Analysis of thin shells by modifications of thin wall beam theory
Childers, Jim Bob
Austin, Walter J.
Master of Science
The use of thin wall beam theory for the analysis of simply supported shells is described and the necessary modifications to the thin wall beam theory are shown which will make the solution as theoretically correct as the basic classical theories used in the analysis of simply supported shells. A simply supported circular cylindrical shell is analyzed by this method and the results compared with a solution by the classical theory for the same shell which is given in the American Society of Civil Engineers Manual No. 31. The results show close agreement. The analysis is similar to the method of analysis of H. Lundgren. Either a successive corrections methods as used by Lundgren, or a successive approximations procedure, developed in this thesis, may be used. Slow convergence, or even divergence, is obtained in many problems. However, very rapid convergence may be obtained by the use of extrapolation formulas based upon the assumption that in successive cycles the differences between the true solution and the trial solution decrease, or increase, in a geometric ratio. The basic purpose for presenting the "mOdified thin wall beam theory" is not just to simplify the analysis of thin shells from the standpoint of the mathematics involved, but rather to provide an addi-tional method to use in the analysis of shells in cases where the goy- , erning differential equations cannot be solved exactly or even be de- fined in explicit mathematical terms.