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At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

NASA NTRS1989

A study of composite plates with holes/inclusions

Delamination characterization of a plate with a hole/inclusion is presented. A closed form solution is developed to obtain stresses on the boundary of hole/inclusion in the plate. Once the location with the highest tangential stress is identified, a Finite Element Method analysis of a laminate under tensile loading is considered. The models are presented for the closed form and Finite Element Method. The examples are for (+ or - 35/0/90)s laminate of AS4/3501-6. Tensile, biaxial, and shear loads are considered.

Bense, Ronald↗

NASA NTRS1989

Gravitation- And Conduction-Driven Melting In A Sphere

Simplifying assumptions lead to approximate closed-form solution. Theoretical paper discusses melting of solid sphere in spherical container. Develops mathematical model of melting process, based in part on simplifying assumptions like those used in theories of lubrication and film condensation. Resulting equation for melting speed as function of melting distance solved approximately in closed form.

Bahrami, Parviz A.↗

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 NTRS1972

Influence of discontinuity stresses on main propellant tankage of a space shuttle orbiter.

Derivation of a general closed-form solution for the calculation of local stresses in cylindrical axial load-carrying pressure vessels which are heavily stiffened in the axial direction and circumferentially restrained by closely spaced ring stiffeners. The ring stiffeners are treated as discrete stiffeners and are allowed to have a temperature variation throughout the radial extension of the stiffener and different material properties compared with those of the vessel.

Meyer, H.-R.↗

DOE OSTI2021

Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys. , vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Physics↗

NASA NTRS1973

Effect of shear on duct wall impedance.

The solution to the equation governing the propagation of sound in a uniform shear layer is expressed in terms of parabolic cylinder functions. This result is used to develop a closed-form solution for acoustic wall impedance which accounts for both the duct liner and the presence of a boundary layer in the duct. The effective wall impedance can then be used as the boundary condition for the much simpler problem of sound propagation in uniform flow.

Goldstein, M.↗

NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗

NASA NTRS2002

Dynamics of a 4x6-Meter Thin Film Elliptical Inflated Membrane for Space Applications

Dynamic characterization of a thin film inflatable elliptical structure is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large Hexameter lightweight inflatable arc identified, including considerable difficulty in obtaining convergence in the nonlinear finite element pressurization solution. It was found that the extremely thin polyimide film material (.001 in or 1 mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. Approaches utilized to overcome these difficulties are described. Comparison of finite element predictions for frequency and mode shapes of the inflated structure with closed-form solutions for a flat pre-tensioned membrane indicate reasonable agreement.

Casiano, Matthew J.↗

NASA NTRS1953

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗

NASA NTRS1954

Impingement of water droplets on wedges and double-wedge airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees r, free stream Mach numbers from 1.1 to 2.0, semiapex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

Serafini, John S↗

DOE OSTI2021

Lie group analysis of the point-reactor neutron kinetics equations for various reactivity models

This work applies Lie Group Theory to the nonlinear point-reactor neutron kinetics equations for several reactivity feedback and reactivity insertion models. The goal of this work is to connect known analytical solutions to their corresponding Lie groups as well as to obtain new analytical solutions and the circumstances from which they arise. The reactivity models we consider are the Nordheim-Fuchs Model, an arbitrary-order polynomial reactivity insertion model, and the Fuchs Ramp-Insertion Model. In all three models, we generalize the analysis when possible and obtain analytical solutions in every case. For the first two models, we succeed in finding the Lie groups corresponding to classical solutions and find additional solutions that were otherwise unknown. Finally, for the final model, we obtain a reduced-order nonlinear kinetics equation which is not analytically solvable, but by applying a second-order truncation, we find a novel closed-form solution and demonstrate its validity with a numerical example.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Energy spectrum of lost alpha particles in magnetic mirror confinement

In a magnetic mirror fusion reactor, capturing the energy of fusion-produced alpha particles is essential to sustaining the reaction. However, since alpha particles are born at energies much higher than the confining potential, a substantial fraction are lost due to pitch-angle scattering before they can transfer their energy to the plasma via drag. The energy of lost alpha particles can still be captured through direct conversion, but designing an effective mechanism requires a description of the energies and times at which they become deconfined. Here we present analytical solutions for the loss velocity, energy, and time distributions of alpha particles in a magnetic mirror. After obtaining the Fokker-Planck collision operator, we asymptotically solve for the eigenfunctions of the Legendre operator to reveal a closed-form solution. In conclusion, our framework applies to any high-energy species, for any applied potential and mirror ratio R > 1, making this work broadly applicable to mirror devices.

Confinement↗

NASA NTRS1990

Analytical estimation for static deformation of wire ropes with fibrous core

This paper develops closed-form solutions for the extension of twisted wire ropes with fibrous cores which are subjected to axial forces as well as axial moments. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of wire ropes with fibrous core is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.

Kumar, K.↗

NASA NTRS1986

Arbitrarily laminated, anisotropic cylindrical shell under internal pressure

An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

Chaudhuri, Reaz Z.↗

NASA NTRS1987

Laminar mixing in a small floating zone

The relationship between the flow and solute fields during steady mass transfer of a dilute component is analyzed for multi-cellular rotating flows in the floating zone process of semiconductor growth. When the recirculating flows are weak in relation to the rate of crystal growth, a closed-form solution clearly shows the link between the convection pattern in the melt and the solute distribution across the surface of the growing solid. In the limit of strong convection, finite element calculations demonstrate the tendency of the composition to become uniform over the majority of the melt. The solute segregation in the product crystal is greatest when the recirculating motion is comparable to the rate of crystal growth, and points to the danger in attempting to grow compositionally uniform materials from a nearly convectionless melt.

Harriott, George M.↗

NASA NTRS1993

A flux-limited treatment for the conductive evaporation of spherical interstellar gas clouds

In this work, we present and analyze a new analytic solution for the saturated (flux-limited) thermal evaporation of a spherical cloud. This work is distinguished from earlier analytic studies by allowing the thermal conductivity to change continuously from a diffusive to a saturated form, in a manner usually employed only in numerical calculations. This closed form solution will be of interest as a computational benchmark. Using our calculated temperature profiles and mass-loss rates, we model the thermal evaporation of such a cloud under typical interstellar medium (ISM) conditions, with some restrictions. We examine the ionization structure of the cloud-ISM interface and evaluate column densities of carbon, nitrogen, oxygen, neon, and silicon ions toward the cloud. In accord with other investigations, we find that ionization equilibrium is far from satisfied under the assumed conditions. Since the inclusion of saturation effects in the heat flux narrows the thermal interface relative to its classical structure, we also find that saturation effects tend to lower predicted column densities.

Dalton, William W.↗

NASA NTRS2013

Extended Analytic Device Optimization Employing Asymptotic Expansion

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Thermoelectric Generators↗

NASA NTRS1991

Reliability and availability modeling of coupled communication networks - A simplified modeling approach

The network-complexity of LANs and of LANs that are interconnected by bridges and routers poses a challenging reliability-modeling problem. The present effort toward these problems' solution attempts to simplify them by reducing their number of states through truncation and state merging, as suggested by Shooman and Laemmel (1990). Through the use of state merging, it becomes possible to reduce the Bateman-Cortes 161 state model to a two state model with a closed-form solution. In the case of coupled networks, a technique which allows for problem-decomposition must be used.

Shooman, Martin L.↗