Instability of composite shells of revolution

Abstract

This thesis deals with the analytical and experimental studies of the instability of geometrically composite shells of revolution. Different axisymmetric composite shells under uniform external pressure are studied analytically for their use as end-closures of submarine hulls or of pressure vessels. The composite shells studied here are (a) cap:cone end-closures (b) cup-cylinder end-closures and (c) dome-cylinder end-closures. In the cap-cone endclosures a spherical cap is attached to the smaller end of a conical frustum in such a way that the tangent at their junction maintains continuity. In the cup-cylinder end-closure, a spherical cup is attached at an end of a cylinder and in the dome-cylinder end-closure, a spherical dome replaces the spherical cup of the cup-cylinder end-closure. A computer program is developed and enclosed here in the appencjix which can find both axisymmetric and asymmetric buckling load of shells of revolution under uniform external pressure. For the study of axisymmetric buckling, the program uses Reissner's theory of large deflection and interprets instability based on the two criteria of Thompson. The non-linear axisymmetric solutions of Reissner's theory are considered as prebuckling solution for asymmetric instability analysis based on eigen-value interpretation. Axisymmetric analyses of the cap-cone end-closure for varying cone height, cone angle (\II) and thickness ratio show that increasing the cone angle or thickness ratio leads to decreasing the buckling load. In the case of varying height, the buckling load remains almost the same over a wide range of height and starts decreasing at a certain small height reaching a minimum at zero height when it is a simple spherical cap. The axisymmetric buckling load for cup-cylinder end-closures is found to be much higher than that of the dome-cylinder for the same thickness ratio, cylinder height and cup or dome angle. In the case of dome-cylinder end-closures, it is found that its buckling load is even lower than that of the cylinder. Circumferential stresses at the junction of a cup-cylinder end-closure at the axisymmetric critical load is.;so high that the failure of this end-closure would always be either due to yielding or asymmetric buckling. A new experimental technique has also been developed for testing the instability of axisymmetric shells. Electrodeposited cap-cone model specimens are tested for instability using this experimental technique. Results of the experiment show that the cap-cone models of tip ratio, r/R, about 0.80 can sustain the highest load and is least imperfection sensitive. The conical portion of the cap-cone end-closures were found to buckle asymmetrically with a number of circumferential lobes. Comparison of the analytical buckling load for both the axisymmetric as well as the asymmetric buckling with the experimental results show that the experimental results are in good agreement with asymmetric buckling load but the axisymmetric buckling loads are found to be about 10 to 15 times higher than the experimental results. At zero cone height, when it is a pure spherical.cap with compatible angle (180°-11'),axisymmetric analytical results are found to agree with the experimental results. It is also found that the spherical cap models are highly sensitive to imperfections.