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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Effect of damage on elastically tailored composite laminates

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Armanios, Erian↗
NASA NTRS1975

Diurnal variations in the thermosphere. I - Theoretical formulation

A nonlinear perturbation theory is formulated for the solution of the multicomponent equations of energy, mass, and momentum conservation in the atmosphere. The theory is three-dimensional and includes the effects of heat conduction and advection, viscosity, ion drag, and diffusion. The theory is described as a superposition of mathematical modes obtained by expanding the physical quantities into vector and spherical harmonics. The coupling between the various modes, both linear and nonlinear, is included. The theory provides a basis for the treatment of the thermosphere and its interaction with the lower atmosphere, where 'mode coupling' is most important. As an example, a comparison is presented between one-dimensional and three-dimensional calculations of the fundamental mode of the diurnal component in the thermosphere. Coupling between the lowest modes is considered to describe the physical conditions of the lower thermosphere where inertia and Coriolis forces become dominant over the ion-drag and viscous forces. In this region, the latitude structures of the temperature, wind field, and diffusively controlled oxygen are shown to change significantly.

Harris, I.↗
NASA NTRS1953

On the application of transonic similarity rules to wings of finite span

The transonic aerodynamic characteristics of wings of finite span are discussed from the point of view of a unified small perturbation theory for subsonic, transonic, and supersonic flows about thin wings. This approach avoids certain ambiguities which appear if one studies transonic flows by means of equations derived under the more restrictive assumption that the local velocities are everywhere close to sonic velocity. The relation between the two methods of analysis of transonic flow is examined, the similarity rules and known solutions of transonic flow theory are reviewed, and the asymptotic behavior of the lift, drag, and pitching-moment characteristics of wings of large and small aspect ratio is discussed. It is shown that certain methods of data presentation are advantageous for the effective display of these characteristics.

Spreiter, John R↗
NASA NTRS1960

Some Divergence Characteristics of Low-Aspect-Ratio Wings at Transonic and Supersonic Speeds

The problem of chordwise, or camber, divergence at transonic and supersonic speeds is treated with primary emphasis on slender delta wings having a cantilever support at the trailing edge. Experimental and analytical results are presented for four wing models having apex half-angles of 5 deg, 10 deg, 15 deg, and 20 deg. A Mach number range from 0.8 to 7.3 is covered. The analytical results include calculations based on small-aspect-ratio theory, lifting-surface theory, and strip theory. A closed-form solution of the equilibrium equation is given, which is based on low-aspect-ratio theory but which applies only to certain stiffness distributions. Also presented is an iterative procedure for use with other aerodynamic theories and with arbitrary stiffness distribution.

Woolston, Donald S.↗
NASA NTRS2001

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Tessler, A.↗
NASA NTRS1989

Numerical test of weak turbulence theory

The analytic theory of weak Langmuir turbulence is well known, but very little has previously been done to compare its predictions with numerical solutions of the basic dynamical evolution equations. In this paper, numerical solutions of the statistical weak turbulence theory are compared with numerical solutions of the Zakharov model of Langmuir turbulence, and good agreement in certain regimes of very weak field strength is found.

Payne, G. L.↗
NASA NTRS1992

The Pekeris problem, and the interior of the pulsating sphere, first success of exact ray theory, and what rays?

This paper presents what is probably the first application of exact ray theory to provide nontrivial exact solutions of the Helmholtz equation. First, the Pekeris problem is considered. This is followed by consideration of the problem of the field maintained within a uniformly pulsating sphere. In the Pekeris problem, an iterative solution provides the exact solution on the second iteration. In the second problem, it is shown that the exact ray theory eliminates the focus of the geometric theory.

Mcaninch, Gerry L.↗
NASA NTRS1987

Thermosolutal convection during directional solidification. II - Flow transitions

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Mcfadden, G. B.↗
NASA NTRSDate not supplied

Convolution-Based Numerical Solutions of Transient Temperature Fields during Powder Bed Fusion Additive Manufacturing: Theory, Accuracy, and Computational Cost

Powder bed fusion (PBF) additive manufacturing has found numerous applications in the aerospace domain. However, components fabricated via PBF have a complex time-temperature history that significantly impacts subsequent mechanical performance. This study examines convolution-based numerical solutions of transient temperature fields that support simulations involving arbitrary beam shapes and paths during PBF. The convolutional approach is verified through comparisons with analytical solutions of the temperature field. The computational speed and accuracy of the method are assessed through comparisons with other explicit and implicit numerical techniques. In addition, the straightforward translation of the approach from a CPU to a GPU implementation and the resultant performance improvement are presented. The role of the technique in predicting microstructure evolution during PBF (for a greater process-structure-property-performance framework) is also demonstrated. This work supports the development of computational materials methods for understanding and controlling the time-temperature history during PBF.

powder bed fusion↗
NASA NTRS1992

Accretion disks in active galactic nuclei - Vertically explicit models

A region of the parameter space accessible to accretion disks in AGN is explored using vertically integrated models to describe the thin-disk structure. Particular attention is paid to the role of convection. From a comparison of strongly convective solutions with varying mixing lengths to solutions obtained using a recent theory of convection developed for accretion disks, it is argued that it may be appropriate to take the mixing length to be roughly one-third of a pressure scale height when applying standard mixing-length theory to disks. Scalings are presented for various critical points in the locus of steady-state solutions, and rough estimates of time scales for behavior associated with disk instability are provided.

Cannizzo, John K.↗
NASA NTRS1995

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Coirier, William J.↗
NASA NTRS2000

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

Young, Richard D.↗
NASA NTRS1973

Electron avalanche structure determined by random walk theory

A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is made possible by a random walk technique. Results show that the electric field patterns in the early formation stages of avalanches in helium are close to those obtained from theory based on constant transport coefficients. Regions of maximum and minimum induced electrostatic potential phi are located on the axis of symmetry and within the volume covered by the electron swarm. As formation time continues, however, the region of minimum phi moves to slightly higher radii and the electric field between the extrema becomes somewhat erratic. In the intermediate formation periods the avalanche growth is slightly retarded by the high concentration of ions in the tail which oppose the external electric field. Eventually the formation of ions and electrons in the localized regions of high field strength more than offset this effect causing a very abrupt increase in avalanche growth.

Englert, G. W.↗
NASA NTRS1985

An experiment to detect gut monopoles

Recent advances in the development of Grand Unification Theories have led to several interesting predictions. One of these states that Grand Unification Monopoles (GUMs) exist as solutions in may nonabelian gauge theories. Another consequence of Unification is the possibility of baryon decay. The efficiency of the water tank detector in registering a Rubakov type decay will vary with both the interaction length and the GUM's velocity, expressed in terms of beta ( 0.01). The efficiency decreases at large values of because of the limited resolving time of the detector (approx. 50 ns). At lower values of Beta the time between interactions is such that the criterion of 4 events in 2 mu s can no longer be satisfied. The Rubakov experiment has now been in operation for almost 2 years with an estimated live time of 80%. During this time no candidate events have been observed leading to an estimated upper limit on the flux of 7.82 x 0.00001 m(-2) d(-1) Sr(-1). The ionization loss detection system has only recently come on line and as yet no results are available from this experiment.

Macneill, G.↗
NASA NTRS1988

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗
NASA NTRS1990

On refined theories of composite laminates

A review of the developments in the displacement-based theories of plates is presented. It is shown that many of the third-order theories reported in the literature are based on the same or equivalent displacement field, and thus lead to the same results. A strain-consistent third-order theory is presented, which contains most existing third-order plate theories as special cases. The layer-wise laminate plate theory proposed is also reviewed. The accuracy of the theories is evaluated by comparing the numerical solutions with those of the three-dimensional elasticity theory.

Reddy, J. N.↗