Browsing by Author "Bowen, Ray M."
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Item Inertia effects in consolidation problems(1981) Lockett, Robert R.; Bowen, Ray M.; Wang, C. C.; Wilhoit, James C.The dynamic behavior of a chemically inert, isothermal mixture of an isotropic elastic solid with an elastic fluid is studied. Geometrically, this mixture is assumed to comprise a layer of fixed depth, bounded below by a rigid, impervious surface, and above by a free surface to which loads are applied. The resulting boundary-initial value problem is solved by use of a Green's function. Two different loading conditions are used to demonstrate the effect of including inertia terms in the equations of motion. In the first example of a constant compressive load, our result is found to agree with the inertia-free solution only for very long times. The second example shows that for a harmonically varying compression, resonance displacements occur at certain loading frequencies, whereas the solution obtained by neglecting inertia does not predict this behavior.Item Natural and induced anistropy in rocks under plastic conditions(1981) Allen, Michael Bruce; Cheatham, John B.; Bowen, Ray M.; Merwin, John E.The object of this study was to investigate the effect of anistropy on wedge indentation tests. These tests are used to qualitatively investigate the deviation forces encountered when drilling through an anisotropic medium. The preliminary investigation of anisotropic rocks lead to the study of an elastic - linear hardening limestone, Cordova Cream Limestone, also known as Austin Chalk. A yield condition and hardening rule, which could accurately account for the strain induced anisotropy, were developed. After carefully weighing the advantages and disadvantages of using this rock in wedge indentation tests, it was decided not to proceed further with this material. Instead, Pierre Shale was used, because preliminary tests indicated a high degree of anisotropy. Conventional triaxial tests were performed, in order to establish a yield condition. This yield condition was used in conjunction with four different theories to predict the vertical and horizontal forces encountered in wedge indentation tests. The four theories consisted of an adaptation of R. McLamore's preferred chip analysis, a plane strain slip-line field solution assuming no lip and a perfectly rough wedge, and two limit analysis solutions using the plane strain yield condition; one assumed a perfectly rough wedge while the other assumed the wedge to be frictionless. The slip-line field solution and the limit analysis solutions successfully bounded the vertical force data. The slip-line and limit analysis solutions for the horizontal force very nearly coincided. Although the scatter in the horizontal force data prevented quantitative confirmation of any of the above theories, the general trends, direction of forces and symmetry, were supported. The scatter in the data also did not convincingly confirm or contradict McLamore's theory, although previous observations and experiments do contradict this theory while supporting the plasticity solutions. Additional tests with various wedge and rock orientations were also performed to investigate the effects on the problem. The conclusions that can be made from this study are: (1) That the strength characteristics of Cordova Cream Limestone can be modeled successfully with Ziegler's modification of Prager's hardening rule in the principal stress space. (2) That plasticity theory can successfully predict the forces on a wedge penetrating anisotropic Pierre Shale. The consequences of this study are that the forces on the wedges and therefore on a drill bit are in the up-dip direction when the bedding plane is inclined less than 45°, while the forces are in the down-dip direction for inclinations greater than 45°.Item Numerical experiments on transformation techniques for minimax problems of optimal control(1982) Kuo, Yan Min; Miele, Angelo; Bowen, Ray M.; Thrall, Robert M.A transformation technique is employed in order to convert mini max problems of optimal control into the Mayer-Bolza problem of the calculus of variations. The transformation requires the proper augmentation of the state vector x(t), the control vector u(t), and the parameter vector TT. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter in being optimized. The transformation technique is then employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. The algorithm considered in this thesis belongs to the class of sequential gradient-restoration algorithms. The sequential gradient restoration algorithm is made up of a sequence of two-phase cycles, each cycle consisting of a gradient phase and a restoration phase. The principal property of this algorithm is that it produces a sequence of feasible suboptimal solutions. Each feasible solution is characterized by a lower value of the minimax performance index than any previous feasible solution. To facilitate numerical implementation, the interval of integration is normalized to unit length. Four test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation technique and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the known analytical solutions. In particular, the converged values of the minimax performance index agree well with the known analytical values.Item One dimensional shear motions in fluid saturated porous media(1981) Roberson, Kyle R.; Bowen, Ray M.; Wilhoit, James C.; Wang, C. C.An analytic solution is presented for shear motions in a binary mixture of a chemically inert, isothermal, elastic isotropic solid and elastic fluid subject to a sinusoidally varying solid displacement on one boundary and free of tractions on the other. It is demonstrated that the retention of inertial terms, and the resulting resonance phenomenon, can cause solid displacements in the interior of the region orders of magnitude greater than the exciting solid displacement on the boundary. Displacement spectra are presented for certain well known porous media.