Closed form solutions are given of the characteristic equation of the Hiigge theory with circumferential series expansion. Specialisations to simplified theories are shown.

The elastic instability of a complete spherical shell under uniform external pressure is studied experimentally and theoretically. The premature snapping of a thin elastic shell, made of polyvinyl chloride, is seen to be classical in nature. The experimental maximum pressure and pre-snapping bending deformation are correlated with the theoretical behaviour of an initially imperfect shell. The large deflection behaviour of a perfect shell is assessed experimentally, and the stable post-buckling states are observed to be rotationally symmetric. A fairly precise theoretical analysis of these states is performed, the use of a high-speed digital computer allowing a considerable advance over previous treatments. The experimental and theoretical post-buckling curves are in good agreement, yielding the first detailed correlation of post-snapping equilibrium states in the field of shell instability.

During thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by Biot’s variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved (i) by digital computer, (ii) by transformation to a Riccati equation soluble in terms of Bessel functions, or (iii) by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain and strain rate, or, equivalently, over ranges of temperature, edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.

The fatigue properties of unmachined extrusions of high-strength aluminium-copper alloys are known to be lower than those of conventional fully-machined test pieces. Work described in this note has shown that the removal of a layer of metal 0·025 in. thick from the surface of B.S. L65-type extrusions results in an increase in fatigue properties to values approaching those obtained from the conventional laboratory test pieces. Because the removal of material from the surface is not always a practical proposition, other methods of improving strength have been examined and the effect of surface compressive stresses has been shown to be beneficial. Sufficient compressive stress can be induced by surface-rolling to increase the fatigue properties to those of conventional specimens, but this method can only be easily applied to round sections and it is suggested that shot-peening or vapour-blasting could be used for more complicated sections.

The fatigue life of a pin-jointed connection can be optimised by using a moderately high degree of interference between the loading pin and plate. Where a joint has to be assembled in confined conditions, difficulty may be experienced in inserting the interference-fit pin and one possible solution is to use a pre-assembled interference-fit bush in the plate, leaving only a light interference-fit pin to be pressed in on assembly of the joint. It is shown that a relatively thick bush of diametral ratio 4/3 will give a reduction in shear stress concentration factor for the plate comparable with that obtained with a solid pin, but that maximum benefit is not obtained with a thinner bush of diametral ratio 8/7. Where thin bushes are essential in order to maintain the ultimate tensile and fatigue strengths of the plate and /or the ultimate and fatigue strengths of the pin, the shear stress concentration factor for the plate is reduced as the modular ratio of bush to plate is increased and as the interference fit of the loading pin in the bush is increased.

Curie and Skan have modified the approximate methods of Thwaites and Stratford to predict separation properties of laminar boundary layers for flow over an impermeable surface. The work of Curie and Skan has been extended by Curle to include the estimation of laminar skin friction for the whole flow. The purpose of the following note is to compare the approximate methods of Curie and Skan and Curle with the numerical results given by the author for flow past a circular cylinder. It is found that there is remarkable agreement between these approximate methods and the exact numerical solutions. This indicates that these methods can be used widely, both on account of their simplicity and their accuracy.