Search NASA⌕ Search

SEARCH · Search NASA

Results for “Displacement theory”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗
NASA NTRS1993

Solitary waves in the atmosphere

The weakly nonlinear theory for internal solitary waves is reviewed, and theoretical results of the vertical and horizontal structure of temperature, vertical displacements, and vertical and horizontal perturbations to the wind field associated with steadily propagating solitary waves are presented in two idealized atmospheric configurations. One configuration is representative of solitary waves observed in the lower troposphere and the other of solitary waves that occupy the entire troposphere. The important results of the theory are presented in a form that can be readily used by observationalists. The results obtained are then analyzed using actual rawinsonde data for two well-documented observations of atmospheric solitary waves, which are analogous to the two idealized configurations. The importance and difficulties of properly identifying the waveguide within which the solitary wave is confined are discussed. The fundamental role of a critical level in ducting the disturbances and thus in defining the thickness of the waveguide is illustrated in the example dealing with the solitary wave occupying the entire troposphere. Together, these two examples illustrate the decisions and compromises that must be made in applying the theory to the real atmosphere.

Rottman, James W.↗
NASA NTRS1987

A simple and efficient shear-flexible plate bending element

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Chaudhuri, Reaz A.↗
NASA NTRS1972

A two dimensional theory for two phase detonation of liquid films.

A theory for the propagation of detonations through tubes coated with a thin fuel film is developed. Vaporization is assumed as the rate limiting process dominating the detonation structure. Inclusion of the boundary layer displacement effect resulted in better agreement between computed and measured propagation speed, pressure ratio, and reaction zone length than was obtained in an earlier theory in which this effect was neglected. New film detonation data is presented covering a wide range of fuel air ratios. A general Chapman-Jouguet condition is formulated for film detonations, and use of the plane of complete film vaporization as the Chapman-Jouguet plane is justified in the case of thin films.

Rao, C. S. R.↗
NASA NTRS1983

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoil in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic "tone bursts' by a supercritical airfoil section.

Ventres, C. S.↗
NASA NTRS1984

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoi in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic 'tone bursts' by a supercritical airfoil section.

Ventres, C. S.↗
NASA NTRS1977

Synthesis of active controls for flutter suppression on a flight research wing

This paper describes some activities associated with the preliminary design of an active control system for flutter suppression capable of demonstrating a 20% increase in flutter velocity. Results from two control system synthesis techniques are given. One technique uses classical control theory, and the other uses an 'aerodynamic energy method' where control surface rates or displacements are minimized. Analytical methods used to synthesize the control systems and evaluate their performance are described. Some aspects of a program for flight testing the active control system are also given. This program, called DAST (Drones for Aerodynamics and Structural Testing), employs modified drone-type vehicles for flight assessments and validation testing.

Abel, I.↗
NASA NTRS1978

Modified lattice-statics approach to dislocation calculations. II - Application

The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.

Esterling, D. M.↗
NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗
NASA NTRS1992

Postbuckling of multilayered composite plates subjected to combined axial and thermal loads

A study is made of the postbuckling response of composite plates subjected to combined axial and thermal loadings. The analysis is based on a first-order shear deformation, von Karman type of nonlinear plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient reduction method is used in conjunction with mixed finite element models for determining the stability boundary and the postbuckling response of the plate. Sensitivity derivatives are evaluated and used to study the sensitivity of the postbuckling response to variations in the different lamination and material parameters of the plate. For quasi-isotropic plates, numerical results are presented showing the effects of variations in the material characteristics and fiber orientation of individual layers on the postbuckling response of the plate.

Noor, Ahmed K.↗
NASA NTRS1993

Modelling of thick composites using a layerwise laminate theory

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

Robbins, D. H., Jr.↗
NASA NTRS1991

On the modeling of delamination in thick composites

The layerwise laminate theory of Reddy (1989) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that provides a convenient format for modeling multiple delaminations. The resulting layerwise model is capable of computing interlaminar stresses, free edge effects, and energy release rates with the same accuracy as a conventional 3D finite element model. Although the total degrees of freedom are comparable in both models, the layerwise, two-dimensional format allows faster computation of the element stiffness matrices. Two example problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses and energy release rates for laminates in bending and extension.

Robbins, D. H.↗
NASA NTRS1942

Ground Effect on Downwash Angles and Wake Location

A theoretical study was made of the reduction in downwash and the upward displacement of the wake in the presence of the ground, and some verification of theory was obtained by means of air-flow measurements made with a ground-board and image-wing combination. Methods are given for estimating the effects and numerous examples are included to illustrate the nature of these effects and to show their order of magnitude.

Katzoff, S↗
NASA NTRS2002

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

Aboudi, Jacob↗
NASA NTRS1972

Displacement interaction and surface curvature effects on hypersonic boundary layers.

The title problem was studied employing implicit finite-difference methods to obtain numerical solutions to a composite set of boundary-layer equations valid to second order. Results are given for flow up a two-dimensional cubic compression ramp for free-stream Mach numbers of 6, 8, and 12.25 and for free-stream Re/inch equal to 85,800 and 25,800 at a wall-to-stagnation temperature ratio of 0.223. Comparisons with independent theories and experimental results are given. Nonsingular separation was produced at a free-stream Mach number of 12.25. For all cases considered, displacement and curvature effects canceled one another when a consistent treatment of inviscid and viscous curvature corrections was employed - the second-order theory virtually reproducing the first-order results.

Wornom, S. F.↗
NASA NTRS1978

The importance of quadrupole sources in prediction of transonic tip speed propeller noise

A theoretical analysis is presented for the harmonic noise of high speed, open rotors. Far field acoustic radiation equations based on the Ffowcs-Williams/Hawkings theory are derived for a static rotor with thin blades and zero lift. Near the plane of rotation, the dominant sources are the volume displacement and the rho U(2) quadrupole, where u is the disturbance velocity component in the direction blade motion. These sources are compared in both the time domain and the frequency domain using two dimensional airfoil theories valid in the subsonic, transonic, and supersonic speed ranges. For nonlifting parabolic arc blades, the two sources are equally important at speeds between the section critical Mach number and a Mach number of one. However, for moderately subsonic or fully supersonic flow over thin blade sections, the quadrupole term is negligible. It is concluded for thin blades that significant quadrupole noise radiation is strictly a transonic phenomenon and that it can be suppressed with blade sweep. Noise calculations are presented for two rotors, one simulating a helicopter main rotor and the other a model propeller. For the latter, agreement with test data was substantially improved by including the quadrupole source term.

Hanson, D. B.↗
NASA NTRS2015

Application of the Refined Zigzag Theory to the Modeling of Delaminations in Laminated Composites

The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resin-rich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.

Groh, Rainer M. J.↗