Steel offshore platforms are typically connected to their foundation pilings by injecting cement grout in the annulus between each pile and its sleeve. In the last few years a good deal of experimental study had contributed to a rational understanding of the design of these grouted connections; however, very few analytical results have accompanied this effort. In the present investigation a mathematical model is developed to simulate the mechanical response of a grouted connection to monotonically increasing axial loads. When shear lugs are included to increase the load capacity of the connection, the local behavior of the grout at the lugs strongly influences the response. A modest experimental program was conducted to study the crushing-type failure of the grout beneath the lugs, and an analytic formulation is proposed which relates the lug load-displacement history to the grout cube strength and volumetric porosity. The predictions of the model are compared with experimental load-deflection curves, and trends resulting from the variation of design parameters are studied. This analysis adequately predicts the measured behavior of grouted connections in many respects, and identifies areas in which further study should be concentrated.

The spherical harmonics method is applied to develop and solve approximate differential equations of radiative transfer in an emitting, absorbing, isotropically scattering and gray medium. Boundary conditions of Marshak type consistent with a particular approximation are derived and used in the solutions. Three types of thermal conditions for the medium are considered: radiative equilibrium, uniform heat generation and a parabolic internal heat generation. Two higher order approximations, P(,3) and P(,5) approximations, are formulated and solved for one-dimensional problems; the medium is bounded by concentric or hollow cylindrical surfaces. Numerical results exhibit great improvement for the P(,3) approximation over the P(,1) approximation and a less rapid improvement for the P(,5) approximation. An axially symmetric problem is also analysed. In this case, only the P(,1) approximation is considered for a gray medium within a finite hollow or finite concentric cylindrical enclosure. The numerical results show that the accuracy of the differential approximation is of the same order for both the axially symmetric and one-dimensional problems under the same geometric and thermal conditions.

An analysis of the melting process for a phase change material in which the solid density is greater than that of the liquid is presented. The mathematical model developed investigates the effect of unequal densities on the shape and location of the solid-liquid interface for a system within a horizontal cylindrical enclosure. This model offers a solution for the coupled conduction and interface balance equations for the three problems of; constant wall temperature, constant heat flux, and constant heat transfer coefficient imposed at the cylinder surface. The numerical method of finite difference is used to solve the system of governing equations. In the solution of the conduction equation, the implicit alternating direction technique is implemented. It is proposed that the heavier solid phase drops to the base of the cylinder as it melts, and maintains a position antisymmetric with respect to the cylindrical axis. To check the validity of this, experimental tests are made in which the interface position is photographed at selected time intervals. These photographs indicate that the mathematical model is physically justified.

In this study the effects of strain-hardening and rate sensitivity in plasticity theory are investigated. Because the method of characteristics cannot be applied to problems involving rate dependent yield conditions (65) therefore a different procedure is developed. In this investigation of large plastic deformation, the displacement field of the wedge indentation and inverted plane strain extrusion problem can be specified by following the trajectory of each element during deformation processes. Therefore, the unit diagram, introduced by Hill, et al (50), and the trajectory equations, derived by Hill (51), are utilized to specify the strain, strain rate fields for wedge indentation and extrusion problem, respectively. The plane strain inverted extrusion with 50% reduction in area is employed in this study because a complete solution has been given by Alexander (3) and the relative motion between the die and billet is prevented. Finite element and finite difference schemes are used to calculate the total work required to produce indentation and extrusion processes; work is then converted to the pressure or force. Atlan and Boulger (4), Adams and Beese (1), and Holzer (54) have presented the empirical equations for describing the strain-hardening and rate dependent characteristics of metals. Due to the simplicity and accuracy power law equations are employed to describe the material properties presented by Dugdale (34, 35) and the author. These material constitutive equations are then used to calculate the stress field which is the basis for the corrections of strain hardening or rate effects for the solutions based on the perfectly plastic theory. The agreement between the published experimental results and the theoretical predictions based on the analyses described in this study indicates the method proposed in this investigation is appropriate in modifying the slip line solutions for rigid, perfectly plastic material when strain hardening and rate effects are involved. Aspects of the theory which demand further investigation in future studies are pointed out.

The P-N approximation is extended to treat nongray radiative transfer problems in planar media. The rectangular model is used to characterize the spectral dependence of the absorption coefficient. The P-1 and P-3 approximation formulations are presented. Solutions are obtained for the cases of radiative equilibrium, internal heat generation and combined conduction and radiation. The effects of the temperature dependence of the absorption coefficient are also investigated. The results show good comparison with the existing exact solutions. As would be expected, the P-3 approximation is superior to the P-1 approximation over the whole range of optical thickness.

The objective of this study was to investigate the physical and biochemical response of platelets subjected to well-defined vaporous cavitation near a decelerating prosthetic surface. Also examined was the hypothesis that two types of shear stress transients, lytic and sublytic, are responsible for platelet lysis, aggregation and functional impairment which has been observed in previous studies of acoustic cavitation. Platelet-rich plasma was exposed to 1000 cycles of low-intensity cavitation in a specially modified apparatus at 23(DEGREES)C for approximately 30 minutes. To determine which of the three known pathways of platelet aggregation might be involved, a small study using 50 (mu)M aspirin was conducted. Particle size data obtained with the Coulter counter indicate that cavitation causes both lysis and aggregation. Biochemical assays indicate that release of granular contents occurs, and that platelet functional capacity is irreversibly damaged after exposure to cavitation. Results of the drug study indicate that aspirin pretreatment of platelets (which inhibits the thromboxane pathway) almost completely abolishes cavitation-induced aggregation and impaired functional capacity. The data from this study are consistent with the dual effect of cavitation postulated by Dube: those platelets sufficiently close to a collapse event are lysed by shear transients, while those somewhat farther away are stimulated to aggregate in response to sublytic shear stresses or to soluble factors leaked from mechanically disrupted platelets and their fragments. The clinical implications of this study are manifold.

In this thesis, we consider two classes of optimal control problems. Problem (P1) involves a functional I, subject to differential constraints and general boundary conditions; it consists of finding the state x(t), the control u(t), and the parameter (pi) so that the functional I is minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem (P2) extends Problem (P1) to include nondifferential constraints to be satisfied everywhere along the interval of integration. A modified quasilinearization algorithm (MQA) is developed. The main property of the algorithm is the descent property in the performance index R. R denotes the cumulative error in the constraints and the optimality conditions. Modified quasilinearization differs from ordinary quasilinearization because of the scaling factor (or stepsize) (alpha) present in the system of variations. The stepsize (alpha) is determined by a one-dimensional search on the performance index R. Since the first variation (delta)R is negative, the decrease in R is guaranteed if (alpha) is sufficiently small. Convergence to the solution is achieved when R becomes smaller than some predetermined value. To start the algorithm, we have to choose some nominal functions x(t), u(t), (pi) and some nominal multipliers (lamda)(t), (rho)(t), (sigma), (mu). In a real problem, we choose the nominal functions based on physical considerations. For the nominal multipliers, no useful guidelines have been available thus far. In this thesis, an auxiliary minimization algorithm (AMA) for the selection of the optimal multipliers is presented. In this auxiliary minimization algorithm, the performance index R is minimized with respect to (lamda)(t), (rho)(t), (sigma), (mu). Since R is quadratically dependent on the multipliers, the resulting variational problem is governed by optimality conditions which are linear; therefore, it can be solved without difficulty. To facilitate the numerical implementation, the interval of integration is normalized to the unit length. Several numerical examples are presented. The numerical results show the feasibility as well as the convergence characteristics of the present algorithms.

The influence of pore fluid flow on the elastic and plastic stresses in a porous material may be determined for a solid body containing a large spherical or cylindrical cavity. A description of the stresses in porous media relies on a separation of the total stress into effective and neutral parts. In the elastic case, the effective stress is that part of the total stress that determines the deformation of the porous solid. The application of Drucker's postulate to a mixture of a solid and a fluid under homogeneous deformation results in a plastic flow rule written in terms of the total stress. The elastic or plastic state of stress in the porous solid surrounding a spherical or cylindrical cavity is significantly affected by a nonuniform pore pressure distribution. For a plastic material obeying a quadratic yield condition, pore fluid flow into a spherical cavity reduces the mean compressive stress in the solid and may lead to cavity expansion. For an elastic material, pore fluid flow into a cylindrical cavity may initiate yielding in the porous solid at an unsupported, fully supported, or partially supported cavity boundary. Application of these analyses to the rock surrounding a perforated casing in a hydrocarbon reservoir gives an estimate for the well pressures that precipitate initial yielding and the production of solid material. Several other problems related to the behavior of rock around a perforated casing may be investigated using elasticity, plasticity, and potential flow theory. An elastic porous cylinder under uniform overburden loading represents more closely the physical boundary conditions in a reservoir than the conventional plane strain analysis. Mechanical loads required for the extrusion of a porous solid are significantly reduced by simultaneous pore fluid flow through the extruded material. Finally conformal mapping provides a simple approximate description of the pore pressure distribution around a slotted casing.

A general model for a multiphase mixture is developed within the framework of the theory of mixtures formulated by BOWEN. Each phase in the mixture is considered to be a mixture itself, composed of multiple substances with independent kinematic, chemical and thermal behaviors. The field equations for the substances in each phase, for the phases in the mixture and for the mixture as a whole are presented. A particular set of constitutive equations is adopted where the volume fractions of the phases in the mixture are treated as internal state variables and required to obey rate type constitutive equations. Certain types of ideal behavior of the mixture are investigated in the limit of a small ratio of the specific area to the volume fraction for a particular phase in the mixture. The concepts of pressure of a fluid phase and capillary pressure between two fluid phases are discussed. In particular, an attempt is made to interpret the capillary pressure defined here in the same manner as in the classical literature on porous media, i.e. as resulting from the surface tension effects in the mixture. A linear version of the general model is derived. Examples of use of the general model are worked in detail for three distinct applications, namely the drying of grains, capillary rise and soil mechanics. In the first application it is shown how equations of balance present in the literature on drying can be obtained from the general model. In the second application the saturation profile of a fluid phase in a porous medium is calculated when static equilibrium is reached in the problem of capillary rise. In particular, circumstances are presented which show that no capillary rise occurs if the jump of the pressure of a fluid phase across the boundaries of a porous medium is zero. The third application contains the derivation of equations of motion customarily used in soil mechanics. The results obtained in this derivation motivate a discussion about TERZAGHI's principle of effective stress, which is then shown to be derivable from the general model.

The system of a poroelastic solid with two pore fluids subject to a certain class of boundary-initial conditions is analyzed. Inertial and capillary effects are retained. A general solution by means of a Green's function is obtained for the system in one space variable. The material properties necessary to valuate the solution are examined, and the solution is applied to the case where there is a sinusoidaly varying boundary condition. Results are shown for the system near resonance.