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Theoretical and experimental work on thin shallow hyperbolic paraboloid shells are reviewed and discussed. In dealing with the hyperbolic paraboloid shell supported along straight line generators, and for which no known direct solution exists, the homogeneous form of the differential equation involved is studied assuming the existence of the typical edge effect phenomenon in which disturbances from an edge may be considered independently of those emanating from other edges. In particular, it is shown that the approximations introduced by Loa are really equivalent to the Scherer Type approximation. An account is given of tests carried out, within the elastic range and to failure, on a reinforced cement mortar hyperbolic paraboloid shell supported on straight line generators. The behaviour of the shell was studied when the latter was subjected to certain types of edge loading, to uniform loading over half of the shell, and to uniform loading over the entire shell. In the tests involving the latter type of loading, the stiffnesses of the tie and edge beam were varied. Comparisons are made between theoretical and experimental results. The The existing approximate methods of analysis failed to predict the behaviour of the shell tested. The shell behaviour is compared with that of a flat plate with different types of boundary conditions. With rigid edge beams, the deflections in the central region of the shell were reasonably predicted by regarding the shell as a flat plate with clamped edges. Attempts are made to separate the edge beam and tie bar influences. It is shown that the stiffer edge beam favourably affects the stress distribution and deflections throughout the shell, although there is not much to be gained by the use of a very rigid edge beam. The results reveal that torsional stiffness of the edge beam i of little importance but this may have been attributable to the manner in which the detachable edge beams were fixed at the edges.

The flow properties of several polymer melts have been investigated in steady shear flow and when shear flow was applied or removed. The results have been compared with the predictions of three rheological equations of state which have been proposed to describe the behaviour of elastic fluids. In steady shear flow the viscosity eta and the normal stress differences alpha1 and alpha2 have been determined for two polyisobutylenes (Vistanex LM-MH and Vistanex LM-MS) and a depolymerised natural rubber (Lorival R25). There is some disagreement about the magnitude of alpha2 and the main objective was to determine if it was zero or not. The data were obtained from total thrust and torque measurements in a Weissenberg Rheogoniometer using cone-plate and parallel plate geometries. For the polyisobutylenes alpha2 was negative but small compared with alpha1; the ratio |alpha[2]/alpha[1]| was less than 0.3. The Lorival R25 data were not inconsistent with these conclusions. Attempts have been made to measure stress relaxation on the cessation of shear flow and stress growth at the onset of shear flow. The measurements were carried out on the Weissenberg Rheogoniometer. For Vistanex LM-MH the form of the relaxation depended on the stiffness of the torque measuring system. This is shown to be due to illdefined boundary conditions for transient measurements with high viscosity fluids. However reliable data could be obtained on the lower viscosity polyisobutylene (Vistanex LM-MS) provided a stiff torsion bar was used. For this material the shear stress relaxation and growth were more rapid as the shear rate increased. The normal stress transient measurements were unreliable but it appeared that relaxation and growth times for p[21] were less than for alpha1. A cone-plate rheometer, which can measure the steady shear viscosity and elastic recovery of polymer melts, is described. The form of the recovery curve can also be obtained. A constant shear stress is applied to the sample and the resultant rotation and recovery when the stress is removed are measured by a capacitance technique. Data obtained on the two polyisobutylenes are reported. It is shown that the Weissenberg and Lodge theories of elastic recovery are not valid. Die swell measurements have been carried out on an elastic fluid (Lorival R25) and a high viscosity Newtonian fluid (Paralac 385, a modified alkyd resin). The measurements were made on a capillary rheometer at shear rates below 1 sec[-1]. Both fluids showed a significant amount of die swell. For the Newtonian fluid the average die swell was 13.5% and independent of the capillary radius, viscosity and volume rate of flow. Die swell increased with shear rate for the elastic fluid but did not depend on the capillary radius, and at low shear rates was asymptotic to the Newtonian value. It is shown that the momentum balance theory of die swell is not appropriate to high viscosity fluids of any type. The data obtained on the two polyisobutylenes have been compared with the predictions of the WJFLMB, OWFS and Kaye integral rheological equations of state. The OWFS theory is not an appropriate model for high viscosity elastic fluids such as polymer melts. It predicts elastic recovery values which are much too high and in stress growth experiments it is incapable of predicting stress overshoot which has been reported in the literature. The agreement between theory and experiment for the WJFLMB and Kaye models is reasonable for steady shear flow, stress relaxation, stress growth and total elastic recovery. However these theories do not describe the form of the recovery curve well. Both the WJFLMB and Kaye models predict stress overshoot in stress growth experiments at high shear rates. There is some evidence that the Kaye theory might be a more useful model than the WJFLMB theory in some applications.

Optical methods have been used to examine the topography of the small erosion areas that are produced at the cathode and anode due to single, short duration, high current discharges. A plane parallel electrode arrangement has been used with gap separation of between one and two millimetres or less, and allowing electrical breakdown to occur under nearly uniform field conditions. The electrode erosion has been studied for discharges passed in oil dielectric, and also hydrogen, air, and argon at atmospheric pressure. High and low melting point metal electrodes have been used in the investigation. Constant current discharges have been produced by using pulse forming networks, but for slower rates of current rise in the external circuit, a single section condenser-inductance network was used. Some of the erosion areas have been suitable for examination by Fizeau reflexion interferometry, and the light profile techniques, which made possible an estimation of the volume of material lost from these areas. Observations were made using reflexion microscopy, which also served as a means for making erosion measurements. The results of the measurements of erosion loss at the anode for discharges in oil and gases, indicate that the electrode material cannot have been removed by a thermal evaporation process alone. From observations on the topography of the anode erosion areas, it would appear that the molten metal within the area is drawn into one or more peaks, and metal is lost from the area by some mechanical force action. The erosion areas at the lower melting point electrodes for discharges in oil and gas dielectric appear similar, but usually more intensive melting is produced for the discharges in oil. The molten multiple marks left on the anode and cathode, have been discussed in the light of recent research by other workers, studying the luminous areas formed at the electrodes during the discharge.