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NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1986

Integral processing in beyond-Hartree-Fock calculations

The increasing rate at which improvements in processing capacity outstrip improvements in input/output performance of large computers has led to recent attempts to bypass generation of a disk-based integral file. The direct self-consistent field (SCF) method of Almlof and co-workers represents a very successful implementation of this approach. This paper is concerned with the extension of this general approach to configuration interaction (CI) and multiconfiguration-self-consistent field (MCSCF) calculations. After a discussion of the particular types of molecular orbital (MO) integrals for which -- at least for most current generation machines -- disk-based storage seems unavoidable, it is shown how all the necessary integrals can be obtained as matrix elements of Coulomb and exchange operators that can be calculated using a direct approach. Computational implementations of such a scheme are discussed.

Taylor, P. R.↗
NASA NTRS1986

Prototyping and implementing flight qualifiable semicustom CMOS P-well bulk integrated circuits in the JPL environment

Presently, there are many difficulties associated with implementing application specific custom or semi-custom (standard cell based) integrated circuits (ICs) into JPL flight projects. One of the primary difficulties is developing prototype semi-custom integrated circuits for use and evaluation in engineering prototype flight hardware. The prototype semi-custom ICs must be extremely cost-effective and yet still representative of flight qualifiable versions of the design. A second difficulty is encountered in the transport of the design from engineering prototype quality to flight quality. Normally, flight quality integrated circuits have stringent quality standards, must be radiation resistant and should consume minimal power. It is often not necessary or cost effective, however, to impose such stringent quality standards on engineering models developed for systems analysis in controlled lab environments. This article presents work originally initiated for ground based applications that also addresses these two problems. Furthermore, this article suggests a method that has been shown successful in prototyping flight quality semi-custom ICs through the Metal Oxide Semiconductor Implementation Service (MOSIS) program run by the University of Southern California's Information Sciences Institute. The method has been used successfully to design and fabricate through the MOSIS three different semi-custom prototype CMOS p-well chips. The three designs make use of the work presented and were designed consistent with design techniques and structures that are flight qualifiable, allowing one hour transfer of the design from engineering model status to flight qualifiable foundry-ready status through methods outlined in this article.

Olson, E. M.↗
NASA NTRS1987

Sensitivity method for integrated structure/active control law design

The development is described of an integrated structure/active control law design methodology for aeroelastic aircraft applications. A short motivating introduction to aeroservoelasticity is given along with the need for integrated structures/controls design algorithms. Three alternative approaches to development of an integrated design method are briefly discussed with regards to complexity, coordination and tradeoff strategies, and the nature of the resulting solutions. This leads to the formulation of the proposed approach which is based on the concepts of sensitivity of optimum solutions and multi-level decompositions. The concept of sensitivity of optimum is explained in more detail and compared with traditional sensitivity concepts of classical control theory. The analytical sensitivity expressions for the solution of the linear, quadratic cost, Gaussian (LQG) control problem are summarized in terms of the linear regulator solution and the Kalman Filter solution. Numerical results for a state space aeroelastic model of the DAST ARW-II vehicle are given, showing the changes in aircraft responses to variations of a structural parameter, in this case first wing bending natural frequency.

Gilbert, Michael G.↗
NASA NTRS1987

Development of an integrated BEM (Boundary Element Mesh) for hot fluid-structure interaction

A boundary integral representation for a coupled approach to fluid flow and solid deformation problems associated with the design of hot-section components such as those in the Space Shuttle Main Engine is discussed. The formulation is based on the fundamental analytical solution of the Navier-Stokes equation for fluid velocity in an infinite domain. This fundamental solution was obtained by decomposing a Navier-Stokes equation into vorticity and dilation transport equations. A boundary integral involving convolutions in time was then constructed in which the convective terms appear in the volume integral.

Dargush, G. F.↗
NASA NTRS1986

Numerical solution of random singular integral equation appearing in crack problems

The solution of several elasticity problems, and particularly crack problems, can be reduced to the solution of one-dimensional singular integral equations with a Cauchy-type kernel or to a system of uncoupled singular integral equations. Here a method for the numerical solution of random singular integral equations of Cauchy type is presented. The solution technique involves a Chebyshev series approximation, the coefficients of which are the solutions of a system of random linear equations. This method is applied to the problem of periodic array of straight cracks inside an infinite isotropic elastic medium and subjected to a nonuniform pressure distribution along the crack edges. The statistical properties of the random solution are evaluated numerically, and the random solution is used to determine the values of the stress-intensity factors at the crack tips. The error, expressed as the difference between the mean of the random solution and the deterministic solution, is established. Values of stress-intensity factors at the crack tip for different random input functions are presented.

Sambandham, M.↗
NASA NTRS1986

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1987

Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability and that the W-transformation can be applied to them without any modifications. Convergence results are stated and numerical examples given.

Sidi, Avram↗
NASA NTRS1986

Integrated air revitalization system for Space Station

Fifty-one distinct functions are encompassed by the Space Station's Environmental Control and Life Support System; one exception to this noninteractivity of functions is the regenerative air revitalization system that removes and reduces CO2 and generates O2. The integration of these interdependent functions, and of humidity control, into a single system furnishes opportunities for process simplification as well as for power, weight and volume requirement reductions by comparison with discrete subsystems. Attention is presently given to a system which quantifies these integration-related savings and identifies additional advantages that accrue to this integrating design method.

Boyda, R. B.↗
NASA NTRS1987

The line integral approach to radarclinometry

Advances over previous work in radarclinometry (Wildey, 1984 and 1986) are proposed, including incorporation of a more exact treatment of the dependence on terrain orientation of the solid angle of integration of the microwave specific energy comprising individual pixel power, and the integration of the theory in the cross-ground-range direction. The local curvature hypothesis, making possible formulation of the theory in terms of a line integral, is expanded to include the possibilities of local cylindricity, local biaxial ellipsoidal hyperbolicity, and least-squares local sphericity. It is suggested that the banding noted in topographic maps which are produced on the basis of variation in the proportioning between curvature assumptions may be due to the lack of radiometric calibration.

Wildey, Robert L.↗
NASA NTRS1987

On the apparent velocity of integrated sunlight. I - 1983-1985

Frequency measurements for the Delta V = 2 transitions of CO in the integrated light spectrum of the sun are presented. The nature and magnitude of systematic errors which typically arise in absolute velocity measurements of integrated sunlight are explored in some detail, and measurements believed accurate at the level of about 5 m/s or less are presented. It is found that the integrated light velocity varies by about 3 m/s or less over a one-day period. Over the long term, the data indicate an increasing blue-shift in these weak infrared lines amounting to 30 m/s from 1983 to 1985. The sense of the drift is consistent with a lessening in the magnetic inhibition of granular convection at solar minimum. Such an effect has implications for the spectroscopic detectability of planetary-mass companions to solar-type stars.

Deming, Drake↗
NASA NTRS1987

Detection of signals by weighted integrate-and-dump filter

A Weighted Integrate and Dump Filter (WIDF) is presented that results in reducing those losses in telemetry symbol signal to noise ratio (SNR) which occur in digital Integrate and Dump Filters (IDFs) when the samples are not phase locked to the input data symbol clock. The Minimum Mean Square Error (MMSE) criterion is used to derive a set of weights for approximating the analog integrate and dump filter, which is the matched filter for detection of signals in additive white Gaussian noise. This new digital matched filter results in considerable performance improvement compared to unweighted digital matched filters. An example is presented for a sampling rate of four times the symbol rate. As the sampling offset (or phase) varies with respect to the data symbol boundaries, the output SNR varies 1 dB for an unweighted IDF, but only 0.3 dB for the optimum WIDF, averaged over random data patterns. This improvement in performance relative to unweighted IDF means that significantly lower sampling and processing rates can be used for given telemetry symbol rates, resulting in reduced system cost.

Sadr, R.↗
NASA NTRS1987

Integrated control and display research for transition and vertical flight on the NASA V/STOL Research Aircraft (VSRA)

Results of a substantial body of ground-based simulation experiments indicate that a high degree of precision of operation for recovery aboard small ships in heavy seas and low visibility with acceptable levels of effort by the pilot can be achieved by integrating the aircraft flight and propulsion controls. The availability of digital fly-by-wire controls makes it feasible to implement an integrated control design to achieve and demonstrate in flight the operational benefits promised by the simulation experience. It remains to validate these systems concepts in flight to establish their value for advanced short takeoff vertical landing (STOVL) aircraft designs. This paper summarizes analytical studies and simulation experiments which provide a basis for the flight research program that will develop and validate critical technologies for advanced STOVL aircraft through the development and evaluation of advanced, integrated control and display concepts, and lays out the plan for the flight program that will be conducted on NASA's V/STOL Research Aircraft (VSRA).

Foster, John D.↗
NASA NTRS1987

Potential flow around two-dimensional airfoils using a singular integral method

The problem of potential flow around two-dimensional airfoils is solved by using a new singular integral method. The potential flow equations for incompressible potential flow are written in a singular integral equation. The equation is solved at N collocation points on the airfoil surface. A unique feature of this method is that the airfoil geometry is specified as an independent variable in the exact integral equation. Compared to other numerical methods, the present calculation procedure is much simpler and gives remarkable accuracy for many body shapes. An advantage of the present method is that it allows the inverse design calculation and the results are extremely accurate.

Nguyen, Yves↗
NASA NTRS1988

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.

Kim, Sang-Wook↗
NASA NTRS1988

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.

Smaoui, H.↗
NASA NTRS1988

Integrated control and display research for transition and vertical flight on the NASA V/STOL Research Aircraft (VSRA)

Results of a substantial body of ground-based simulation experiments indicate that a high degree of precision of operation for recovery aboard small ships in heavy seas and low visibility with acceptable levels of effort by the pilot can be achieved by integrating the aircraft flight and propulsion controls. The availability of digital fly-by-wire controls makes it feasible to implement an integrated control design to achieve and demonstrate in flight the operational benefits promised by the simulation experience. It remains to validate these systems concepts in flight to establish their value for advanced short takeoff vertical landing (STOVL) aircraft designs. This paper summarizes analytical studies and simulation experiments which provide a basis for the flight research program that will develop and validate critical technologies for advanced STOVL aircraft through the development and evaluation of advanced, integrated control and display concepts, and lays out the plan for the flight program that will be conducted on NASA's V/STOL Research Aircraft (VSRA).

Foster, John D.↗