【作者】 王和慧；

【导师】 徐秉业； 薛明德；

【作者基本信息】 清华大学 ， 固体力学， 1999， 博士

【摘要】 带径向接管的圆柱壳是压力容器与管道工业中量大面广的重要构件之一。由于有限元数值解的局限性以及薄壳理论解在数学分析上的困难，从五十年代至今，寻求某种基于理论解的分析设计规范一直都是各国压力容器界与力学界所共同瞩目与期待解决的重要课题。继前人的工作，本文在主壳外力矩及热载荷的薄壳理论解方面获得了有意义的研究结果与进展。 本文系统地总结并导出热弹性圆柱薄壳的基本方程与定解方程。在此基础上，采用混合解法，建立了具有薄壳理论精度量级O（T／R）的复位移应力函数—复热载形式的圆柱薄壳复热弹性混合型方程，并将其转换为便于求解的极坐标形式，为精确求解大开孔圆柱壳的热弹性薄壳理论解确定了理论基础。 本文将修正的Morley方程的具有两个对称面的单—工况解扩展到更为复杂的可以包括对称与反对称不同组合的多种工况解。在主壳展开面极坐标（α，β）系中给出了大开孔圆柱壳在受端部力矩作用时的齐次解，既保持了薄壳理论的精度量级，又不受开孔率的限制；选择主坐标（ξ，φ）系中的薄膜解作为主壳特解。利用Goldenveizer提出的位移函数解，在支管展开面主坐标（θ，ζ）系中求得了非平齐端头支管的齐次解。主壳与支管的交贯线厂上各自的边界广义力和位移在分别由（α，β）、（θ，ζ）系转换到总体柱坐标系（ρ，θ，Ζ）后均为θ的周期函数，从而可将它们分别展成Fourier级数，各谐的Fourier系数可由数值积分获得，最后由连续条件确定待定复系数，得到整体结构的薄壳理论解。本文正确给出且程序实现了可适用于大开孔率（ρ₀≤0.8）的带径向接管的圆柱壳在受端部三种力矩作用时的薄壳理论解，经前人的实验和三维有限元计算结果的检验，证明本文解及其计算程序是可靠的。在此基础上，本文详细给出Tresca应力强度随三通结构各几何参数的变化与分布规律，并给出可直接适用于工程设计的应力集中系数曲线，其适用范围达到开孔率为0.8。 本文基于三维稳态热传导方程与温度场沿薄壳厚度的线性化假定，导出适合于薄壳的复形式稳态热传导方程。进而利用它将极坐标（α，β）系下的复热弹性混合型方程的右端温差热载荷项转换成薄壳内外壁的复表面热流，以便于方程求解。在对复热弹性混合型方程按β进行Fourier展开后，发现关于α的三个复常微更多还原

【Abstract】 Cylindrical thin shells with normally intersecting nozzles subjected to internal pressure, external moments and thermal loads are of common occurrence and great importance in the pressure vessel and piping industry. It is well known that there is great difficulty in the stress analysis by the thin shell analytical solution of this problem because of its complication in mathematics. Since 1950?s, a design code based on thin shell analytical solutions has still been expected by many pressure vessel organizations and researchers. Based on the previous work on internal pressure, the thin shell analytical solution including the cases of thermal loads and external moments on the ends of main shells with large diameter ratios are successfully acquired in the present dissertation.The basic equations of thermoelastic cylindrical thin shells are deduced and discussed. By using a hybrid method, a complex thermoelastic thin shell equation with the accuracy of thin shell theory 0（T/R） which contains the variable of the complex displacement stress functions is established, and its corresponding form in the polar coordinates（α,β） is also given. It is called by the name of the complex thermoelastic hybrid cylindrical shell equation（CTHCSE） in the present thesis.The solutions of the modified Morley equation which is applicable to the cases of large diameter ratios are developed from the symmetrical case into the asymmetrical cases. The solution in terms of displacement function for the nozzle with a non-planar end is based on the Goldenveizer equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates （α,β） on the shell, or Gaussian coordinates （θ,ζ） on the nozzle into three-dimensional cylindrical coordinates（ρ,θ,z）. Their expressions on the intersecting curve are periodic functions of θ and expanded in Fourier series. Every harmonic of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature. The results obtained are in agreement with those from the three-dimensional finite element method and experiments. A set of design diagrams which can be applied to ρ₀≤0.8 are given by the present analytical method.更多还原