The Stress Analysis Of Cylindrical Shells With Nozzles Having A Large Ratio Of Radii

In this paper a stress analysis method of cylindrical shells with nozzles having a large ρ₀ , the ratio of radii of the two cylindrical shells, has been developed based on the theory of thin shells. When the previous approximate analysis methods for the small openings are used in the case of large openings, the following three questions have been analyzed in this paper:1. Which kind of cylindrical shell equations should be used,2. The geometric description of the intersection curve of two cylindrical shells and the coordinate systems used should be convenient for solution and have enough accuracy,3. The continuity conditions of generalized forces and displacements at the intersection curve of two cylindrical shells should have enough accuracy.In this paper the intensity of errors of previous approximate methods are analyzed quantitatively. The conclusions are as follows: the error caused by approximate continuity conditions has order 0( ρ₀);the error caused by approximate geometric description of the intersection curve has order 0(ρ₀²);and when ρ₀ ≤0.7, the error caused by using Donnell shallow shell equation is very small.The questions mentioned above have been solved in this paper by following methods:1. The asymptotic expanding method with small parameter p. has been used. Three coordinate systems used in this paper are: 3-dimensional cylindrical coordinates, (ρ ,θ ,z), polar coordinates, ( α , β ), in the middle surface of vessel and Cartesian coordinates, (θ,ζ), in the middle surface of nozzle. The coordinate transformation coefficients, the expression of intersection curve in coordinates ( α , β ) and the expression of height difference of intersection curve on the middle surface of nozzle are all expanded in terms of powers of ρ₀.2. The solutions of vessel are obtained by Morley's equation modificated for the complex stress-displacement function and expressed as the double series of Bessel-Henkel functions and trigonometric functions;the displacement function solutions given by Vlasov are used for obtaining the solutions of nozzle.3. The expressions of generalized forces and displacements at the boundary of hole on vessel in coordinates (α_r, β ) are transformed to that in coordinates (ρ₀, θ ). The displacement...