线载荷作用下圆柱壳环向弯曲变形的研究

通过引入单三角级数形式的位移函数, 求解了法向任意分布载荷作用下对 边简支时圆柱壳的环向弯曲问题, 把线载荷近似为微元矩形区的分布载荷, 推导出了线 载荷作用下圆柱壳的环向弯曲变形计算式, 并给出了线载荷为均布和线性变化时的具体解. 计算表明, 该种边界约束条件下圆柱壳的环向弯曲变形位移分布场的理论计算结果与有限元 分析结果基本吻合.     

正交各向异性功能梯度圆柱壳的应力分析及材料剪裁

假设正交各向异性功能梯度材料的弹性系数沿圆柱壳的径向按照任意连续函数变化,采用应力函数法和加权残值法导出了圆柱壳在非轴对称载荷作用下应力分析的一种新的数值解.建立了圆柱壳内部应力状态给定时材料剪裁问题的基本方程,提出了实现圆柱壳内部一种特殊的应力分布时所需要的材料弹性系数沿径向变化的解析解.通过数值算例验证了本文所导出的应力分析的数值解的正确性和收敛性,分析了弹性系数沿径向的变化对圆柱壳内部应力分布的影响.数值算例还给出了实现圆柱壳内部环向应力和切应力沿径向均匀分布时功能梯度材料的弹性系数沿径向的三种不同变化形式.所得研究结果可为正交各向异性功能梯度材料圆柱壳的设计提供一定的参考,同时材料剪裁的解析结果也可作为其他数值方法计算结果验证的考题.     

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。     

圆柱壳波动振动响应分析

采用Flugge的壳体理论,计算出有阻尼圆柱壳的固有频率并且推导出波动振动响应的模态解,得到了波动共振转速的计算公式。为了提高计算精度,采用高斯迭代法解计算固有频率的超越函数方程;计算了悬臂圆柱壳的固有频率及共波动响应,绘制了振型图,并与NASA试验值作了对比。     

一种特殊梯度分布的功能梯度圆柱壳的二维分析

功能梯度材料是一种新型材料,其结构分析已成为当今力学研究的热点。本文对一种特殊梯度分布的功能梯度材料圆柱壳进行了二维精确分析。从弹性力学平面应变问题的基本方程出发,引入应力函数,导出功能梯度材料圆柱壳受静载作用下的控制微分方程。假设材料的杨氏模量沿半径方向呈幂函数分布,泊松比为常数,利用分离变量法,导出了简支边界情况下功能梯度圆柱壳的精确解。通过算例分析了不同梯度变化时,功能梯度圆柱壳内的应力和位移变化规律。计算结果表明不同梯度分布的圆柱壳结构中的应力、位移沿厚度方向的变化规律是不同的,有时甚至差别很大。因此对于材料性质梯度变化的功能梯度材料圆柱壳,必须针对其自身特点,建立相应的理论分析模型。     

沿圆柱壳母线开有两个圆形切口问题的解析分析

本文给出了圆柱壳母线开有两个圆形切口问题的计算方法。借助Thomson函数的多项式逼近式来计算解中的特殊函数U_(nm)、V_(nm)、P_(nm)、Q_(nm)。利用计算机,仅需几十秒钟便能给出数值计算结果。这与有限元法计算这一问题,耗机时,需大容量计算机,显然本文方法优越。文末将沿圆柱壳母线开有两个圆形切口问题的解与圆柱壳开单圆孔问题的解作了比较。     

变厚度圆柱壳的强度优化设计

对在任意轴对称分布荷载作用下体积保持常数的变厚度圆柱壳的强度优化设计问题进行了研究。当中面形状固定时 ,采用阶梯折算法 ,用传递矩阵导出了变厚度圆柱壳的初参数解的显式表达式。根据Huber-Mises-Hencky强度准则 ,将变厚度圆柱壳的强度优化转化为极小化当量应力的非线性规划问题 ,并采用投影梯度法建立了问题的优化方法。文中对几个典型问题进行了计算。与等厚度圆柱壳相比较 ,优化圆柱壳的最大当量应力得到了显著降低。本文的研究方法和结果可以用于指导大型圆柱壳体的加肋设计     

基于混合变量条形传递函数方法的圆柱壳屈曲分析

提出了一种分析交各向异性圆柱壳和阶梯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Fluegge薄壳理论，通过定义广义位移变量和对应的广义力变量，建立了圆柱壳混合变量能量泛函；然后通过引入条形单元，定义混合状态变量和采用传递函数方法对超级壳单元求解，得到具有多种边界条件圆柱壳屈曲问题的半解析解；最后通过位移连续和力平衡条件，可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。     

水平圆柱薄壳非轴对称载荷作用内力分析

近年来大直径圆柱形薄壳结构烟风煤粉管道的使用呈增长趋势.水平圆柱薄壳在非轴对称载荷作用下的内力常按整体梁理论或壳的无矩理论计算,无法反映载荷作用边界的弯曲应力.本文结合圆柱壳的无矩理论和弯矩理论,得到了简支水平圆柱薄壳在任意高度内部积灰(粉)、风、雪、自重、地震作用下的内力解析解,且理论解与三维有限元分析结果非常接近.研究结果可推广到类似的非轴对称变形圆柱壳,并为水平薄壁圆柱壳结构设计提供依据.     

壳结构的无网格局部Petrov-Galerkin方法

无网格近似函数具有高度光滑性,能够很好的逼近曲壳表面及其位移场。无网格局部Petrov-Galerkin方法不论插值还是离散都不需要单元,是一种真正的无网格方法。本文基于无网格局部Petrov-Galerkin方法的基本原理,采用移动最小二乘插值,利用控制微分方程弱形式,建立了Mindlin壳结构的无网格局部Petrov-Galerkin分析方法,用屋顶壳、受夹圆柱壳、几何非线性圆柱壳作为计算实例分析了求解精度、收敛性和稳定性,并与精确解和有限元计算结果进行了对比,表明该方法计算精度高及收敛性好。     

The Somigliana ring dislocation

A basic elasticity solution applicable to an important class of internal stress problems related, for example, to fiber-matrix composites and spalling of cylindrical coatings is obtained. The basic problem that has been solved is that of the singular stress-displacement field resulting from the introduction of a Somigliana ring dislocation in an isotropic linear elastic solid. The Burgers vector of this dislocation has two components, one being normal to the plane of the circular ring dislocation (Volterra type) and the other being in the radial direction of the ring dislocation everywhere (Somigliana type). The analytical solution, in terms of complete elliptic integrals of the first, second and third kinds, is obtained using the Love stress function and Fourier transform. The results are verified numerically and by examining various limiting cases, including the straight edge dislocation as the radius of the dislocation loop tends to infinity, the orthogonal pair of dipoles as the radius tends to zero, and the Lamé solution of a cylindrical bar and a cylindrical hole in an infinite medium as the axial location of the dislocation tends to minus infinity. The resulting analytical solution is considered as a step towards evaluating both the extended stress field around and interactions among various three-dimensional defects such as cylindrical cracks, fiber-tips and fiber-matrix debonding.     

Electro-elastic analysis of fiber-reinforced multilayered cylindrical composites with integrated piezoelectric actuators

Based on the electro-mechanical coupling theory and the laminate elasticity theory, an electro-elastic solution is obtained for the fiber-reinforced cylindrical composites with integrated piezoelectric actuators when subjected to mechanical and electrical loadings. The hybrid composite is composed of three parts: internal piezoelectric actuator, fiber-reinforced laminated interlayer, and external piezoelectric actuator. The general solution in each piezoelectric smart layer is obtained by introducing three undetermined constants, and the general solutions in the fiber-reinforced laminated interlayer are obtained by means of the state-space method. The mechanical behaviors of the hybrid fiber-reinforced cylindrical composites are investigated. The illustrative examples show that the fiber’s angle, the stacking sequence as well as the applied electric loading strongly affect the physical fields in the fiber-reinforced multilayered cylindrical composites.     

Three-dimensional solution of smart laminated anisotropic circular cylindrical shells with imperfect bonding

This paper presents an exact solution for a simply-supported and laminated anisotropic cylindrical shell strip with imperfect bonding at the off-axis elastic layer interfaces and with attached anisotropic piezoelectric actuator and sensor subjected to transverse loading. In this research, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective discontinuities in displacements. The solution for an elastic (or piezoelectric) layer of the smart laminated cylindrical shell strip is obtained in terms of the six-dimensional (or eight-dimensional) pseudo-Stroh formalism, solution for multilayered system is then derived based on the transfer matrix method. Finally, a numerical example is presented to demonstrate the effect of imperfect interface on the static response of the smart laminated cylindrical shell. The derived solutions can serve as benchmark results to assess various approximate shell theories and numerical methods.     

Analysis of wave propagation in piezoelectric coupled cylinder affected by transverse shear and rotary inertia

In this paper, we examine the wave propagation in a piezoelectric coupled cylindrical shell affected by the shear effect and rotary inertia. A complete mathematical analysis of wave propagation solution in this piezoelectric coupled cylindrical shell is provided. The dispersion characteristics are derived through the solving an eigenvalue problem. Results are validated by the classical solution of a metallic cylinder. Besides providing and discussing the dispersion curves for different wave modes, we also examine the piezoelectric effects on the dispersion curves. Further to the above investigation, comparison of dispersion solutions from different shell theories is also conducted. This work may serve as a benchmark for wave propagation in piezoelectric coupled cylindrical shells.     

Simultaneous extension, inflation, and shear of a cylindrical tube

Summary Rivlin's solution [1] of the title problem for Mooney materials is generalized by dropping the assumption that the hydrostatic pressure is a function of the radial distance only. Due to this generalization the normal tractions over the cylindrical surfaces are not constant as in the previous solution but vary linearly along the axis of the tube. Further, the longitudinal forces per unit length of the deformed tube, over the cylindrical surfaces, are no longer equal. Solutions for a solid cylinder are then deduced from the general solution. The effect of self-weight on the solutions is briefly dealt with.     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法，对无限大含孔曲板弹性波散射及动应力问题进行了分析研究，将经典薄板弯曲波动问题的分析解作为本问题的主项，给出了在稳态波下孔洞附近散射波的零阶渐近解。建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法，利用积分方程法可获得问题的近似分析解。并给出了无限大曲板圆孔附近动应力集中系数的数值结果，且对计算结果进行了分析与讨论。     

Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion

This paper contains an exact solution for the stresses arising from torsion of an elastic circular cylinder with a prolate spheroidal cavity. The solution, which is represented as a combination of a solution that is regular outside the cavity and a solution regular in the solid infinite circular cylinder, is deduced with the aid of a harmonic displacement potential. The two harmonic functions needed are given by simple expressions referred to cylindrical and prolate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between cylindrical and prolate spheroidal harmonics. Numerical results are presented for different shapes and sizes of the cavity, and the ensuing stress distribution in the neighborhood of the cavity is illustrated graphically.     

A THEORETICAL SOLUTION OF CYLINDRICAL SHELLS FOR AXISYMMETRIC PLAIN STRAIN ELASTODYNAMIC PROBLEMS

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Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation

The analytic solution of the problem of forced vibrations of a rigid body with cylindrical surface on a horizontal foundation is given. It is assumed that the dry friction force acts at the point of contact between the cylindrical surface of the body and the foundation and the foundation moves by a harmonic law in the horizontal direction perpendicularly to the cylindrical surface element. The averaging method is used to determine the forced vibration mode near the natural frequency of the body vibrations on the fixed foundation. The results are presented as amplitude-frequency and phase-frequency characteristics.     

轴对称层合圆柱壳混合状态方程的弱形式及其边值问题

从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，在柱坐标系中，导出圆柱壳轴对称问题的弱形式混合状态方程和边界条件，联用状态空间法给出强厚度叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。