基于区域分解的环肋圆柱壳-圆锥壳组合结构振动分析

提出了一种区域分解法来分析不同边界条件下环肋骨圆柱壳-圆锥壳组合结构的振动特性.首先把组合壳体分解为自由的圆柱壳、圆锥壳段;视环肋骨为离散元件,根据肋骨与圆柱壳段之间的变形协调条件,将肋骨的动能和应变能附加于圆柱壳段能量泛函中.然后基于分区广义变分和最小二乘加权残值法将所有分区界面的位移协调方程引入到组合壳体的能量泛函中.圆柱壳段、圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开.以自由-自由、自由-固支和固支-固支边界条件的环肋骨组合壳体为例,采用区域分解法分析了其自由振动及在不同激励下的振动响应.通过与有限元软件ANSYS结果进行对比,发现两种方法计算结果非常吻合,验证了区域分解方法的计算精度和高效性.     

舱壁和环肋加强的无限长圆柱壳声弹耦合模型及其声特性

基于最一般情况，借助线弹性薄壳理论，建立了加肋圆柱壳声辐射计算模型，分析模型考虑了环肋和舱壁对圆柱壳的径向、切向、纵向作用力以及纵向弯矩，导出了分析模型的怕弹耦合控制方程，利用傅氏变换和模态展开给出了辐射声压的计算方法，通过大量数值计算，研究了舱壁、环肋刚度与间距以及结构阻尼等因素对辐射声压的影响，分析模型与工程实际比较接近，有较广的应用范围。     

Braking of a Body by a Soft Inflatable Shell on Impact on a Surface

The results of mathematical simulation of a solid velocity damping by a soft skeleton fabric shell filled with air on impact on a hard surface are given. The equations of motion of a falling body and of the loading dynamics of membrane shells and the reinforcement rings in the fabric shell are considered together. Themathematical model and the numerical algorithm for solving the spatial problem of the dynamics of inflation of a shell with reinforcement rings are explicitly realized by the finite difference method. The boundary conditions are posed with regard to the contact of the shell elements in compression near the ring belts. The results of numerical experiments considering the interaction of the falling body with the deformable skeleton shell are discussed. The parameters influencing the process of the body braking on impact on a surface are determined.     

Experimental techniques employed for photoelastic analysis of cellular shells

The search for a shell construction superior to the usual ring-stiffened shells in strength and stability under external pressure with minimum weight has led to consideration of several other shell wall constructions.¹ The cellular-shell structure is one of the most promising designs of shells because of its ability to withstand high-pressure loading while maintaining a high degree of material efficiency. The analytical treatment of cellular shells has been undertaken only recently² and limited experimental study of these shells has been conducted. Thus, for obtaining reliable design formulas for the cellular-shell construction, these studies were undertaken. The cellular-shell construction may be visualized as two concentric thin cylinders spaced radially by a series of thin rings along their common longitudinal axis. The optimum wall thickness, rib thickness and rib spacing for a cellular shell of a given diameter and material which will result in the most efficient utilization of the material when the shell is placed under external pressure is the information required for shell design. The experimental techniques described in this paper have been employed to assist in the determination of the necessary design parameters.     

Superior aeroelastic behaviors of axially functional graded cylindrical shells in supersonic airflow

It is well known that mode localization occurs in the panel flutter structural systems. Therefore, it is reasonable to expect the aeroelastic stability of the structure to be enhanced by changing the geometrical sizes and material properties of the structure along the airflow direction. In this investigation, an axially functionally graded (AFG) cylindrical shell is designed and its super aeroelastic behaviors in supersonic airflow are studied. The enhanced aeroelastic stability and the excellent capability in the passive flutter suppression are achieved by the present AFG design. For the thickness of the cylindrical shell, three types of functions are analyzed. Numerical results show that all these three functions can increase the flutter bound of the cylindrical shell to some extent. It is also noted that in some situations, local mode coalescence happens. In this study, an effective method is proposed to eliminate the local mode coalescence by adding the lumped mass. For the material properties, two groups of functions are considered. It is found that under suitable parameters of the functions, even if the effective stiffness of the whole structural system decreases, the flutter bound of the structure can still be increased due to the AFG design. In addition, the flutter stability of the AFG cylindrical shell is much better than that of the traditional transversely functionally graded shell. The present study is significant in the aeroelastic design of aerospace vehicles.     

基于参数曲面描述的层合壳体结构分析的分片Ritz法

为了对层合壳体结构进行准确和有效的分析，给出了基于分片参数曲面描述的适用于层合壳体结构分析的分片Ritz法。该方法首先将壳体结构的参考曲面进行分片处理，利用参数曲面来描述分片的壳体参考曲面并将分片按照C^0连续性进行拼接。构造壳体参考曲面分片上的具有参数曲面特征的Ritz法的试解函数，并得到相应问题的泛函和控制方程。最后给出了两个典型的层合壳体结构的数值算例，结果表明该方法准确有效。     

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。     

Nonlinear bending response and buckling of ring-stiffened cylindrical shells under pure bending

In this paper, the nonlinear bending response of finite length cylindrical shells with stiffening rings is investigated by using a modified Brazier approach. The basic assumptions for the present study are that the deformation of a shell subjected to pure bending can be simplified into a two-stage process. One is that the shell ovalizes but its axis remains straight; the other is that the bending of the shell is regarded as a beam with nonuniform ovalization. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding critical moment, associated with local buckling, is determined by employing the Seide–Weingarten approximation. Numerical results are shown and compared with those obtained from other methods, which demonstrates that the assumptions used in the present study are reasonable.     

Dispersion Curves for Harmonic Waves Propagating Along the Directrix of a Cylindrical Shell Reinforced with Rings

A method is proposed to study the influence of discrete ribs on the dispersion curves for harmonic waves propagating along the directrix of a simply supported cylindrical shell reinforced with rings. A numerical example is considered to demonstrate the necessity of accounting for this factor, the possibility of using a simplified formulation of the problem, and the necessity of accounting for the asymmetry of rib arrangement about the median surface of the shell     

任意边界条件下环肋圆柱壳振动特性的建模与求解

边界条件对环肋圆柱壳的振动特性有重要影响。基于能量法,把环肋看作离散模型,构建了任意边界条件下加环肋圆柱壳的动力学模型。采用一种改进的傅里叶级数作为位移容许函数,通过瑞利里兹程序求解结构的拉格朗日方程,得到环肋圆柱壳的振动模态和频响特性。通过与实验和有限元(FEM)方法的计算结果进行对比,验证了论文方法的准确性,在此基础上分析了环肋偏心方式、截面尺寸、位置分布和边界弹簧刚度等参数对环肋圆柱壳振动特性的影响。     

Influence of the eccentricity of ribs on the natural frequencies of ribbed cylindrical shells

A polynomial approximation of displacement components is used for the numerical analysis of the natural vibrations of a cylindrical shell reinforced with stringers and rings. It is shown by way of numerical examples that the sign of the eccentricity of ribs has a weak effect on the natural frequencies     

Thermal buckling and free vibration of FG truncated conical shells with stringer and ring stiffeners using differential quadrature method

In this paper, thermal buckling and free vibration of orthogonally stiffened functionally graded truncated conical shells in thermal environment is investigated. Conical shell has been stiffened by rings and stringers, and the influences of the stiffeners are evaluated by the aid of smearing method. The material properties of the structure are assumed to be changed continuously in the thickness direction. First, the initial thermal stresses are obtained accurately by solving the thermoelastic equilibrium equations. Then, by taking into account the initial thermal stresses, equations of motion as well as boundary conditions are obtained, applying the Hamilton’s principle and the first-order shear deformation theory. The natural frequencies of the system have been achieved, solving these governing equations with considering Differential Quadrature Method (DQM). In addition to Eigen frequency analysis, the critical buckling-temperature of the conical shell has been computed. Moreover, the effects of geometrical parameters, number of stiffeners, thermal environment and various boundary conditions on natural frequency of the system have been investigated. Finally, in order to validate the present work, the results are compared with those of other researches available in literature.     

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.     

Boundary Integral Equations Method for the Analysis of Acoustic Scattering from Line-2 Elastic Targets

The prediction of the acoustic scattering from elastic structures is a recurrent problem of practical importance as, for example, in underwater detection and target identification. We aim at setting out the diffraction problem of a transient acoustic wave by an axisymmetric shell composed of a cylinder bounded by hemispherical endcaps, called Line-2. Its time-dependent response is expanded in terms of the resonance modes of the fluid-loaded structure. The latter are well suited when the structure is submerged in a heavy fluid: it is an alternative to modal methods whose expansions as series of natural modes of the in vacuo shell are much better for describing the interaction between a structure and a light fluid. The resonance frequencies are defined as solutions of the nonlinear eigenvalue problem described by the set of homogeneous equations governing the structure displacement coupled to the acoustic radiated pressure. The resonance modes of the coupled system are the corresponding eigenvectors. Both hemisphere and cylinder equations are modeled by the approximation of Donnel and Mushtari which governs thin shells oscillations. The modeling of the sound pressure by a hybrid potential integral representation leads to a system of integro-differential equations defined on the surface of the structure only (boundary integral equations). The unknowns, the hybrid potential density as well as the shell displacement vector, are developed into Fourier series with respect to the natural cylindrical coordinate. Each angular component of the unknown functions is then expanded as series of Legendre polynomials, the coefficients of which are calculated thanks to a Galerkin method derived from the energetic form of the equations. The whole method can also be applied to predict the response of the coupled structure to a harmonic or a random excitation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solution of a Problem of Free Vibrations of a Nonclosed Shell of Revolution under Conditions of its Singular Perturbation

We develop a variational method for solving the spectral problem of free vibrations of a shell of revolution nonclosed in the meridional direction. This method is equally efficient for both medium and small values of the relative thickness of the shell. Coordinate systems of functions are constructed with regard for the structure of formal asymptotic expansions of a fundamental system of solutions of the initial equations. As an example, we calculate frequencies and forms of vibrations of a circular cylindrical shell and show that the algorithm proposed for solving the considered problem guarantees the uniform convergence of solutions and their first three derivatives in the entire region of integration of the equations. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 415–432, July–September, 2005.     

复合材料旋转壳自由振动分析的新方法

提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动. 沿壳体旋转轴线将壳体分解为一些自由的层合壳段, 视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中, 使层合壳的振动分析问题归结为无约束泛函变分问题. 层合壳段位移变量采用Fourier 级数和Chebyshev 多项式展开. 以不同边界条件的层合圆柱壳、圆锥壳及球壳为例, 采用区域分解法分析了其自由振动, 并将计算结果与其他文献值进行了对比. 算例表明, 该方法具有高效率、高精度和收敛性好等优点.     

对膨胀壳体材料失稳的一种简化处理

提出一种简化的塑性失稳处理并被作为高应变率拉伸下材料破坏的粗估判据。这种准则假设局部化失稳在如下条件下发生:应变及应变率硬化率恰被几何及热软化率平衡。指出了经验本构方程及本征本构方程对膨胀断裂应变的影响。通过算例也说明了热软化壳体在内压作用下的破裂过程。     

Buckling of cooling tower shells with ring-stiffeners

With the stability analysis of hyperbolic cooling tower shells with ring-stiffeners, our paper proposes the linear pre-buckling consistent theory. The numerical result shows that this linear analysis method is very effective and practical in engineering, for its precision of computation is up to the level of the nonlinear analysis when it is used for the study of critical loads of the hyperbolic cooling tower which is mainly governed by wind pressure and for the study of the effect of some other factors concerned in design on the buckling of shells. Based on that, we have obtained a series of conclusions which will greatly benefits the engineering design when discussing the effect on the critical wind loading of the shell which is caused by the following factors such as the position of rings, the number of rings and the dead weight.     

一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

Effect of closure of collinear cracks on the stress-strain state and the limiting equilibrium of bent shallow shells

The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.