The modified couple stress functionally graded cylindrical thin shell formulation

In this article, the functionally graded (FG) cylindrical thin shell formulation is developed by using modified couple stress theory. The equations of motion and classical and nonclassical boundary conditions are extracted based on Hamilton's principle. As a special case, the equations of motion in conjunction with the boundary conditions for simply supported FG cylindrical shell are obtained, and then Navier solution procedure is used for analysis free vibration of nano shell. Afterwards, the influences of different parameters like length scale parameter, distribution of FG properties, and length to radius ratio on dimensionless natural frequency are investigated and compared with classical theory.     

The eigenvalue problem for hollow circular cylinders

In three-dimensional elasticity the solution of the biharmonic equation for a hollow circular cylinder can be presented in terms of Bessel functions. If there are no surface tractions on either of the radial faces and no thermal effects, an eigenvalue problem arises. A method of establishing these eigenvalues and tables of them for various types of hollow cylinders are presented. Two special cases are investigated, namely, as the ratio of radii tends to unity, that is, a ‘thin shell’, and as the ratio tends to infinity, which can either be regarded as the inner radius tending to zero for a fixed outer radius or as the outer radius tending to infinity for a fixed inner.The eigenvalues are subsequently used for the calculation of the effect of end loading on a semi-infinite length cylinder. From this a quantitative comparison can be made with thin shell theory in the transition region between thin and thick shells of this type.     

Flutter of delaminated cross-ply laminated cylindrical shells

In this study, the instability of delaminated cross-ply thin laminated cylindrical shells and panels when subjected to supersonic flow parallel to its length edge is investigated. The delamination is parallel to the shell reference and it extends along the entire length of the cylindrical shell. The Love’s shell theory and Von-Karman–Donnell type of kinematic relations along with first-order potential theory have been employed to construct the aeroelastic equations of motion. The effects of several parameters such as length to radius ratio, delamination position, size and thickness on the critical values are discussed in the details. The results indicate that the presence of delamination reduced the overall stiffness of the structure and thereby decreases the flutter critical boundaries.     

Electro-magneto temperature-dependent vibration analysis of functionally graded-carbon nanotube-reinforced piezoelectric Mindlin cylindrical shells resting on a temperature-dependent,orthotropic elastic medium

Vibration smart control analysis of a temperature-dependent functionally graded-carbon nanotube-reinforced piezoelectric cylindrical shell embedded in an orthotropic elastic medium is investigated. The mixture law is used for obtaining the material properties of the structure. The structure is subjected to a 2D magnetic field. Considering the first-order shear deformation theory, the motion equations are obtained. Based on an analytical method and differential quadrature method, the frequency is calculated. The effects of applied voltage, magnetic field, volume percent, and distribution type of carbon nanotubes, temperature, orthotropic elastic medium, and length to radius ratio of the shell are shown on system frequency.     

轴向冲击下薄壁圆柱壳的屈曲行为的实验研究

由于薄壁圆柱壳比厚壁圆柱壳的不均匀性更大，薄壁圆柱壳的轴向动力屈曲比厚壁复杂得多。了解轴向冲击下薄壁圆柱壳的屈曲行为，有助于进行吸能构件设计。介绍了采用落锤实验进行圆柱壳的动力屈曲行为研究中，超薄壁圆柱壳的一些特殊屈曲行为，在实验中观察到随着径厚比的增加，折屈边数有相应增加的趋势，存在过渡区。经吸能特性分析，随着圆柱壳径厚比的增加，平均压垮载荷和一个基本变形单元能量吸收量增加，有效压缩距离和一个基本变形单元的初始长度增加，但有效压缩距离与基本变形单元长度之比保持不变；在壁厚相同的条件下，能量吸收量与圆柱壳半径成正比。     

Three-dimensional elasticity solution for static response of simply supported orthotropic cylindrical shells

This paper deals with the analysis of homogeneous and laminated cylindrical panels made of an orthotropic material, such as the fiber reinforced composites, using the three-dimensional elasticity equations. Solution is obtained by utilizing the assumption that the ratio of the panel thickness to its middle surface radius is negligible as compared to unity. However, it is shown that by sub-dividing the panel thickness into sub-layers of smaller thickness and matching the interface displacement and stress continuity conditions, very accurate results can be obtained. The two-dimensional shell theories have been compared for their accuracy in the light of the present three-dimensional elasticity analysis. Numerical results for some orthotropic panels show that the two-dimensional shell theories are very inaccurate when the thickness to length ratio of the panel is more than 1/20. Also, it is observed that the predictions of the two-dimensional shell theories are relatively poor in the case of two-layered panels as compared to three-layered and homogeneous panels.     

On the validity of nonlinear shear deformation theories for laminated plates and shells

This paper addresses the validity of the recently introduced so-called nonlinear shear deformation theories for laminated composite plates and shells. The finite element method is used to determine the maximum stresses for a wide range of statically loaded plate and shell panels. Various thickness ratios are included. This paper concludes that for the vast majority of composite materials and for moderately thick plates and shells. stresses normally reach the maximum allowable stress before nonlinear terms can become important. This has been demonstrated by showing that for the limiting case of shear deformation theories (in which the minimum span length (or radius) to thickness ratio is 20), the material usually fails before the maximum deflection reaches the magnitude of the thickness (where nonlinear terms start to become significant). Therefore, the nonlinear shear deformation theories, which are considerably more complicated than linear ones, have limited applications.     

A circumferential crack in a cylindrical shell under tension

A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.     

Transmission probability for Knudsen diffusion in a single chamber-throat pore

In this study the transmission probability for Knudsen diffusion through a single chamber-throat pore is simulated by the test-particle Monte Carlo method. The effects of the ratios of the length to the throat radius and the chamber radius to the throat radius on transport properties are investigated. The mechanisms affecting the transmission probability are revealed and discussed in detail. It is found that the transmission probability strongly depends on the ratio of the length to the throat radius of a pore and the transmission probability remarkably decreases with increasing the ratio of the length to throat radius. However, the ratio of the chamber radius to the throat radius has little effect on the transmission probability.     

Investigations on Load Capacity and stability of deformation of rubber cylindrical shells under internal pressure

The paper presents a wide analysis of conditions under which a loss of deformation stability can be observed as well as local bulges form in axially-symmetric (rotational) shells of any length. Analytical relations of the theory of shells were used for the analysis. If the maximum pressure in the shell was exceeded, the deformation process was investigated too. In such a case, strains begin to develop more intensely in the central part of a long cylindrical shell and, owing to that, one or more superimposed bulges (blisters) form. Symmetry of the shell deformation in relation to the centre of its length can be disturbed. A set of algebraic equations was derived for determination of critical pressure and critical strains on the falling part of the relation between pressure and the shell radius. The analysis of deformation stability is of a general type, because the used form of elastic potential of the material is a function characteristic for all the rubber-like materials. The experiments proved the results obtained from the analysis of the assumed theoretical models of shells, which were cylindrical at the beginning.     

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

ABSTRACT

We analyze static infinitesimal deformations of doubly curved shells using a third-order shear and normal deformable theory (TSNDT) and delineate effects of the curvilinear length/thickness ratio, a/h, radius of curvature/curvilinear length, R/a, and the ratio of the two principal radii on through-the-thickness stresses, strain energies of the in-plane and the transverse shear and normal deformations, and strain energies of stretching and bending deformations for loads that include uniform normal tractions on a major surface and equal and opposite tangential tractions on the two major surfaces. In the TSNDT the three displacement components at a point are represented as complete polynomials of degree three in the thickness coordinate. Advantages of the TSNDT include not needing a shear correction factor, allowing stresses for monolithic shells to be computed from the constitutive relation and the shell theory displacements, and considering general tractions on bounding surfaces. For laminated shells we use an equivalent single layer TSNDT and find the in-plane stresses from the constitutive relations and the transverse stresses with a one-step stress recovery scheme. The in-house developed finite element software is first verified by comparing displacements and stresses in the shell computed from it with those from either analytical or numerical solutions of the corresponding 3D problems. The strain energy of a spherical shell is found to approach that of a plate when R/a exceeds 10. For a thick clamped shell of aspect ratio 5 subjected to uniform normal traction on the outer surface, the in-plane and the transverse deformations contribute equally to the total strain energy for R/a greater than 5. However, for a cantilever shell of aspect ratio 5 subjected to equal and opposite uniform tangential tractions on the two major surfaces, the strain energy of in-plane deformations equals 95–98% of the total strain energy. Numerical results presented herein for several problems provide insights into different deformation modes, help designers decide when to consider effects of transverse deformations, and use the TSNDT for optimizing doubly curved shells.     

Review of shell models for contrast agent microbubbles

Micrometer-scale encapsulated gas bubbles, known as ultrasound contrast agents, are used in ultrasound medical diagnostics for enhancing blood-tissue contrast during an ultrasonic examination. They are also employed in therapy as an activator of drug incorporation or extravasation. Adequate modeling of the effect of encapsulation is of primary importance because it is the encapsulating shell that determines many of the functional properties of contrast agents. In this review, existing approaches to the modeling of the radial motion of an encapsulated bubble are discussed and comparative analysis of available shell models is conducted. The capabilities of the shell models are evaluated in the context of recent experimental observations, such as compression-only behavior and the dependence of shell material properties on initial bubble radius. It is shown that for early shell models, the main problem is that the behavior of encapsulation is described by linear elastic and viscous laws, whereas recent experimental data attest to complicated rheological properties inherent in shell materials. Currently, a trend toward models involving nonlinear laws for shell elasticity and viscosity is observed. In particular, nonlinear models have been proposed that allow one to reproduce compression-only behavior. However, the problem of the radius dependence of shell material parameters remains unsolved.     

腹板开洞的工形截面拱的平面内特征值屈曲性能

用有限元模型分析了受径向均布荷载的腹板开洞的工形截面圆弧拱的平面内特征值屈曲性能。选用板壳单元构建了有限元模型,得出了较准确的特征值屈曲荷载和屈曲模态,获得了三种典型的特征值屈曲模态;通过选用一种代表开洞拱效率的特征值屈曲荷载参数,研究了腹板孔洞的半径和间距的优化尺寸。通过一系列拱的数值分析,给出了拱的矢跨比、长细比、孔洞的半径和间距对特征值屈曲荷载的影响,并把这些参数的影响归结为两个参数k和α,给出了这种腹板开洞拱的特征值屈曲荷载的简化计算公式。     

Dynamic response of an FGM cylindrical shell under moving loads

This paper presents an analytical study on the dynamic behavior of the infinitely-long, FGM cylindrical shell subjected to combined action of the axial tension, internal compressive load and ring-shaped compressive pressure with constant velocity. It is assumed that the cylindrical shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The problem is studied on the basis of the theory of vibrations of cylindrical shells. Derived formulas for the maximum static and dynamic displacements, dynamic factors and critical velocity for the FGM cylindrical shell subjected to moving loads. Numerical calculations have been made for fully metal, fully ceramic and FGM (Si₃N₄/SUS304) cylindrical shells. A parametric study is conducted to demonstrate the effects of the material property gradient, the radius to thickness ratio and the velocity of the moving load on the dynamic displacements and dynamic factors of the inner and ring-shaped pressures for FGM cylindrical shells.     

Vibration control of laminated truncated conical shell via magnetostrictive layers

Abstract

In this study feedback control is applied to control the free vibration response of an isotropic truncated conical shell embedded with magnetostrictive layers. Classical shell theory is applied to derive the shell vibration equations. The results are derived based on the Galerkin method and the results are compared with published results and the results of finite element software in order to determine the accuracy of using method. The influence of several parameters such as the thickness of magnetostrictive layers, control gain, length and radius of the large edge of the shell on the vibration suppression of fundamental frequency is determined.     

Nonlinear spatial instability of an annular swirling viscous liquid sheet

Instability and breakup of a viscous annular liquid sheet that is exposed to co-flowing inner and outer gas streams have been investigated using a nonlinear spatial stability analysis. A perturbation expansion method is used with the initial amplitude of the disturbance as the perturbation parameter. The evolution of the two gas–liquid interfaces is tracked until the sheet breaks up and the breakup length is determined. The model is validated by comparison with available experimental data. The effects of liquid swirl strength, gas-to-liquid density ratio, radius of curvature ratio, and liquid viscosity on the sheet instability and breakup have been studied. The results show that at very low values of liquid swirl, it has a stabilizing effect on sheet breakup, but as the swirl strength increases, it strongly destabilizes the sheet. Also, with increasing swirl strength, the occurrence of the large surface deformations moves from the inner interface to the outer interface. The sheet breakup length increases slightly and then decreases rapidly with an increase in liquid swirl strength. Without liquid swirl, the axisymmetric mode is the dominant instability mode. However, with increasing liquid swirl strength, the higher helical modes become dominant and the breakup becomes increasingly asymmetric. When the undisturbed liquid sheet has a purely axial motion, the inner gas stream is more effective in sheet breakup than the outer gas stream. In the presence of liquid swirl, the outer gas stream is more disruptive than the inner gas stream. The breakup length becomes shorter as gas-to-liquid density ratio and the radius of curvature ratio increases. Increase in liquid viscosity tends to slow the disturbance growth and increases the sheet breakup length.     

Crack closure effect on stress intensity factors of an axially and a circumferentially cracked cylindrical shell

Crack-face closure occurs when a shell or plate containing a through-the-thickness crack is subjected to a bending load, which leads to lower stress-intensity factors than those expected from non-closure assumption. This article presents a theoretical analysis of the effect of crack-face closure on the stress intensity factors of an axially and a circumferentially cracked cylindrical shell subjected to bending moment respectively. The presented analysis extends the shallow shell theories of Delale and Erdogan by incorporating the effect of crack-face closure. In keeping consistent with the shear deformation shell theory, crack-face closure is modeled by a line contact at the compressive edges of the crack face. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, i.e. along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. The results show that the distribution of the contact force along the crack is generally nonuniform. Furthermore, it is found that, similar to the case of spherical shells, crack closure may occur over the full length or only some segments of the crack in cylindrical shells, depending on the geometry of the shell and the nature (direction) of applied bending load. Comparisons of the stress intensity factor ratios between the closure solutions and the non-closure solutions reveal that the crack-face closure influences significantly the magnitude of the stress intensity factors and it tends to reduce the maximum stress intensity factor. The closure effect of crack face on the stress intensity factors is highest when the shell radius becomes very large for a given crack length and shell thickness.     

新疆杏核破壳最佳截面的探讨

通过对新疆杏核形状结构的定义,对其结构物理特性进行分析研究,发现其核长、核宽、核厚及其之间不应仅为简单的线性关系,而可近似为关于横、竖、纵三椭圆截面对称的壳体,作为具有椭圆截面的异形薄壳壳体来研究。同时设定该壳体所受破壳压力大小一致、均匀分布,在弯矩公式中引入回转半径,简化计算;进行分析探讨其综合应力和危险截面;通过统计验证,最终得出结论:杏核破壳的最佳截面为杏核所具有的最大应力截面,即椭圆截面的最小回转半径处。     

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

复合材料层合厚圆柱壳高阶理论的改进及其应用

建立了一个改进的LCW型的精化高阶理论,以分析厚圆柱壳的振动。提出u,v为三次多项式、w为二次多项式的位移模式,并利用上、下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,将三阶剪切变形理论的未知数缩减为7个,在此基础上建立了相应的有限元列式。通过一个典型算例,与Soldatos和Lam的高阶剪切变形理论的解析解作了比较,说明笔者的精化高阶理论是可行的,而且具有较高的精确性,比LCW高阶理论更具有实用性。还通过频率参数随长度半径比L/R的变化,说明由于考虑了法向应力和法向应变,本文方法更适用于长度半径比较小的结构。