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At least 127 records · Page 7

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NASA NTRS1978

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗

NASA NTRS1978

Analysis of a VTOL hover task with predictor displays using an optimal control model of the human operator

The influence of different types of predictor displays in a longitudinal VTOL hover task is analyzed in a theoretical study. It was assumed that pitch angle and position are presented to the pilot in separate displays namely the artificial horizon and position display. The predictive information is calculated by means of a Taylor series. From earlier experimental studies it is well known that predictor displays improve human and system performance and result in reducing human workload. In this study, an optimal control model is used to prove this effect theoretically. Several cases with differing amounts of predictive and rate information are compared.

Johannsen, G.↗

NASA NTRS1979

Approximation methods for combined thermal/structural design

Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

Haftka, R. T.↗

NASA NTRS1974

The application of MINIQUASI to thermal program boundary and initial value problems

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Source record↗

NASA NTRS1973

Program for the solution of multipoint boundary value problems of quasilinear differential equations

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Source record↗

NASA NTRS1978

Second order approximation of natural frequency constraints in structural synthesis

The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.

Miura, H.↗

NASA NTRS1979

Combined strength and aeroelastic wing synthesis via constraint approximation

A numerical optimization program using constraint approximations for preliminary sizing of wing structural design parameters to satisfy simultaneous strength and aeroelastic requirements is described. The effects of wing flexibility on loads and flutter are included. The iterative procedure approximates wing internal load distributions and flutter response in generating design constraints. Though a linear Taylor series approximation to the variation of flutter speed is made, constraints in general are formulated as nonlinear and solved in a minimum weight problem using a feasible directions search. The technique is demonstrated for the determination of the optimal ply orientations and for simultaneous sizing for strength and flutter with simple constraint approximations.

Mullen, J., Jr.↗

NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗

NASA NTRS1979

Shuttle program. Onorbit navigation integrator results for typical shuttle orbits

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software. The Pines formulation method with a Runge-Kutta-Gill fourth-order integrator method produces excellent results up to 300 second time steps. On orbit prediction with this method was implemented in the onboard onorbit navigation scheme. The Runge-Kutta third order, using Cowell's method, is an excellent general purpose determination integrator for time steps up to a 60 second duration.

Olszewski, O. W.↗

NASA NTRS1980

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Aiken, E. W.↗

NASA NTRS1979

A new propagation method for the radial Schroedinger equation

A new method for propagating the solution of the radial Schroedinger equation is derived from a Taylor series expansion of the wavefunction and partial re-summation of the infinite series. Truncation of the series yields an approximation to the exact propagator which is applied to a model calculation and found to be highly convergent.

Devries, P. L.↗

NASA NTRS1979

SCF and CI calculations of the dipole moment function of ozone

The constant and linear terms in a Taylor series expansion of the dipole moment function of the ground state of ozone are calculated with Cartesian Gaussian basis sets ranging in quality from minimal to double zeta plus polarization. Results are presented at both the self-consistent field and configuration-interaction levels. Although the algebraic signs of the linear dipole moment derivatives are all established to be positive, the absolute magnitudes of these quantities, as well as the infrared intensities calculated from them, vary considerably with the level of theory.

Curtiss, L. A.↗

NASA NTRS1980

Neutral stability calculations for boundary-layer flows

An analysis is presented of the parallel neutral stability of three-dimensional incompressible, isothermal boundary-layer flows. A Taylor-series expansion of the dispersion relation is used to derive the general eigenvalues. These equations are functions of the complex group velocity. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.

Nayfeh, A. H.↗

NASA NTRS1980

Polynomial approximation of functions in Sobolev spaces

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.

Dupont, T.↗

NASA NTRS1980

Predicting major element mineral/melt equilibria - A statistical approach

Empirical equations have been developed for calculating the mole fractions of NaO0.5, MgO, AlO1.5, SiO2, KO0.5, CaO, TiO2, and FeO in a solid phase of initially unknown identity given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. An internally consistent precision of approximately 0.94 is obtained, that is, the nature of the liquidus phase in the input data set can be correctly predicted for approximately 94% of the entries. The composition of the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage.

Hostetler, C. J.↗

NASA NTRS1982

Dielectrophoretic levitation of droplets and bubbles

Uncharged droplets and bubbles can be levitated dielectrophoretically in liquids using strong, nonuniform electric fields. The general equations of motion for a droplet or bubble in an axisymmetric, divergence-free electrostatic field allow determination of the conditions necessary and sufficient for stable levitation. The design of dielectrophoretic (DEP) levitation electrode structures is simplified by a Taylor-series expansion of cusped axisymmetric electrostatic fields. Extensive experimental measurements on bubbles in insulating liquids verify the simple dielectrophoretic model. Other have extended dielectrophoretic levitation to very small particles in aqueous media. Applications of DEP levitation to the study of gas bubbles, liquid droplets, and solid particles are discussed. Some of these applications are of special interest in the reduced gravitational field of a spacecraft.

Jones, T. B.↗

NASA NTRS1982

Toward a better understanding of helicopter stability derivatives

An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unsable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation.

Hansen, R. S.↗

NASA NTRS1983

Simplified Modeling of Tetrahedral Trusses

Tetrahedral-lattice structure exhibits great complexity in mathematical analysis, and complexity quickly increases with number of elements. Solutions for static and dynamic behavior of structure obtained with model consisting of analogous structure with fewer repeating elements. Advantage of continuum models is analytic solutions can be obtained, either in closed form or in relatively-tractable Taylor series.

Leondis, A.↗