Solving Stress Problems for Elastic Systems of Anisotropic Shells of Revolution with Regard for Transverse Shear and Reduction

An approach is proposed for refined solution of stress problems for elastic systems consisting of coaxial shells of revolution. Transverse shear and reduction are taken into account. Multivariant calculations made for orthotropic cylindrical shells with elliptical end-plates allow us to analyze the influence of the semiaxis ratio and intermediate supports on the stress–strain state of the shell systems under consideration     

Analysis of Stresses and Displacements in Orthotropic Noncircular Cylindrical Shells Under Centrifugal Loads

This paper addresses the class of stress–strain problems for thin orthotropic cylindrical shells of arbitrary cross section under centrifugal loads. Separating out the variables for a simply supported shell yields a system of ordinary differential equations for which the boundary-value problem is solved by a stable numerical method. Study is made of the distribution of displacements in shells of elliptical cross section versus the ratio of ellipse exes and the eccentricity of the axis of revolution relative to the geometrical axis of symmetry     

前屈曲应力状态对组合加肋旋转壳失稳临界压力影响的探讨

推导了包含前屈曲弯矩和横剪力的旋转壳弹性稳定性基本方程.运用Riccati传递矩阵法对组合加肋旋转壳算例进行了稳定性分析,并与假设前屈曲状态为薄膜应力状态计算出的失稳临界压力进行了比较.结果表明,前屈曲弯矩和横剪力对组合加肋旋转壳失稳临界压力的影响较小,随着壳板厚度和肋骨尺寸的增大及肋骨间距的缩短,影响略有增大.因而,分析组合加肋旋转壳弹性稳定性时,前屈曲状态采用薄膜应力状态的假设是合理的.     

Determining the Axisymmetric Geometrically Nonlinear Thermoviscoelastoplastic State of Laminated Shells by the Theory of Deformation Along Paths of Small Curvature

A technique is developed for determining the thermoviscoelastoplastic geometrically nonlinear axisymmetric stress–strain state of laminar shells of revolution under loads that induce meridional stress and torsion. The technique is based on the hypotheses of rectilinear element for the whole stack of layers. The relations of the theory of deformations along paths of small curvature are used as equations of state. The solution is reduced to the numerical integration of a system of ordinary differential equations. The technique is tried out by a test example and illustrated by determining the geometrically nonlinear thermoviscoelastoplastic state of a corrugated shell     

内压椭球壳塑性变形的发生部位与扩展过程分析

对内压椭球的就发布作了图形描述，指出椭球壳上一点的应力状态只与壳体的轴比λ和该点在壳体上的位置有关，并进一步分析了内压椭球壳的塑性变形的发生部位及其扩展过程。     

分区样条等参元方法分析加肋轴对称组合壳

本文提出分区样条等参元方法分析加肋轴对称组合壳在静水外压作用下的应力及稳定性。该方法根据母线几何形状、壳板厚度变化及边界约束状况将加肋轴对称组合壳划分为若干个区域，在不同区域采用不同步长的样条等参元进行分析，因而便于对复杂的组合壳进行分析，并可大大减少计算所需自由度数，减少计算工作量，同时计算精度很高，并且易于进行边界约束处理。应用该方法对加肋锥－柱、加肋锥－环－柱组合壳进行了计算，其结果与其它方法计算值及实验值吻合良好。     

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.     

Axisymmetric thermoviscoelastoplastic state of thin laminated shells made of a damageable material

A technique for the determination of the axisymmetric thermoviscoelastoplastic state of laminated thin shells made of a damageable material is developed. The technique is based on the kinematic equations of the theory of thin shells that account for transverse shear strains. The thermoviscoplastic equations, which describe the deformation of a shell element along paths of small curvature, are used as the constitutive equations. The equivalent stress that appears in the kinetic equations of damage and creep is determined from a failure criterion that accounts for the stress mode. The thermoviscoplastic deformation of a two-layer shell that models an element of a rocket engine nozzle is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 87–100, April 2008.     

Determining the stress state of flexible orthotropic shells of revolution in magnetic field

A two-dimensional nonlinear magnetoelastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity. It is assumed that the principal axes of orthotropy are aligned with the coordinate axes and that the orthotropic body is magnetically and electrically linear. The coupled nonlinear differential equations derived describe the stress-strain state of flexible current-carrying orthotropic shells of revolution that have an arbitrarily shaped meridian and orthotropic conductivity and are in nonstationary mechanical and electromagnetic fields. A method to solve this class of problems is proposed Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 64–76, August 2008.     

碟形薄壳的塑性屈曲

本文采用非线性前屈曲一致理论分析均布外压下碟形薄壳的塑性屈曲问题，建立了这类壳体的能量表达式和屈曲方程，给出了简明的计算格式。数值分析结果表明，所导出的算法具有较好的精度，计算过程也简单方便。     

球壳轴对称弯曲问题共轭二阶挠度微分方程

提出球壳轴对称弯曲问题共轭二阶挠度微分方程并给出了初等函数解. 球壳微分方程是薄壳理论三大壳之一旋转壳的典型方程. 共轭二阶挠度微分方程是球 壳中微分方程形式最简单的, 是人们最喜爱的挠度微分方程. 挠度微分方程满足边 界条件非常简单, 使球壳的计算得到很大的简化.     

一般夹层旋转壳在轴对称变形下的大挠度方程

应用最小势能原理建立了具有不同质不等厚薄表层和软夹心的一般夹层旋转壳在轴对称变形下的非线性理论,得到了一组相对简单的夹层壳大挠度方程和边界条件。在分析壳体的变形时,将表层视作薄膜,假设夹心沿厚度方向不可压缩且只能承受横向剪应力,参考面的法线在变形时保持为直线。为便于实际应用,给出几种特殊壳体情况下的大挠度方程。     

A new kind of mixed elements for shells of revolution subjected to arbitrary loads

In this paper a generalized variational principle with two-field variables is derived from the Reissner principle of elasticity in the curvilinear coordinates of a revolution shell, based on which, a new kind of mixed elements with independent transverse rotations is formulated for revolution shells subjected to harmonic external loads. The resultant-stress interpolations are carefully selected so that the shear part of the element stiffness contains the Kirchhoff hypothesis for thin shells and element stiffness matrices have correct ranks. The elements are free from shear locking and spurious kinematic modes. Numerical examples show that the new elements have good generality and high accuracy for thin and moderately-thick revolution shells.     

用样条函数法分析旋转组合壳

本文采用不等距三次Ｂ样条函数对旋转壳在整体坐标下的位移进行插值，给出了周向插值所必需满足的周期性条件，采用罚单元法，给出了组合壳体在整体坐标下的协调关系，与惯用方法相比，这种方法简单明了直观性强，易于接受。文末给出了算例。     

Stress state of a piezoelectric elastic medium with an arbitrarily oriented triaxial ellipsoidal inclusion

We determine the electrostressed state of a piezoceramic medium with an arbitrarily oriented triaxial ellipsoidal inclusion under homogeneous mechanical and electric loads. Use is made of Eshelby’s equivalent inclusion method generalized to the case of a piezoelectric medium. Solving the problem for a spheroidal cavity with the axis of revolution aligned with the polarization axis demonstrates the high efficiency of the approach. A numerical analysis is carried out. The stress distribution along the surface of the arbitrarily oriented triaxial ellipsoidal inclusion is studied     

计算旋转壳振动的一种半解析方法

从锥壳理论出发,导出计算旋转壳自由振动的一阶微分方程组,采用离散变量法进行求解。对于经线出现尖角及具有分支结构的情况,介绍了相应的处理方法。     

Determining the Thermoviscoplastic State of Shells of Revolution Subject to Creep Damage

A technique is developed for determining the thermoviscoplastic state of shells of revolution with allowance for creep damage. The technique is based on the hypotheses of rectilinear element and the theory of deformation along paths of small curvature. The equivalent stress appearing in the kinetic equations of damage and creep is determined using a creep-rupture criterion that accounts for the stress mode and the level of irreversible strains. The technique is tested by determining the thermoviscoplastic state and time to failure of tubular specimens under a tensile force and a torque     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

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GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.