Search

Summary Earlier solutions for this pipeline lateral-buckling problem are reviewed. A new, straightforward solution procedure is presented with illustrative problems and design curves. The new procedure can be implemented easily with a simple digital computer program. The solution gives a theoretical upper bound for the axial load that can be developed through heating. This upper bound can be helpful in the early stages of pipeline design.

For economic reasons S-Lay is often preferred to J-Lay. However in very deep water S-Lay requires a high curvature of the stinger to achieve the required close-to-vertical departure angle (or a large, low curvature stinger). Choosing the high curvature stinger can lead to plastic deformations of the pipe. The high top tension increases the plastic deformations in two ways: firstly it adds an overall tensile component to the strains, thereby increasing the strains at the 12 o’clock position. Secondly, it increases the strain concentrations, which arise due to discontinuous support of the pipe on the stinger. Typically, the pipe is guided over a series of roller beds. The high top tension tends to straighten the spans between the rollerbeds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures occur at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an arbitrary pipe material models, provided that: (i) the moment-curvature relation for the pipe under tension is known, and (ii) no cyclic plastic ratchetting occurs due to repeated bending of the pipe over the roller beds and straightening in the spans between roller beds. Agreement between the analytical and numerical (finite element) results is excellent. Proper loading history must be used in the numerical simulation, otherwise the level of strain concentration can be overpredicted.

Barite sag is the undesirable fluctuation in drilling mud density that occurs due to downhole settling of the weighting agent. Barite sag causes problems such as differential sticking, lost circulation, and can lead to serious well control events. This paper describes a fundamental theoretical effort to describe dynamic sag in drilling muds by considering the behavior of a system of particles in a non-Newtonian Bingham fluid. A continuum mechanics based model of dynamic sag in an inclined annulus is presented in terms of the fluid and particle properties. The results of the model are used to understand the influence of typical oilfield variables in precipitating sag. The analysis presented in this paper represents one of the first modeling/computational efforts to predict sag using phenomenological models (rather than empirical correlations or observational rules of thumb).

Current models of slip crushing treat the rotary slip as an axisymmetric wedge that generates an axisymmetric radial load on the drillpipe lateral surface. However, recent tests on strain gauged drillpipe specimens suggest that this model does not adequately capture the mechanical response of the drillpipe. The tests show that drillpipe response is a complex and non-axisymmetric function of slip geometry, friction between the slip and the bowl in the rotary table, and the mechanics of load transfer between the slip and drillpipe. This paper presents a new model of slip behavior that represents the slip system as a series of line loads. Analysis of the suspended tubular under these forces and axial tension leads to a limit load that characterizes slip crushing. A corollary of this analysis is the minimum slip length required to support a given axial tension.

Normality of the plastic strain increment vector to the loading surface is not always observed for granular media. Beginning from a thermodynamic basis and considering only isothermal processes, a series of physically appealing assumptions is employed to increasingly delimit the possible directions of the plastic strain increment vector. The results of the analysis indicate that on certain portions of the loading surface normality should hold while on the remainder, envelopes or fans are possible. Finally, several alternative restrictions are offered which provide a unique stress-strain relation at every point on the loading surface.

A plasticity theory is developed for a specific type of material characterized by coplanar motion of dislocation. Several results of the theory are given which make an experimental evaluation of the theory straightforward. The results of a limited experimental program for a particular nickel-base alloy are presented.

The role of the abdominal and erector spinae muscles is included in a simplified model for the human spine. The particular situation investigated here is a sudden stopping of the base of the spine model when it is travelling at constant velocity. The spine model motion predicted here is thought to be an appropriate first approximation to the spine motion resulting when a person with a seat belt, but no shoulder strap, is subjected to vehicle impact.

Simplified governing equations for line length, velocity, and lure hydrodynamic characteristics are used to determine the depth at which a lure runs in typical noncommercial fishing. The hydrodynamic characteristics of five typical lures were determined experimentally and their line length-velocity-depth relations, as predicted by the governing equations, are reported graphically.

A general three-dimensional plasticity theory is presented for describing the plastic flow of homogeneous, isotropic rock. Normality of the deformation-rate vector to the yield surface is incorporated into the stress-deformation rate law used in the theory. The rock is assumed to be perfectly plastic or nonwork-hardening with a dependence of the yield strength on the hydrostatic component of stress. A particular type of yield surface, which is representative of the behavior of rock, is assumed in an application of the theory. The specific problem considered is the solution for the incipient plane flow under a flat lubricated punch.

The relationship between the linear distance from the finger tip to the cardinal line of the hand and loss of flexion of the individual interphalangeal and metacarpophalangeal joints was studied using mathematical techniques. Mathematical functions were developed and a table was prepared from which impairment values could be derived directly. The results by this method correlate well with those by the time-consuming angular method for the measurement of impairment, and it was concluded that this procedure offers a simple, valid alternate method useful in some circumstances.

An analysis of the statically indeterminate problem of the creep of a biaxially loaded, anisotropic hollow cylinder is presented. The anisotropy of the material leads to a nonuniform axial stress distribution which is evaluated by numerical techniques. Single crystal, tubular specimens of a nickel-base alloy were creep-tested at 1400 deg F with an crystallographic axis nearly coincident with the tube axis in order to evaluate the theoretical analysis. Comparison of predicted and measured creep rates shows fair agreement.

The oscillation of a gas‐filled bubble in a fluid has been studied previously by several approaches. In general, the fluid is considered incompressible, and the gas is assumed to behave as a linear spring. Surface tension and gravity effects are usually ignored. Radiation losses of such bubbles are often determined experimentally. The analysis presented here includes surface‐tension effects. The gas considered is a perfect gas and the fluid an inviscid compressible fluid. The field equations for the fluid are linearized so that the nonlinearities of the problem arise from the following two sources. (1) The boundary condition at the fluid‐gas interface has a time dependent radius; and (2) the adiabatic pressure‐volume relation for the gas is nonlinear. Free oscillations of the bubble are studied. In order to induce free motion, the gas‐fluid interface of the bubble is considered to be initially at rest and then a pulse of pressure is delivered to the interior of the bubble. The ensuing motions are analyzed by a numerical integration scheme. Numerical results are presented for air bubbles in water. The most remarkable result is that the frequency of oscillation is essentially independent of amplitude for the cases studied. The results further indicate, as one would expect, that the numerical integration scheme used here is not practical for the determination of the radiation damping. When the small radiation damping is neglected, the motion becomes periodic and—for cases studied—a harmonic analysis of the pressure field was performed that shows that the radius and pressure variations can differ appreciably from the sinusoidal waves predicted by the linearized theory.

The orientation and stress dependence of the primary creep rate in single crystals of a nickel-base superalloy is predicted from crystallographic deformation mechanisms. An experimentally determined relationship between the deformation rate and applied stress is employed to calculate the independent contributions of each of the possible slip systems to the strain rate. Calculations were made for single crystals of a nickel-base superalloy tested in tensile creep at 1400 deg F, at which temperature the active slip planes are known to be {111}, and the slip directions either 〈110〉 or 〈112〉 at high or low strain rates, respectively. Comparison with measured primary creep rates showed the 〈110〉 contribution to be negligible and that while semi-quantitative agreement with the 〈112〉 analysis was obtained, an accurate prediction of creep rates may require inclusion of strain hardening in the analysis.

The Rayleigh inextensional theory for thin shells is employed to predict the natural frequencies of a sphere‐cone combination. For a particular case, the calculated and measured natural frequencies of shells of nonuniform thickness are determined. In comparing the experimental values of the lowest five “bell” frequencies with the predicted theoretical inextensional theory, there is very good agreement. This indicates that the method may be used for many missile configuration and jet engine applications.

The solutions for three cases of retarded flow of a rigid-viscous material are given. These cases are: (a) Sliding parallel plates; (b) Couette flow between concentric cylinders; and (c) axial flow through a circular pipe. For Couette flow two types of loading-unloading paths are found. The results of this analysis explain some of the discrepancies between experimental results and theoretical predictions for a Bingham material.

The results of an experimental and analytical program to develop stress-strain relations for a granular medium are presented. Explicit three-dimensional relations are given which represent the inelastic deformation of the medium. A simple version of the formulation is used to represent experimental results for a locally quarried quartz, and an evaluation of the relation is presented. The simplified relations are seen to be a compromise between mathematical tractability on the one hand and accuracy of prediction on the other.

Based on an earlier analytic formulation for the isothermal flow of an idealized cohesionless soil, several implications are deduced for the triaxial test (a compression test in the presence of a hydrostatic pressure). A specific form for the loading surface and the flow rule are selected. Since normality is generally absent uniqueness is not expected and a criterion is established to choose the best solution from a group of possible solutions. The question of stability is examined. Finally, the effect of the elastic membrane normally used in triaxial testing on the behavior of the granular material is discussed. In certain important respects the limited analytical and numerical results appear to agree with experience in soil mechanics testing.

The possibility of local panel buckling in the hull is investigated. The configuration of a section of the hull is idealized to be a thin cylindrical shell with discrete, internal, circumferential and longitudinal stiffeners. The loading is idealized to be composed to two parts which are (1) A uniform external pressure applied to the hull and to the bulkheads, and (2) an axial load which is applied through the bulkheads. An analytical procedure is presented which predicts the pressure necessary for buckling in the case of a specified axial load. Results of the analytical procedure are given for five possible hull configurations as well as for a case whose experimental buckling pressure had been reported earlier. Consequently the results of this study can be used to help evaluate various hull designs. Results deduced by the procedure presented here have application to the design of caissons, tunnels and possibly large pipelines.

Solutions are presented for the plane-strain plastic flow of rock under a pointed punch for two cases. In the first problem the indentation of a half space by a pointed punch is considered, and in the second the influence of a previous indentation on the formation of the next indentation is evaluated. The plasticity theory used in this analysis was developed by the authors earlier for rock mechanics applications. This theory incorporates a yield surface which is dependent on the mean normal stress and normality of the deformation rate vector to the yield surface. Work-hardening and elastic strains are neglected in the theory. These solutions furnish the analytical basis for some elementary experiments which may help to evaluate the theory.

IN A PREVIOUS REPORT THE AUTHORS PROPOSED AN ANALYTICAL FORMULATION FOR THE PREDICTION OF ISOTHERMAL FLOW OF AN IDEALIZED COHESIONLESS SOIL SUBJECTED TO MECHANICAL LOAD. THE MATERIAL WAS ASSUMED TO BE TIME-INDEPENDENT, ISOTROPIC, AND RIGID-PLASTIC. SEVERAL IMPLICATIONS OF THIS FORMULATION ARE DEDUCED FOR THE TRIAXIAL TEST (A COMPRESSION TEST IN THE PRESENCE OF A HYDROSTATIC PRESSURE). A SPECIFIC FORM FOR THE LOADING SURFACE IS ADOPTED IN ORDER TO ILLUSTRATE CERTAIN DIFFICULTIES ASSOCIATED WITH UNIQUENESS AND STABILITY. THE NUMERICAL RESULTS INDICATE A BEHAVIOR WHICH IS CONSISTENT WITH OBSERVED SOIL TESTS.

The dependence of the stress field on a continuous periodically varying stiffness which approximates a layered material is studied. This dependence is compared to the solution for the usual approximation of converting this class of problems to the superposition of an anisotropic one and a residual boundary problem. The region of applicability of the usual approximation is found to be as expected geometrically but surprisingly large as far as variation of stiffness is concerned.

A Rayleigh‐Ritz procedure is used to determine the natural frequencies for a certain class of mode shapes of a thin conical shell built in on the edge with the smaller radius and either simply supported free on the other edge. Both bending and extensional energies are included in the analysis. The results show that, for a sufficiently large number of circumferential nodes, the natural frequency predicted by these analyses is very close to the inextensional natural frequency for the same number of circumferential nodes and simply supported at the edge with the smaller radius. The comparison with the inextensional theory predictions is consistent with what has already been found experimentally; i.e., boundary conditions for this type of shell are not as influential on the higher natural frequencies as the lower ones.