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At least 955 records · Page 53

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NASA NTRS1978

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Stein, M.↗

NASA NTRS1982

An analytic solution to the classical two-body problem with drag

An analytic solution to the two-body problem with a specific drag model is obtained. The model treats drag as a force proportional to the vector velocity and inversely proportional to the square of the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time-of-flight is expressed as a quadrature in the 'true anomaly'.

Mittleman, D.↗

NASA NTRS1983

Solutal diffusion coefficient for liquid PbTe-SnTe

The solutal diffusion coefficient has been determined for liquid lead telluride-tin telluride using a modified shear cell technique. Postdiffusion concentration profiles are presented for several diffusion couples. The best analytical curve fit to the data gives a composition-dependent diffusion coefficient of (/3/7/ to the C power) x 0.00014 sq cm/sec, where C is the PbTe concentration. In addition, data are presented to show the importance of solutal convection in the lead-tin-telluride system.

Clark, I. O.↗

NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗

NASA NTRS1983

Numerical solution of the problem of flame propagation by the use of the random element method

A numerical, grid-free algorithm is presented for one-dimensional reaction-diffusion model of laminar flame propagation in premixed gases. It is based on the random element method we developed for the analysis of diffusional processes. The effect of combustion is taken into account by applying the principle of fractional steps to separate the process of diffusion, modeled by the random walk of computational elements, from the exothermic effects of chemical reaction, monitoring their strength. The validity of the algorithm is demonstrated by application to flame propagation problems for which exact solutions exist. The flame speed evaluated by its use oscillates around the exact value at a relatively small amplitude, while the temperature and species concentration profiles are self-correcting in their convergence to the exact solution. A satisfactory resolution is obtained by the use of quite a small number of computational elements which automatically adjust their distribution of fit sharp gradients.

Ghoniem, A. F.↗

NASA NTRS1982

The use of solution adaptive grids in solving partial differential equations

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Anderson, D. A.↗

NASA NTRS1982

Solution of viscous internal flows on curvilinear grids generated by the Schwarz-Christoffel transformation

The combination of an orthogonal, curvilinear coordinate generation procedure with a stable forward marching viscous flow solution technique is presently employed in the solution of flow fields for arbitrary, axisymmetric ducts. Coordinate generation is accomplished by means of both potential lines and plane potential flow streamlines. Since the coordinate streamlines approximate actual ones, the equations of motion for viscous compressible flow can be parabolized in order to solve for both the boundary layer and the core flow in a single streamwise pass. The method's versatility is demonstrated by two examples of viscous compressible swirling flow through complex radial gas turbine passages.

Anderson, O. L.↗

NASA NTRS1983

Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm

A multiple-grid algorithm for use in efficiently obtaining steady solutions to the Euler and Navier-Stokes equations is presented. The convergence of the explicit MacCormack algorithm on a fine grid is accelerated by propagating transients from the domain using a sequence of successively coarser grids. Both the fine and coarse grid schemes are readily vectorizable. The combination of multiple-gridding and vectorization results in substantially reduced computational times for the numerical solution of a wide range of flow problems. Results are presented for subsonic, transonic, and supersonic inviscid flows and for subsonic attached and separated laminar viscous flows. Work reduction factors over a scalar, single-grid algorithm range as high as 76.8. Previously announced in STAR as N83-24467

Chima, R. V.↗

NASA NTRS1982

The effect of solute on the homogeneous crystal nucleation frequency in metallic melts

A complete calculation that extends the classical theory for crystal nucleation in pure melts to binary alloys has been made. Using a regular solution model, approximate expressions have been developed for the free energy change upon crystallization as a function of solute concentration. They are used, together with model-based estimates of the interfacial tension, to calculate the nucleation frequency. The predictions of the theory for the maximum attainable undercooling are compared with existing experimental results for non-glass forming alloys. The theory is also applied to several easy glass-forming alloys (Pd-Si, Au-Si, Fe-B) for qualitative comparison with the present experimental experience on the ease of glass formation, and for assessment of the potential for formation of the glass in bulk.

Thompson, C. V.↗

NASA NTRS1983

Formulation and solution of rotary-wing aeroelastic stability and response problems

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Friedmann, P. P.↗

NASA NTRS1983

Nonparametric solution of the Euler equations for steady flow

A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.

Garabedian, P. R.↗

NASA NTRS1983

Green's function solution and applications for cracks emanating from a circular hole in an infinite sheet

Stress-intensity factors are obtained for point loaded equal length cracks emanating from a circular hole in an infinite plate. A series approach and the Muskhelishvili formulation in the two-dimensional theory of elasticity are used to derive the solution. The applicability of the solution is demonstrated by using it as a Green's function to obtain stress-intensity factors in the case of (1) biaxial tension and pure shear of an infinite plate and (2) tension and pin loading of a plate with cracks emanating from one hole in a row of holes.

Shivakumar, V.↗

NASA NTRS1985

Solution Potentials Indicate Aluminum-Alloy Tempers

Report discusses use of solution potential as measure of temper of aluminum alloys. Technique based on fact that different tempers or heat treatments exhibit different solution potentials as function of aging time.

Danford, M. D.↗

NASA NTRS1983

Specification for a Program for an Interative Aeroelastic Solution (PIAS)

An engineering and software specification which was written for a computer program to calculate aeroelastic structural loads including the effects of nonlinear aerodynamics is presented. The procedure used in the program for an iterative aeroelastic solution (PIAS) is to alternately execute two computer codes: one to calculate aerodynamic loads for a specific wing shape, and another to calculate the deflected shape caused by this loading. A significant advantage to the design of PIAS is that the initial aerodynamic module can be replaced with others. The leading edge vortex (LEV) program is used as the aerodynamic module in PIAS. This provides the capability to calculate aeroelastic loads, including the effects of a separation induced leading edge vortex. The finite element method available in ATLAS Integrated structural analysis and design system is used to determine the deflected wing shape for the applied aerodynamics and inertia loads. The data management capabilities in ATLAS are used by the execution control monitor (ECM) of PIAS to control the solution process.

Manro, M. E.↗

NASA NTRS1983

The mechanics of delamination in fiber-reinforced composite materials. Part 1: Stress singularities and solution structure

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites.

Wang, S. S.↗

NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗

NASA NTRS1983

Compositional Segregation in Unidirectionally Solidified Solid Solution Crystals

A computer program was developed to model compositional segregation in unidrectionally solidified solid-solution-semiconducting crystals. The program takes into account the variations of the interface segregation constant and solidification rate with composition. Calculations are performed for the HgCdTe solid solution system that is compared with experimental data.

Wang, J. C.↗

NASA NTRS1983

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗