The Analysis of Stresses in a Thin Cylindrical Shell of Circular Cross-Section

In Part I., the equations of equilibrium and expressions for the strain components are set up, for a thin shell of a general shape, by the use of the methods of vector analysis. The simplicity of the vector method of approach to this problem is shown. In Part II., the theory developed in Part I. is particularized for the case of a circular cylindrical shell. Expressions for force components are obtained in terms of the deformation components, and three equations of equilibrium in terms of the three deformation components are derived. In Part III., the expression for strain energy for a circular cylindrical shell is set up, and, by means of the Principle of Virtual Work, equilibrium equations and boundary conditions for a general type of boundary are deduced. The boundary conditions are then particularized for the cases in which the boundaries are parametric curves. In Part IV., an exact solution of the differential equations derived in Parts II. and III. is obtained. This solution is applicable to circular cylindrical shells of the type which occurs in the problem of the design and construction of barrel roofs. In Part V., the exact solution of Part IV. is carried out numerically for two particular cases. In Part VI., an account of several approximate methods of solution of this problem is given. A brief summary of some of the 1iterature on this subject is included. The thesis is concluded with a rather detailed account of several of the methods by which the author attempted to obtain short and approximate solutions of this problem