Analytical Solution For Cylindrical Thin Shells With Normally Intersecting Nozzles

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.