Search NASA⌕ Search

SEARCH · Search NASA

Results for “Formulation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method

A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.

Spalart, P. R.↗
NASA NTRS1986

Alternative mathematical programming formulations for FSS synthesis

A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem.

Reilly, C. H.↗
NASA NTRS1987

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗
NASA NTRS1986

Nonlinear flexure and torsion of rotating beams, with application to helicopter rotor blades. I - Formulation. II - Response and stability results

The dynamic response and aeroelastic stability of rotating beams such as helicopter blades is investigated analytically. The Hamilton principle is used to formulate the equations of motion for extensional and inextensional beams with precone angles and variable pitch angles, taking higher-order nonlinearities into account. The derivation of the equations and their approximate solution by a Galerkin procedure are explained in detail, and numerical results of equilibrium solutions and stability analyses are presented graphically.

Crespo Da Silva, M. R. M.↗
NASA NTRS1986

On the numerical performance of three-dimensional thick shell elements using a hybrid/mixed formulation

Three-dimensional thick shell elements with 8, 16, and 18 nodes are formulated by using the hybrid/mixed method. In bending applications, these elements are free from locking effect and give improved stress predictions. Finite element equations are derived from the Hellinger-Reissner variational principle in which both the displacement and stress fields are approximated by independent interpolation functions. For the assumption of stress parameters, three guidelines are followed: (1) suppression of kinematic deformation modes, (2) invariant element property, and (3) the constraint index exhibited by the element, when applied to constrained-media problems, must be greater than or equal to one. Numerical results are presented to show the element's behavior characteristics regarding sensitivity to locking, distortion effect (patch tests), mesh convergence and the accuracy of stress evaluation.

Graf, W.↗
NASA NTRS1987

Use of an implicit formulation based on quasilinearization for the aeroelastic response and stability of rotor blades in forward flight

This paper describes a new methodology for the formulation of the aeroelastic stability and response problem for helicopter rotor blades. The mathematical expressions for the aerodynamic loads need not be explicit functions of the blade displacement quantities. This methodology is combined with a finite element model of the blade, and a quasilinearization solution technique. The resulting computer program is used to study the behavior of blades with noncoincident elastic axis, aerodynamic centers, and centers of mass.

Celi, R.↗
NASA NTRS1988

Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells

A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.

Rankin, C. C.↗
NASA NTRS1988

A formulation for the boundary-layer equations in general coordinates

This is a working paper in which a formulation is given for solving the boundary-layer equations in general body-fitted curvilinear coordinates while retaining the original Cartesian dependent variables. The solution procedure does not require that any of the coordinates be orthogonal, and much of the software developed for many Navier-Stokes schemes can be readily used. A limited number of calculations has been undertaken to validate the approach.

Steger, Joseph L.↗
NASA NTRS1988

A scalar/vector potential formulation of an airfoil in nonuniform stream

A recent innovation in aerodynamic calculation techniques is the formulation based upon scalar and vector potentials (Stokes-Helmholtz decomposition) for the velocity field. This technique is presented: an implementation involving classical panel method is studied. The application of interest is to two-dimensional airfoils moving into a nonuniform approach flow. Comparisons with theoretical and numerical results are included. Furthermore the variations of lift and moment coefficients of quasi-steady simulated flight of an airfoil through microburst wind shear data are studied.

Wang, J. C. A.↗
NASA NTRS1987

Re-analysis procedure based on the mixed formulation

An analysis procedure is presented for large-scale structural systems, with large numbers of degrees of freedom and design variables. The procedure uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. Other elements of the procedure include: (1) lumping the design variables into a single tracing parameter; (2) operator splitting or additive decomposition of different arrays in the finite element equations into the corresponding arrays of the original structure plus correction terms; and (3) application of a reduction method through the use of the finite element method and the classical Bubnov-Galerkin technique. The re-analysis procedure is applied to the linear static and free vibration problems of plate and shell structures.

Noor, Ahmed K.↗
NASA NTRS1988

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗
NASA NTRS1987

Nonlinear/linear unified thermal stress formulations - Transfinite element approach

A new unified computational approach for applicability to nonlinear/linear thermal-structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.

Tamma, Kumar K.↗
NASA NTRS1988

Optimization of helicopter airframe structures for vibration reduction considerations, formulations and applications

Several key issues involved in the application of formal optimization technique to helicopter airframe structures for vibration reduction are addressed. Considerations which are important in the optimization of real airframe structures are discussed. Considerations necessary to establish relevant set of design variables, constraints and objectives which are appropriate to conceptual, preliminary, detailed design, ground and flight test phases of airframe design are discussed. A methodology is suggested for optimization of airframes in various phases of design. Optimization formulations that are unique to helicopter airframes are described and expressions for vibration related functions are derived. Using a recently developed computer code, the optimization of a Bell AH-1G helicopter airframe is demonstrated.

Murthy, T. Sreekanta↗
NASA NTRS1988

Transfer and redistribution of polarized light in resonance lines. I - Quantum formulation with collisions

Equations are derived quantum mechanically for the radiative transfer of polarized light and statistical equilibrium governing the formation of resonance lines in nonhydrogenic species. Redistribution due to collisions is specifically included, but magnetic fields are neglected. The formulation accounts for excited level interference and optical pumping and is applicable to solar resonance lines such as Ca II H and K and Mg II h and k.

Streater, A.↗
NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗
NASA NTRS1989

Evaluation of thermally induced non-Fourier stress wave disturbances via tailored hybrid transfinite element formulations

Accurate solutions have been obtained for a class of non-Fourier models in dynamic thermoelasticity which are relevant to the understanding of thermally-induced stress wave disturbances. The method employs tailored hybrid formulations based on the transfinite element approach. The results show that significant thermal stresses may arise due to non-Fourier effects, especially when the speeds of propagation of the thermal and stress waves are equal.

Tamma, Kumar K.↗
NASA NTRS1989

A finite element formulation for the large deflection random response of thermally buckled beams

The effects of temperature and acoustic loading are included in a theoretical finite element large deflection formulation for thin, isotropic beams. Thermal loads are applied as steady-state temperature distributions, and acoustic loads are taken to be ergodic and Gaussian with zero mean and uniform magnitude and phase along the length of the beam. Material properties are considered presently to be independent of temperature. Also, inplane and rotary inertia terms are assumed to be negligible, and all inplane edge conditions are taken to be immovable. For the random response analysis, both auto- and cross-correlation terms are included. The nature of the loads leads to the solution of two separate problems. First, the problem of thermal postbuckling is solved to determine the deflections and stresses due to the thermal load only. These deflections and stresses are then used as initial deflections and stresses for the random vibration analysis. Root-mean-square (RMS) maximum deflections and strains are obtained and compared with previous classical equivalent linearization results.

Locke, James↗