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The contour integral method is extended to general boundary value problems involving imperfect bonding of dissimilar materials. The loading and restraints are shown to have a significant effect on the stress intensity. Example problems are presented to illustrate the results.
There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.
For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.
A theoretical model for an electric discharge consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field is developed to study the rotation of the discharge plasma in the crossed electric and magnetic fields. The associated boundary-value problem for the coupled partial differential equations which describe the electric potential and the plasma velocity fields is solved in closed form. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number and the Hall coefficient. As a result of Lorentz forces, the plasma rotates with speeds as high as 1 million cm/sec around its axis of symmetry at typical conditions. As an application, it is noted that rotating discharges of this type could be used to develop a high-density plasma-ultracentrifuge driven by j x B forces, in which the lighter (heavier) ion and atom components would be enriched in (off) the center of the discharge cylinder.
Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.
The paper studies thermal microwave emission from an inhomogeneous slab of a random medium, with possible nonuniform absorption, scattering, and temperature profiles, bounded by different dielectrics on both sides. The invariant imbedding method is used to cast the boundary value problem of the radiative transfer equations into an initial value problem at zero slab thickness. As a numerical example, the angular and polarization variations of brightness temperatures for ice over water are considered.
This paper discusses nonlinear stress-wave propagation in a perfectly flexible string obeying a quasilinear (rate-dependent) constitutive equation. Wave speeds and compatibility relations valid along various families of characteristics were determined. It was shown that the compatibility relations associated with the transverse as well as the longitudinal waves readily yield a physical interpretation when they are expressed in suitable variables and in vector form. Coding based on the present information was completed for the machine solution of a class of mixed initial- and boundary-value problems of practical interest. Computer simulation of the stress-wave interaction in the 40-foot lanyard in the Arcas 'Rocoz' system during deployment was carried out using a stress-strain relation for nylon at the strain rate of 30/second. A method for estimating the maximum tension and strain in a string during the initial loading phase is proposed.
The paper describes the modal dispersion characteristics of electromagnetic waves traveling along the azimuthally magnetized ferrite-loaded coaxial transmission line and the ferrite-loaded wire. The modal dispersion curves are used to determine the pass and stop bands of normal propagation. Boundary-value problems were solved with Bolle-Heller functions. The dispersion characteristics of transverse electric modes are presented as plots of the normalized propagation constant vs the normalized frequency.
A class of singular integral equations is considered which arise in various two-dimensional mixed boundary-value problems with simple harmonic time variation. A problem typical of this class is that of determining the lifting pressure distribution on an oscillating airfoil in an unbounded incompressible potential flow. It is shown that Theodorsen's (1935) solution to this problem, with some modification, is valid for a general class of unsteady kernel functions. The technique employed is to consider an equivalent steady problem and then show that the unsteady resolvent and unsteady homogeneous solution can be written directly in terms of the steady solutions and a single frequency-dependent function which reduces to the Theodorsen function for the steady kernel.
Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.
A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.
System analyses of cylindrical plasma centrifuges are presented, for which the velocity field and electromagnetic fields are calculated. The effects of different electrode geometrics, induced magnetic fields, Hall-effect, and secondary flows are discussed. It is shown that speeds of 10000 m/sec can be achieved in plasma centrifuges, and that an efficient separation of U238 and U235 in uranium plasmas is feasible. The external boundary-value problem for the deposition of sputtering products is reduced to a Fredholm integral equation, which is solved analytically by means of the method of successive approximations.
The superposition principle is used to derive the approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. The derivation requires the linearity of the boundary value problems that underlie the electrical characteristics. The shifting approximation is invalid if considerable photocurrent and considerable dark current both occur within the junction space-charge region; it is invalid also if sizable series resistance is present or if high-injection concentrations of holes and electrons exist within the quasi-neutral regions.
The use of the method of complex extension to achieve better aerodynamic designs for supercritical cascades applicable to transonic turbomachinery is discussed. The method permits the computation of analytical solutions to elliptic, hyperbolic or mixed second-order partial equations in two dimensions. Boundary value problems formulated to develop an airfoil shape having a prescribed speed distribution for subsonic flow and a nearby speed distribution in the transonic case are also considered. Computing times necessary to run the blade design program are described as acceptably short.
A mixed boundary-value problem is formulated for an imperfect rectangular contact to a semiconducting sheet (layer). An exact model for derivation of contact resistance is developed and its solution by conformal mapping and eigenfunction expansion is presented. The expression for contact resistance is similar to that for a perfect (lossless) contact but includes an additional term containing the lowest-order coefficient in the infinite series expansion of the complex potential function. The calculated contact resistances are compared with those obtained from three approximate models: lossless contact, transmission line, and extended transmission line models. The extended transmission line model appears to be a very satisfactory approximation provided the ratio of contact length to sheet thickness is no less than 0.5.
A finite-element analysis was made of crack growth in a center-cracked specimen subjected to monotonically increasing load until the point of fast fracture. Since part of the specimen experienced unloading, the boundary value problem which was formulated was based upon incremental theory of plasticity. Experimental load and crack size records were utilized. Linear relations between plastic energy and crack growth were observed. Fracture toughness parameters, which were evaluated at the onset of unstable crack propagation from finite-element analysis, were in good agreement with those determined experimentally.
Numerical research program helps establish "proof-of-concept" for newly developed higher-order panel method applicable to both subsonic and supersonic flows about nearly-arbitrary aircraft configurations. It is intended to solve variety of boundary-value problems in steady-subsonic or supersonic inviscid flow.
Experimental methods of mapping the equipotential surfaces near some structure of interest rely on the detection of charged particles which have traversed the regions of interest and are detected remotely. One method is the measurement of ion energies for ions created at a point of interest and expelled from the region by the fields. The ion energy at the detector in eV corresponds to the potential where the ion was created. An ionizing beam forms the ions from background neutrals. The other method is to inject charged particles into the region of interest and to locate their exit points. A set of several trajectories becomes a data base for a systematic mapping technique. An iterative solution of a boundary value problem establishes concepts and limitations pertaining to the mapping problem.