This paper presents the first phase in the analysis of the deformation of a shell of revolution when it is being crushed by a rigid wall. In this paper, the analysis accounts for finite deflections and rotations but assumes that the material remains linearly elastic. The load-deflection behavior is obtained for a hemispherical shell, and it shows that the shell cannot collapse with a flat contact region. The conditions for the buckling of the contact region are determined.

The authors have previously shown that a thin, complete spherical shell compressed between two parallel rigid plates deforms initially with the polar portion of the shell flattened against the plates and that at a critical deformation the flat region may buckle into an axisymmetric inward dimple. The present paper presents an analysis of the stresses and deflections produced during axisymmetric postbuckling and determines the deformation states at which the shell may buckle into a nonsymmetric shape. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. An experiment shows that both the primary axisymmetric bifurcation point and the secondary nonsymmetric bifurcation point are stable for a shell with R/h ≃ 40.

A theoretical analysis for the determination of the contact pressure between a uniform elastic spherical shell and a rigid plate is developed. The results are directly applicable to the theory of applanation tonometry which is concerned with the measurement of intraocular pressure. Numerical results are presented for a shell having a radius to thickness ratio of 30.

The behavior of a rigid perfectly plastic spherical shell loaded by means of contact with a flat rigid surface is investigated. The predictions of the analysis are restricted to overall displacements lying between a few thicknesses and about one tenth the shell radius. At each stage of deformation an approximate limit load and corresponding velocity field are found for an assumed deformed shape of the shell, which later is shown to be very close to the calculated deformed shape. A simple formula relating the total axial force on the shell to the displacement of the shell is derived, and its range of validity is investigated. Finally, the results of some static tests of shells are shown to agree favorably with the theory.

A theoretical model of an expanded tube-to-tubesheet joint is developed and examined with the objective to determine the residual stresses in the transition zone, which lies between the expanded and unexpanded regions of the tube. Owing to their effect on the development of stress corrosion cracks, the residual tensile stresses on the surfaces of the tube are of particular interest. A mathematical model that can predict these residual stresses is developed. Results of the model show that the maximum tensile residual stresses are axial and occur on the inside diameter of the expanded tube. It is shown in a parameter study that, for expansions that ensure a leak-tight joint, the maximum residual tensile axial stress on the inside surface of the tube reaches 80–95 percent of the yield stress of the tube, regardless of the geometrical and material parameters of the tube and tubesheet.