献中有限元法和其它数值方法的结果作了比较。作为一个标准,该文给出的精确解对于检验各种近似方法的精密度是有价值的。     

On the bending and tension of thermoelastic shells undergoing phase transitions

Applying the general non-linear theory of shells undergoing phase transitions, we derive the balance equations along the singular surface curve modelling the phase interface in the shell. From the integral forms of balance laws of linear momentum, angular momentum, and energy as well as the entropy inequality we obtain the local static balance equations along the curvilinear phase interface. We also derive the thermodynamic condition allowing one to determine the interface position on the deformed shell midsurface. The theoretical model is illustrated by the example of thin circular cylindrical shell made of two-phase material subjected to tensile forces and bending couples at the shell boundary. The elastic solution reveals the existence of the hysteresis loop whose size depends upon values of several loading parameters. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

正交异性悬臂柱壳轴对称问题的弱形式解

导出层合柱壳轴对称问题的平衡方程和边界条件的弱形式,提供了方程和边界条件放在一起的算子形式,建立了悬臂柱壳轴对称问题的热应力混合方程,给出了正交异性层合悬臂柱壳在热荷载和机械荷载作用下的弱形式解。本文提出的方法弱化了求解方程和边界条件,化解了问题,具有一般性并便于推广。     

Some features of the natural flexural vibrations of circular rings with initial imperfections

The effect of small initial deviations from an ideal circular shape on the frequencies and modes of the natural oscillations of a thin ring under conditions of plane deformation is investigated. The analysis is based on the equations of motion of the shallow shell theory when the length of the shell tends to infinity. A new approach is proposed to the construction of a finite-dimensional model of a ring in which it is assumed that initial imperfections lead to the interaction of flexural and radial vibrations. A number of assertions are formulated and proved regarding the specific features which accompany the vibrations of an imperfect ring that apparently also have to be taken into account when investigating the dynamic characteristics of thin circular cylindrical shells with initial imperfections.