半圆环截面细环壳的屈曲

本文由Sanders非线性平衡方程和Koiter小应变协调方程推导出细环壳的非线性微分方程和稳定方程。用伽辽金法求解了静水压或边界载荷作用下的半园环截面细环壳的稳定方程。对于不同的边界条件及一系列几何参数,计算得到了临界载荷及屈曲模态。     

细环壳钱伟长方程的精确解

1979年钱伟长对细环壳进行了非常系统的研究,推导出一个细环壳复变量方程,并给出了一个用连分式表达的级数精确解,但没有提及这个级数解是否可以化成为已知的特殊函数.本文利用一个线性变换,把细环壳的钱伟长方程变换成Mathieu方程,用Mathieu函数表示了问题的解,这样就把钱伟长的连分式解与Mathieu函数联系了起来.由于Mathieu函数是已知的特殊函数,这里的工作可为今后有关的细环壳具体计算带来方便.     

环壳屈曲的渐近解

本文提出分析圆环壳屈曲的一种渐近解析方法,由Sanders非线性平衡方程和壳中面变形协调方程推导出静水外压下环壳的稳定方程,求出了方程的渐近解,理论计算的临界压力值与Fishlowitz的实验结果符合良好,并研究了屈曲前非线性变形对临界载荷的影响。     

用复变量表示的环壳几何非线性方程及其摄动解

本文从小应变,中小转动问题的弹性薄壳一般方程出发,导出用复未知函数表示的非线性的环壳轴对称变形的基本方程,并用摄动方法分別求解了整环壳和开口环壳问题.所得到的结果与其他作者用数值方法得到的结果吻合很好。     

圆弧形波纹壳的应力和变形分析

作者由弹性薄壳基本方程出发,略去h/r级小量,得到可用于讨论粗,中,细环壳的齐次方程。B.B.诺沃日洛夫(?)所导出的环壳齐次方程(?) 是作者所导出方程的一个特定结果。本文所得方程在不同特定尺寸比例的情况下,可化为贝赛耳方程,便于工程应用。由文中所得方程,提出了计算不同圆弧大小,对称与不对称圆弧波纹壳的变形与应力的公式。     

关于轴对称薄圆环壳方程级数解的收敛性

轴对称薄圆环壳齐次方程的复量形式为:式中所用符号,其意义与文献[1]中相同。设则式(1)可写为式(3)是一个具有奇点的富克斯型方程。文献[1]对于环壳的五种情况给出了在每个有意义奇点上展开的级数解,并研究了它们的收敛性。本文的目的则是证明在某些情况下的级数解,在环壳的全域上都是收敛的。     

轴对称薄圆环壳方程级数解收敛性的研究

本文研究轴对称薄圆环壳齐次方程级数解的收敛性,证明了每种环壳都有在全域上收敛的级数解。     

具有平直条状几何缺陷圆柱壳的弹塑性应力分析

1 引言在实际工程中,由于制造方面的原因,金属圆柱壳结构常常出现平直条状初始几何缺陷.为了探求几何缺陷对壳体应力分布的影响,本文基于初挠曲理论将初始几何缺陷以初挠度引入基本方程.考虑到壳体结构形状的不规则特点,建立了结点任意分布的广义样条子域位移模式,用内时理论构造壳体本构方程.该理论与经典塑性理论相比,具有方程形式简单、应用方便、收敛速度快等特点.2 基本方程与位移模式本文以圆柱壳的子午线和环线为曲线坐标,其中子午向坐标参数为z,环向坐标为转     

纳米尺度压电球壳的径向自由振动分析

基于非局域弹性理论研究了纳米尺度压电球壳的径向自由振动,为了得到控制方程的解析解忽略了非局域效应对电位移的影响.假设球壳沿径向极化,推导了用径向位移表达的非局域微分控制方程.考虑到尺度效应,应用边界条件得到了球壳径向自由振动的频率方程.利用频率方程本文讨论了自然频率与非局域参数以及半径比之间的关系.根据计算结果,径向振动频率受到非局域效应的显著影响.     

任意形状弹性厚壳的运动方程

本文以位移和转角作为独立变量,运用变分原理推演出任意形状弹性厚壳的运动方程.该方程除了包含通常的薄膜内力项和内矩项外,还反映了横向剪切影响、转动惯性效应和横向挤压影响.本文提供的方程还可以蜕化为由V.Z.Vlasov提出的厚壳方程,I.Mirsky和G.Herrmann提出的厚圆柱壳方程,R.D.Mindlin提出的厚板方程。     

Refined Stress Analysis of Flexible Multilayered Shells of Revolution with Orthotropic Layers of Variable Thickness

A refined theory of flexible layered shells with orthotropic layers of variable thickness is considered. The theory assumes that each layer has a local rotation angle due to lateral shear. This makes it possible to derive equations whose order does not depend on the number of layers. The basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading     

Spline-approximation solution of problems of the statics of orthotropic shallow shells with variable parameters

An approach to the solution of problems of the statics of shallow orthotropic shells is proposed. It is based on reducing a two-dimensional boundary value problem to a one-dimensional one using the spline-collocation method and solution of the problem by the stable numerical method of discrete orthogonalization. Solutions are presented for problems on the stress state of orthotropic shells of double curvature for several values of the elastic constants of the material. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 60–66, July, 2000.     

轴对称正交异性圆环壳的齐次完全渐近解

承受轴对称载荷的正交异性圆环壳的静力分析,归结为求解一非齐次二阶复变量方程.当所含参数μ较大时,常采用渐近解法.因方程含一阶转点,所以求全域一致有效且达到薄壳理论精度的完全渐近解较为困难.过去,齐次解只求到一级近似.本文采用广义Airy函数方法,求出了高级近似.这样,轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开.     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Nonlinear elastic state of thin-walled toroidal shells made of orthotropic composites

A study is made of problems on the statics of circular toroidal shells made of nonlinear elastic orthotropic composites. The study is conducted on the basis of the method of successive approximation, the variational-difference method, and the method of Lagrangian multipliers. The parameters of the circular torus are varied within broad ranges of values in the calculations. Numerical results are presented in the form of tables and graphs and are analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 49–55, December, 1999.     

Non-linear studies of orthotropic shallow spherical shells on elastic foundation

Governing non-linear integro-differential equations for cylindrically orthotropic shallow spherical shells resting on linear Winkler-Pasternak elastic foundations, undergoing moderately large deformations are presented. Three problems, namely, non-linear static deflection response, non-linear dynamic deflection response and dynamic snap-through buckling of orthotropic shells have been investigated. The influences of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply- supported immovable edge conditions accurately. Orthotropy, foundation interaction and material damping play significant roles in improving the load carrying capacity of the shell structures.     

The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied     

The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells

The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell׳s non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge–Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.     

用初参数法解C型波纹管在子午面内整体弯曲

波纹管是一种呈波纹状的管形薄壁结构,作为弹性敏感元件、密封元件和位移补偿器,在现代工业、国防和民用设备中的应用日益广泛.波纹管的计算,特别是在非轴对称受力和变形方面亟待完善.本文讨论了C型波纹管在子午面内整体弯曲的应力分布和端面角位移.从柔性圆环壳在子午面内整体弯曲的复变量方程出发,化边值问题为初值问题,用S.Gill法,得到了该波纹管的数值解,适用于0＜α＜1的范围.通过3个例子,将本文的数值解和已有的细环壳一般解(解析解)作了比较.结果表明,两者基本一致,并且,当环壳较细(α较小)时,两种计算结果更为接近.     

正交异性扁壳的等价关系式和不变量

提出各向同性扁壳比拟法,分析满足条件D_3=D_(12)=(D_1D_2)~(1/2)的正交异性扁壳大挠度弯曲和超屈曲问题,导出了正交异性扁壳与各向同性扁壳之间,两种不同正交异性扁壳之间坐标变量、扁壳厚度和曲率半径、荷载、挠度、转角、弯矩、扭矩、中面应力的等价关系式,还证明了等价正交异性扁壳的几个等价不变量。