## Dissertations

Dissertation

Fall 1-31-1997

#### Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

#### Department

Mechanical Engineering

Benedict C. Sun

Bernard Koplik

Rong-Yaw Chen

John Tavantzis

Zhiming Ji

#### Abstract

Since several decades ago, many authors have published their research results about local stress distributions of shells and shell-nozzles both analytically and numerically. However, there has not been a published paper, which deals with analytical solutions of cylindrical shell and oblique nozzle, even though in the case of openings formed by intersection of a cylindrical shell and an oblique nozzle.

A comprehensive analytical study of local stress factors at the area of openings formed by intersection of a cylindrical shell and an oblique nozzle under internal pressure is presented in this dissertation.

By means of traditional approach in theory of elasticity, geometric equations, physical equations and equilibrium equations are derived and then simplified under the conditions of thin shell and internal pressure. The concepts of normalized forces and moments in the mid-surface are established to make all governing partial differential equations mathematically solvable.

This dissertation mathematically determines the exact geometric description of intersection formed by a cylindrical shell and an oblique nozzle. This result is not only the boundary conditions of the present study, but also a basis for analytical solutions of intersection formed by a cylindrical shell and an elliptical nozzle in the future.

Introducing the displacement function, this study combines the geometric equations, physical equations, equilibrium equations and boundary conditions to obtain the analytical solutions.

Finally, this dissertation calculates the results of five cases, which correspond to the intersection angles of 90°, 75°, 60°, 45° and 30° respectively. The results are presented in the forms of stress concentration factors (SCF) and described in the fourteen figures. The typical calculations indicate:

1. When the intersection angle is 90°, the stress results are in good agreement with the existing literature .
2. At the neighborhood of point A, both of circumferential stresses and longitudinal stresses increase as the intersection angle decreases from 90° to 30°, and the closer to the 30°, the faster the increase becomes. Therefore, among all angles from 90° to 30°, the intersection angle 90° has the least local stresses.
3. At the neighborhood of point C, when the intersection angle varies from 90° to 30°, circumferential stresses remain virtually constant, however, longitudinal stresses are compressive and they remain constant on the outside surface, but, increase on the inside surfaces.
4. After consideration of all influential factors, it is suggested that the intersection angles from 90° to 60° should be the best choices. The intersection angles from 60° to 45° can be selected if the internal pressure is not too high. The intersection angles less than 45° should be avoided as practical as possible.

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