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。     

圆柱壳开孔的应力分析

本文研究圆柱壳开孔附近的应力分析问题。由于开孔问题的边界形状较为复杂,使用圆柱壳的 Morley 方程进行求解较为困难。本文在进行误差分析的基础上提出修正 Mo-rley 方程,并给出适合于开孔问题边界的一般解。以圆柱壳受轴向拉伸和内压为例分析了开孔附近的应力分布。给出了开孔率为 1/2以下的开孔解,并对 Donnell 方程解的适用范围给予了新的评价。     

轴对称载荷下正交异性圆环壳的一般解

本文导出了在Kirchhoff假设下受轴对称载荷时、材料正交异性的圆环壳的复变量方程,给出了该方程的一般解,该解可用于α=a/R<1,其中a为环壳截面的半径,R为环壳的总体半径,文中并举例说明其应用,结果表明本文所提出的解是很有效的。     

Green函数法在轴对称板壳理论中的应用

本文从轴对称板壳理论的基本方程出发,通过建立Green函数,导出了轴对称线载荷下解的一般表述式,由此可以求出任意轴对称载荷下的解,然后本文分别讨论了圆板和扁球壳受线载问题的解,文中的结果适用于各种边界条件。     

扁壳圆孔附近的应力集中

本文用Hankel变换的方法,将解表成级数的形式,求得了一般扁壳齐次方程的解。由齐次方程的一般解,叠加无孔无限壳的特解,可得扁壳圆孔附近应力集中问题的解。     

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.     

锥壳一般弯曲,稳定和振动问题的位移型统一方程及其应用

1.前言弹性锥壳的一般弯曲、稳定和振动问题,在实际工程中经常遇到,但对其研究基本上限于轴对称问题且都是以挠度函数和应力函数为基本未知量.我们认为,对于锥壳的特征值问题、弹性地基锥壳以及锥壳组合结构,则宜采用锥壳的位移解法.本文作者之一曾对锥壳一般弯曲问题的位移解法进行了系统的研究,以广义超几何函数给出了一般解.在应用文献[1]结果的基础上,本文通过引入一个广义载荷q_n(s,θ,t),得到了以位移函数U(s,θ,t)表示的弹性锥壳一般弯曲、稳定和振动(包括弹性地基影响)问题的统一型式的控制方程.文献[2]用级数给出了锥壳横向自由振动问题的解,但应指出,由于文献[2]中     

基于渐近传递函数解的截锥壳单元

普通截锥壳单元是分析旋转壳结构的常用单元,但应力计算的精度较差;而渐近传递函数解在圆锥壳的应力分析方面具有很高的计算精度。本文针对一般截锥壳单元应力计算精度不高的缺点,将传递函数法与有限元法进行结合,以圆锥壳的渐近传递函数解为插值函数,直接构造了一种高精度的截锥壳单元,该单元位移插值模式满足相容性和完备性要求,并具有力学概念清楚、计算精度高等特点。数值算例表明,采用该单元进行圆锥壳的内力和自由振动     

基于混合变量的脱层壳屈曲分析

提出一种分析脱层圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于一阶剪切理论，通过定义广义位移变量和对应的广义力变量，建立壳的改进的混合变量能量泛函；然后引入条形单元，对混合变量在环向进行离散，从而导出超级壳单元的混合变量能量泛函，由变分原理得到控制方程，采用传递函数方法得到其形式解；最后，将含环向贯穿脱层的复合材料层合壳作为超级壳单元的组合体，得到脱层壳的屈曲方程。给出了脱层大小和深度以及脱层壳边界条件对屈曲载荷的影响。     

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.     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

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锥壳固有振动的精确解

本文从锥壳的Mushtari-Donnell型位移微分方程组出发,通过引入一个位移函数U(s,θ,τ)(在极限情况下,它将退化成对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程。这个方程的解用级数形式给出。     

任意形状薄壳的弹性稳定性方程

本文用张量导出了任意形状薄壳的统一的弹性稳定性方程组,并且在正交曲线坐标系下化成了以张量的物理分量表示的方程,进而可以将正圆锥壳、球壳、圆柱壳、椭球壳、圆板、矩形板等形状的壳和板作为特例来研究。     

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。     

Boundary element method for arbitrary elastic thin shell

In this paper, a boundary element scheme for arbitrary elastic thin shells is elaborated, Based on BEM of 3D linear elasticity and Kirchhoff's hypothesis, boundary integral equations for shells are deduced. As a result, only Kelvin's solution is used, the difficulty in finding a fundamental solution of arbitrary shells is successfully avoided. The project supported by National Natural Science Foundation of China     

A Donnell type theory for finite deflection of stiffened thin conical shells composed of composite materials

A Donnell type theory is developed for finite deflection of closely stiffened truncatedlaminated composite conical shells under arbitrary loads by using the variational calculusand smeared-stiffener theory.The most general bending-stretching coupling and the effectof eccentricity of stiffeners are considered.The equilibrium equations,boundary conditionsand the equation of compatibility are derived.The new equations.of the mixed-type ofstiffened laminated composite conical shells are obtained in terms of the transversedeflection and stress function.The simplified equations are also given for some commonlyencountered cases.     

THE ANALYSIS OF INTERLAMINAR STRESSES FOR COMPOSITE LAMINATED SHALLOW SHELLS WITH INTERFACIAL DAMAGE

Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis and nonlinear theory of shallow shells, considering the damage effect of the interlaminar interface and using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated shallow shells with interfacial damage are derived. Then, considering a simply supported laminated shallow shell with damage and under normal load, an analytical solution is presented by using finite difference method to obtain the interlaminar stresses. Numerical results show, the stiffness of the shell is weakened, greater absolute values of displacements as well as smaller interlaminar stresses are obtained by interfacial damage. When the interfacial damage is further increased, delamination occurs obviously under normal pulling load and pure shear slip occurs under normal pressure load. The portion of the load undertaken by the two sides of the interface is more different. Different mechanical behaviors are shown in both sides of the interface, and the discontinuation of stresses and displacements takes place in the interface.     

Nonlinear vibration of corrugated shallow shells under uniform load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells     

板锥网壳结构的连续化分析

板锥网壳结构是一种受力性能合理，技术经济效益良好的新型空间结构形式。本文将板锥网壳结构连续化为能共同作用的特殊形式的三层薄壳，按薄壳理论建立其位移法和混合法的基本微分方程。通过对微分方程的求解，计算其整体位移及结构内力。该法具有一定的精度，可宏观地了解结构的力学性能，并可用于板锥网壳结构的初步设计。