Date of Award

Spring 1991

Document Type


Degree Name

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


Mechanical and Industrial Engineering

First Advisor

Benedict C. Sun

Second Advisor

Bernard Koplik

Third Advisor

Harry Herman

Fourth Advisor

Rong-Yaw Chen

Fifth Advisor

Harry V. Kountouras


This dissertation studies the local stresses and spring constants of a spherical shell with a nozzle attachment when it is under various loadings, namely radial force, overturning moment, horizontal shear force, and torsional moment. Because of the mathematical difficulty in modeling the nozzle-sphere configuration, particularly with nozzle opening, the finite element method (ANSYS package) is utilized in this study. The model used in this study is a quadrilateral thin shell element model when the γs (spherical radius/thickness) value is larger than 10. Otherwise the isoparametric solid element is used. The resulting stresses are basically biaxial state of stresses. It is observed that the local membrane and bending stresses are produced due to the radial force and the overturning moment as well as the shear force, and the local shear stresses are produced by both the torsional moment and the shear force. These individual stresses are presented as stress factors, which are functions of the dimensionless parameters, β ( radius of nozzle/radius of sphere) and γs. They are reported in graphical plots.

The spring constants considered due to various loadings (Κyfor radial force, ΚϕM for overturnment moment, ΚθΤ, for torsional moment, ΚV for shear force) are also presented in this dissertation. Again, these spring constants are presented in normalized forms which are also functions of β and γs. Throughout the dissertation, the β values considered are from 0.1 to 0.5 while the γs values are from 7 to 100. These values cover the range of the practical applications in pressure vessel design. In this work, the finite element method employed 22 elements along the juncture for the thin shell model, and 9 elements along the juncture with 4 elements across the thickness for the isoparametric model to ensure that the elements are small enough to provide convergence of the results. Stresses obtained from this study are in good agreement with the data extracted from Wichman's paper (W.R.C. bulletin 107,1968) and experimental results from other literature sources. The spring constants are in good agreement with data extracted from Batra & Sun's work and other theoretical results.