Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Methods”

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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗
NASA NTRS1986

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.

Kopriva, D.↗
NASA NTRS1986

A direct and inverse boundary layer method for subsonic flow over delta wings

A new inverse boundary layer method is developed and applied to incompressible flows with laminar separation and reattachment. Test cases for two dimensional flows are computed and the results are compared with those of other inverse methods. One advantage of the present method is that the calculation of the inviscid velocities may be determined at each marching step without having to iterate. The inverse method was incorporated with the direct method to calculate the incompressible, conical flow over a slender delta wing at incidence. The location of the secondary separation line on the leeward surface of the wing is determined and compared with experiment for a unit aspect ratio wing at 20.5 deg incidence. The viscous flow in the separated region was calculated using prescribed skin friction coefficients.

Woodson, S. H.↗
NASA NTRS1986

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Sidi, A.↗
NASA NTRS1985

Preconditioned minimal residual methods for Chebyshev spectral calculations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗
NASA NTRS1985

Topics in spectral methods

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Gottlieb, D.↗
NASA NTRS1985

Mixed models and reduction method for dynamic analysis of anisotropic shells

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Noor, A. K.↗
NASA NTRS1985

Durability predictions of adhesively bonded composite structures using accelerated characterization methods

The utilization of adhesive bonding for composite structures is briefly assessed. The need for a method to determine damage initiation and propagation for such joints is outlined. Methods currently in use to analyze both adhesive joints and fiber reinforced plastics is mentioned and it is indicated that all methods require the input of the mechanical properties of the polymeric adhesive and composite matrix material. The mechanical properties of polymers are indicated to be viscoelastic and sensitive to environmental effects. A method to analytically characterize environmentally dependent linear and nonlinear viscoelastic properties is given. It is indicated that the methodology can be used to extrapolate short term data to long term design lifetimes. That is, the method can be used for long term durability predictions. Experimental results for near adhesive resins, polymers used as composite matrices and unidirectional composite laminates is given. The data is fitted well with the analytical durability methodology. Finally, suggestions are outlined for the development of an analytical methodology for the durability predictions of adhesively bonded composite structures.

Brinson, H. F.↗
NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗
NASA NTRS1986

Methods for estimating the optical constants of atmospheric hazes based on complex optical measurements

The methods of multifrequency laser sounding (MLS) are the most effective remote methods for investigating the atmospheric aerosols, since it is possible to obtain complete information on aerosol microstructure and the effective methods for estimating the aerosol optical constants can be developed. The MLS data interpretation consists in the solution of the set of equations containing those of laser sounding and equations for polydispersed optical characteristics. As a rule, the laser sounding equation is written in the approximation of single scattering and the equations for optical characteristics are written assuming that the atmospheric aerosol is formed by spherical and homogeneous particles. To remove the indeterminacy of equations, the method of optical sounding of atmospheric aerosol, consisting in a joint use of a mutifrequency lidar and a spectral photometer in common geometrical scheme of the optical experiment was suggested. The method is used for investigating aerosols in the cases when absorption by particles is small and indicates the minimum necessary for interpretation of a series of measurements.

Zuev, V. E.↗
NASA NTRS1987

Applicability of linearized-theory attached-flow methods to design and analysis of flap systems at low speeds for thin swept wings with sharp leading edges

Low-speed experimental force and data on a series of thin swept wings with sharp leading edges and leading and trailing-edge flaps are compared with predictions made using a linearized-theory method which includes estimates of vortex forces. These comparisons were made to assess the effectiveness of linearized-theory methods for use in the design and analysis of flap systems in subsonic flow. Results demonstrate that linearized-theory, attached-flow methods (with approximate representation of vortex forces) can form the basis of a rational system for flap design and analysis. Even attached-flow methods that do not take vortex forces into account can be used for the selection of optimized flap-system geometry, but design-point performance levels tend to be underestimated unless vortex forces are included. Illustrative examples of the use of these methods in the design of efficient low-speed flap systems are included.

Carlson, Harry W.↗
NASA NTRS1986

A second-order accurate kinetic-theory-based method for inviscid compressible flows

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Deshpande, Suresh M.↗
NASA NTRS1987

A quasi-analytical method for non-iterative computation of nonlinear controls

An optimal control solution process was developed for a general class of nonlinear dynamical systems. The method combines control theory, perturbation methods, and Van Loan's recent matrix exponential results. A variety of applications support the practical utility of this method. Nonlinear rigid body optimal maneuvers are routinely solved. Flexible body dynamical systems of an order greater than 40 were solved. The method fails occasionally due to poor convergence of the perturbation expansion or numerical difficulties associated with computing the matrix exponential. The method is attractive because it appears to be a good candidate for semi-automation; no initial guess is required, and it usually converges at 2nd or 3rd order in minutes of machine time.

Junkins, J. L.↗
NASA NTRS1987

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system structural components

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

Cruse, T. A.↗
NASA NTRS1987

Advanced probabilistic method of development

Advanced structural reliability methods are utilized on the Probabilistic Structural Analysis Methods (PSAM) project to provide a tool for analysis and design of space propulsion system hardware. The role of the effort at the University of Arizona is to provide reliability technology support to this project. PSAM computer programs will provide a design tool for analyzing uncertainty associated with thermal and mechanical loading, material behavior, geometry, and the analysis methods used. Specifically, reliability methods are employed to perform sensitivity analyses, to establish the distribution of a critical response variable (e.g., stress, deflection), to perform reliability assessment, and ultimately to produce a design which will minimize cost and/or weight. Uncertainties in the design factors of space propulsion hardware are described by probability models constructed using statistical analysis of data. Statistical methods are employed to produce a probability model, i.e., a statistical synthesis or summary of each design variable in a format suitable for reliability analysis and ultimately, design decisions.

Wirsching, P. H.↗
NASA NTRS1987

Modified independent modal space control method for active control of flexible systems

A modified independent modal space control (MIMSC) method is developed for designing active vibration control systems for large flexible structures. The method accounts for the interaction between the controlled and residual modes. It incorporates also optimal placement procedures for selecting the optimal locations of the actuators in the structure in order to minimize the structural vibrations as well as the actuation energy. The MIMSC method relies on an important feature which is based on time sharing of a small number of actuators, in the modal space, to control effectively a large number of modes. Numerical examples are presented to illustrate the application of the method to generic flexible systems. The results obtained suggest the potential of the devised method in designing efficient active control systems for large flexible structures.

Baz, A.↗
NASA NTRS1987

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗
NASA NTRS1987

Multigrid methods for bifurcation problems: The self adjoint case

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Taasan, Shlomo↗