Dissertations

Dissertation

Spring 5-31-1977

Degree Name

Doctor of Engineering Science in Civil Engineering

Department

Civil and Environmental Engineering

William J. Stack

Raj P. Khera

Gideon Peyser

R. John Craig

Franklin Salek

Abstract

The work presented in this dissertation is devoted to the analysis of nonlinear buckling of thin cylindrical shells with imperfections. The nonlinearity of the problem treated in this dissertation is that associated with large displacements in the linear elastic range. The method used is not restricted by the magnitude of the displacements provided that the strains do not exceed the limit of proportionality.

Thus, based upon the large deflection theory, cylindrical shell panel is investigated for buckling under the action of uniform external pressure. Certain higher order infinitesimal terms which are usually neglected in the shallow shell theories, have been retained in the present paper to study their effect on buckling, and also to test the validity of shallow shell assumptions. The shell is clamped at the two longitudinal edges while it is simply supported at the transverse edges.

The general nonlinear theory with respect to strains is applied to deep shells to formulate the set of equations, which are nonlinear partial differential equations. These nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations by applying the Kantorovitch method.

Further these differential equations are reduced to a set of nonlinear finite difference equations by conventional methods in terms of central differences. These nonlinear finite difference equations are linearized by incremental method, and transformed into a suitable matrix form.

An iterative procedure to solve this system of incremental equations in the matrix form is developed. A computer program is written in Fortran IV to solve these equations, following the interative procedure.

The following different cases of buckling have been investigated in this paper.

a) Symmetric buckling of deep shells.

b) Symmetric buckling of shallow shells.

c) The effect of initial imperfections on the buckling loads.

d) Asymmetric buckling as a bifurcational buckling of symmetric case.

The findings of this study may be stated as follows:

From buckling point of view, deep shells are stronger than shallow shells.

When only shallow shell parameters are employed, neglecting deep shell parameters, the corresponding deflection caused by an increment in load tends to be smaller. And therefore the buckling load when shallow shell parameters are employed tends to be higher.

In case of shallower shells, though, no appreciable difference in the unit load is found by employing deep shell parameters.

Initial imperfections if present even to a minute degree can affect the buckling load significantly. Also, this paper establishes the validity of certain assumptions of shallow shell theory for the first time.

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