Non-linear heat transfer of solids in orthogonal coordinate systems.
Nonlinear partial differential heat conduction equation /Poisson type/ obtained by using Kirchhoff transformation
Cobble, M. H.↗
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Analysis of elastic-plastic circular plates.
Bending analysis of elastoplastic circular plates for small deflection and axisymmetric loadings and support conditions, based on Kirchhoff hypothesis
Khojesteh-Bakht, M.↗
MTRAC - Computer program for transient analysis of circuits including magnetic cores
MTRAC program for transient analysis of circuits with square loop magnetic cores based on linearization of nonlinear circuit elements and Kirchhoff current law
Nitzan, D.↗
On the interaction forces and responses of structural rings subjected to fragment impact Interim technical report, 1 Aug. 1969 - 31 Jul. 1970
FORTRAN 4 program for calculating dynamic Kirchhoff deformation of structural rings subjected to fragment impact
Leech, J. W.↗
Deformation of prestressed thin shells
Prestressed thin shells elastic deformation, using Kirchhoff hypothesis of shell theory
Biricikoglu, V.↗
The calculation of electromagnetic fields in the Fresnel and Fraunhofer regions using numerical integration methods
Some results obtained with a digital computer program written at Goddard Space Flight Center to obtain electromagnetic fields scattered by perfectly reflecting surfaces are presented. For purposes of illustration a paraboloidal reflector was illuminated at radio frequencies in the simulation for both receiving and transmitting modes of operation. Fields were computed in the Fresnel and Fraunhofer regions. A dual-reflector system (Cassegrain) was also simulated for the transmitting case, and fields were computed in the Fraunhofer region. Appended results include derivations which show that the vector Kirchhoff-Kottler formulation has an equivalent form requiring only incident magnetic fields as a driving function. Satisfaction of the radiation conditions at infinity by the equivalent form is demonstrated by a conversion from Cartesian to spherical vector operators. A subsequent development presents the formulation by which Fresnel or Fraunhofer patterns are obtainable for dual-reflector systems. A discussion of the time-average Poynting vector is also appended.
Schmidt, R. F.↗
Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
Wu, R. W.↗
Computer program: Jet 3 to calculate the large elastic plastic dynamically induced deformations of free and restrained, partial and/or complete structural rings
A user-oriented FORTRAN 4 computer program, called JET 3, is presented. The JET 3 program, which employs the spatial finite-element and timewise finite-difference method, can be used to predict the large two-dimensional elastic-plastic transient Kirchhoff-type deformations of a complete or partial structural ring, with various support conditions and restraints, subjected to a variety of initial velocity distributions and externally-applied transient forcing functions. The geometric shapes of the structural ring can be circular or arbitrarily curved and with variable thickness. Strain-hardening and strain-rate effects of the material are taken into account.
Wu, R. W.↗
Elasto-plastic bending of cracked plates, including the effects of crack closure
A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.
Jones, D. P.↗
Multipath modeling for aeronautical communications.
One of the fundamental technical problems in aeronautical digital communications is that of multipath propagation between aircraft and ground terminal. This paper examines in detail a model of the received multipath signal that is useful for application of modern detection and estimation theories. The model treats arbitrary modulation and covers the selective and nonselective cases. The necessarily nonstationary statistics of the received signal are determined from the link geometry and the surface roughness parameters via a Kirchhoff solution.
Painter, J. H.↗
Parabolic cylinder antennas
Some of the features of single and dual parabolic-cylinder reflector antenna systems are discussed in terms of wave conversions, field divergence, and wavefronts in Fresnel and Fraunhofer regions. Beam-squinting, by mechanical displacement and electrical phase gradient methods, is introduced together with the combination of these methods. In the case of dual parabolic cylinders there is also a discussion of surface-truncation, parametric representation of surface intersections, main-aperture blockage by the subsystem, and beam squinting. A few diffraction patterns are presented to illustrate the type of data available via a formulation equivalent to the complex-vector Kirchhoff-Kottler formulation. Main and cross-polarization components of the solution are available as they are inherently part of the field solution in the Cartesian coordinate system. A means of displaying main and cross-polarization components for arbitrary beam-scanning in space is outlined. Extensions to monopulse tracking with variable-beamwidth (zooming) capability are introduced.
Schmidt, R. F.↗
Variable-beamwidth monopulse antennas
The merits of nine methods for zooming microwave amplitude-sensing monopulse antenna patterns are discussed. Of these, six are directly related to the TDRSS (Tracking Data Relay Satellite System) and are compatible with a deployable-mesh pseudo-paraboloidal main reflector. The remaining three methods utilize radically different geometrical configurations that depart considerably from the TDRSS parameters existing at this time. Preservation of the monopulse postulates is considered to be of prime importance for any variable-beamwidth candidate, however, it is allowed that approximate satisfaction of the postulates should be accepted for practical reasons. All of the methods discussed admit free choice of the polarization state, and the zooming function is never predicated on polarization. Exploration of the zooming techniques was carried out almost entirely by means of the Kirchhoff-Kottler vector diffraction program. The program generates electric and magnetic field intensity, associated phase, and time-average Poynting vector power flow in the intermediate near-field and far-field zones in both receive and transmit modes of operation. A few of the concepts have been verified experimentally with excellent agreement between theory and practice.
Schmidt, R. F.↗
The radiation from slots in truncated dielectric-covered surfaces
A theoretical approach based on the geometrical theory of diffraction is used to study the electromagnetic radiation from a narrow slot in a dielectric-covered perfectly-conducting surface terminated at an edge. The total far-zone field is composed of a geometrical optics field and a diffracted field. The geometrical optics field is the direct radiation from the slot to the field point. The slot also generates surface waves which are incident at the termination of the dielectric cover, where singly-diffracted rays and reflected surface waves are excited. The diffraction and reflection coefficients are obtained from the canonical problem of the diffraction of a surface wave by a right-angle wedge where the dielectric-covered surface is approximated by an impedance surface. This approximation is satisfactory for a very thin cover; however, the radiation from its vertical and faces cannot be neglected in treating the thicker dielectric cover. This is taken into account by using a Kirchhoff-type approximation, which contributes a second term to the diffraction coefficient previously obtained. The contributions from the geometrical optics field, the singly-diffracted rays and all significant multiply-diffracted rays are summed to give the total radiation. Calculated and measured patterns are found to be in good agreement.
Hwang, Y. M.↗
Diffraction studies applicable to 60-foot microwave research facilities
The principal features of this document are the analysis of a large dual-reflector antenna system by vector Kirchhoff theory, the evaluation of subreflector aperture-blocking, determination of the diffraction and blockage effects of a subreflector mounting structure, and an estimate of strut-blockage effects. Most of the computations are for a frequency of 15.3 GHz, and were carried out using the IBM 360/91 and 360/95 systems at Goddard Space Flight Center. The FORTRAN 4 computer program used to perform the computations is of a general and modular type so that various system parameters such as frequency, eccentricity, diameter, focal-length, etc. can be varied at will. The parameters of the 60-foot NRL Ku-band installation at Waldorf, Maryland, were entered into the program for purposes of this report. Similar calculations could be performed for the NELC installation at La Posta, California, the NASA Wallops Station facility in Virginia, and other antenna systems, by a simple change in IBM control cards. A comparison is made between secondary radiation patterns of the NRL antenna measured by DOD Satellite and those obtained by analytical/numerical methods at a frequency of 7.3 GHz.
Schmidt, R. F.↗
Variable beamwidth monopulse feed for Tracking and Data Relay Satellite (TDRS)
The Tracking and Data Relay Satellite with a set of circularly-polarized, amplitude-sensing monopulse patterns suitable for acquiring and tracking user spacecraft at Ku-band (15.0 GHz) is discussed. The possibility of increasing the less than 0.4-degree half-power beamwidth of the data beam to almost 1.0 degree during the acquisition phase is predicated on the use of feeds situated in the first bright-ring of the Airy diffraction structure. A complex-vector simulation equivalent to the Kirchhoff-Kottler or Franz formulations is used to compute transmitted and received field information for a dual-reflector (Cassegrain) antenna configuration in a three-dimensional space.
Schmidt, R. F.↗
Automated statistical analysis program (ASAP)
Pattern recognition subprogram is used to produce table which indicates sections of input data. Program then uses data to write set of Kirchhoff equations algebraically solved by Gaus reduction method.
Bavuso, S. J.↗
Depolarization of light back scattered from rough dielectrics
The depolarization of laser light backscattered from inhomogeneous dielectrics was investigated both experimentally and theoretically. A theoretical model that includes backscattering from both the surface and subsurface was developed by use of the Kirchhoff approach. The subsurface polarized and depolarized backscattered components are independent of surface roughness. The model predicts results in agreement with experimental measurements performed with a dual-polarized laser backscattering system. The measurements indicate that a significant contribution to the total backscattered power results from subsurface contributions; in some cases, this contribution completely masks the effects due to the surface.
Wilhelmi, G. J.↗
General instability analysis
HOLBOAT computer program provides instability analysis of inhomogeneous, anisotropic, right-circular cylinder or segment under combined loading. Program is based on Kirchhoff-Love hypothesis, general anisotropic constitutive equations, and Flugge's differential equations of equilibrium.
Bianca, C. J.↗