Deformation of sand in plane strain and oxisymmetric compression

Small scale laboratory experiments, in which the specimen is considered to represent an element of soil in the soil mass, are essential to the evolution of fundamental theories of mechanical behaviour. In this thesis, plane strain and axisymmetric compression tests, performed on a fine sand, are reported and the results are compared with various theoretical predictions. A new apparatus is described in which cuboidal samples can be tested in either axisymmetric compression or plane strain. The plane strain condition is simulated either by rigid side platens, in the conventional manner, or by flexible side platens which also measure the intermediate principal stress. Close control of the initial porosity of the specimens is achieved by a vibratory method of sample preparation. The strength of sand is higher in plane strain than in axisymmetric compression, and the strains required to mobilize peak strength are much smaller. The difference between plane strain and axisymmetric compression behaviour is attributed to the restrictions on particle movement enforced by the plane strain condition; this results in an increase in the frictional component of shear strength. The stress conditions at failure in plane strain, including the intermediate principal stress, are accurately predicted by a theory based on the stress- dilatancy interpretation of Mohr's circles. Detailed observations of rupture modes are presented and measured rupture plane inclinations are predicted by the stress-dilatancy theory. Although good correlation with the stress-dilatancy theory is obtained during virgin loading, in both axisymmetric compression and plane strain, the stress-dilatancy rule is only obeyed during reloading if the specimen has been unloaded to approximate ambient stress conditions. The shape of the stress-strain curves during pre-peak deformation, in both plane strain and axisymmetric compression, is accurately described bv a combined parabolic-hyperbolic specification.

The structural properties of glassfibre reinforced plastics

The research work described in this thesis is concerned with the development of glassfibre reinforced plastics for structural uses in Civil Engineering construction. The first stage was primarily concerned with the design of GRP lamintes with structura1 properties and method of manufacture suitable for use with relatively large structural components. A cold setting, pressure moulding technique was developed which proved to be efficient in reducing the void content in the composite and minimising the exothermic effect due to curing. The effect of fibre content and fibre arrangement on strength and stiffness of the cornposite was studied and the maximum amount of' fibre content that could be reached by the adopted type of moulding technique was determined. The second stage of the project was concerned with the introduction of steel-wire "sheets" into the GRP cornposites, to take advantage of the high modulus of steel wire to improve the GRP stiffness and to reduce deformation. The experimental observations agreed reasonably well with theoretical predictions in both first and second stages of the work. The third stage was concerned with studying the stability of GRP flat rectangular plates subjected to uniaxial compression or pure shear, to simulate compression flanges or shear webs respectively. The investigation was concentrated on the effect of fibre arrangement in the plate on buckling load. The effect of the introduction of steel-wire sheets on the plate stability in compression was also investigated. The boundary conditions were chosen to be close to those usually assumed in built-up box-sections for both compression flanges and webs. The orthotropic plate and the mid-plane symmetric were used successfully in predicting the buckling load theoretically. In determining the buckling load experimentally, two methods were used. The Southwell plot method and electrical strain gauge method. The latter proved to be more reliable in predicting the buckling load than the former, especially for plates under uniaxial compression. Sample design charts for GRP plates that yield and buckle simultaneously under compression are also presented in the thesis. The final stage of the work dealt with the design and test of GRP beams. The investigation began by finding the optimum cross-section for a GRP beam. The cross-section which was developed was a thin walled corrugated section which showed higher stiffness than other cross-sections for the same cross-sectional area (i.e. box, I, and rectangular sections). A cold setting, hand layings technique was used in manufacturing these beams wbich were of nine types depending on the type of glass reinforcement employed and the arrangement of layers in the beam. The simple bending theory was used in the beam design and proved to be satisfactory in predicting the stresses and deflections. A factor of safety of 4 was chosen for design purposes and considered to be suitable for long term use under static load. Because of its relatively low modulus, GRP beams allowable deflection was limited to 1/120th of the span which was found to be adequate for design purposes. A general discussion of the behaviour of GRP composites and their place relative to the more conventional structural material was also presented in the thesis.

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.