Thin Shell Theory Solutions Of Two Normally Intersecting Cylindrical Shells For Large Diameter Ratio And Its Verification

Intersecting cylinders are widely used in industry. Due to the importance of such structures, there is a great need for a reliable analysis method based on the theory of thin shells. This kind of analytical solutions have been difficult to obtain because of the complicated geometry. In this thesis, the thin shell theory solutions of such structures subjected to internal pressure and several kinds of external loading have been given. These solutions are applicable up to diameter ratio ρ₀≤0 .8Several distinct cylindrical shell equations with the same error as the theory of thin shells are used. Polar coordinate system (α,β) on the surfaces of the cylindrical shell is taken to solve the problems of shells with cutout. The general solution can be got by solving modified Morley equation in (α,β) system. The particular solution is obtained in (ζ,φ) system by using Flugge equation, and then transformed into (α,β) system. The displacement function is used for the solution for nozzles with curved end. The boundary forces and displacments in both cylinder and nozzle are all transformed from (α,β) on the cylinder or (ζ,θ) on the nozzle into global coordinates (ρ,θ,z). All of them 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. According to the continuity conditions which should be satisfied by general forces and displacements in the shell and the nozzle on the intersecting curve, the equations for all harmonic can be obtained.Experimental research has been carried out on two models (r/R=0.66, 0.75). A complete elastic stress analysis has been made for the models subjected to internal pressure p and out of plane bending M_xn The test result are in good agreement with both the results of thin theory and those of 3-D finite element method.The analytical solution of two normally intersecting cylindrical shells with large r/R presented by this thesis is successful. The results have been verified by a number of experimental results and FEM results. A design procedure of two normally intersecting cylindrical shells subjected to internal pressure p based on the thin shell theory solutions has been given. This procedure is reasonable and easy to be used, and has been adopted by the Chinese Pressure Vessel Code-Design by Analysis (JB 4732).