Analytical solution for cylindrical thin shells with normally intersecting nozzles due to external moments on the ends of shells

Abstract

The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio(ρ 0 «0. 8). Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable toρ 0(R/T)1/2 »1, is used for the analysis of the shell with cutout. The solution in terms of displacement function for the nozzle with a nonplanar 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 (ζ, θ) on the nozzle into three-di-mensional cylindrical coordinates(ρ,θ, z). Their expressions on the intersecting curve are periodic functions ofθ 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.