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At least 289 records · Page 16

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NASA NTRS1974

Finite element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.

Mcmeeking, R. M.↗

NASA NTRS1974

Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers

The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.

Klein, L. R.↗

NASA NTRS1973

Comments on 'Elastically scattered recoil nuclei in solid-state detectors'

Horn and Von Oertzen (1967) have shown that tracks in mica are produced by an irradiation with 32-MeV O-16 ions. These tracks were attributed to K and Fe recoils produced by elastic scattering of the incident oxygen beam. In the present work an alternate explanation of their observations is provided. The measured characteristics of the tracks are shown to be compatible with theoretical predictions for production of tracks by inelastic (mostly compound nucleus) reactions with silicon and to be inconsistent with the previously proposed elastic scattering process. The possibility that the tracks are produced by contaminant ions in the beam cannot be ruled out.

Maurette, M.↗

NASA NTRS1973

Elastic wave velocities of Apollo 14, 15, and 16 rocks

Elastic wave velocities of two Apollo 14 rocks, 14053 and 14321, three Apollo 15 rocks, 15058, 15415, and 15545, and one Apollo 16 rock 60315 have been determined at pressures up to 10 kb. For sample 14321, the variation of the compressional wave velocities with temperature has been measured over the temperature range from 27 to 200 C. Overall elastic properties of these samples except sample 15415 are very similar to those of Apollo 11, 12, and 14 rocks and are concordant with Toksoz et al.'s (1972) interpretation that lunar upper crust is of basaltic composition. Temperature derivative of the P wave velocity for sample 14321 is a half to one order of magnitude larger than that for single crystalline minerals. This suggests that the seismic velocity in the lunar crust may be affected significantly by the temperature distribution.

Mizutani, H.↗

NASA NTRS1974

An experimental-theoretical study of free vibrations of plates on elastic point supports

A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. An experiment is conducted in which the bending stiffness of horizontal beams is used to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured and is compared with results from a theoretical model in which a Rayleigh-Ritz analysis is used which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modeled both as massless translational springs and springs with tip masses, which are included to better represent the experimental supports.

Leuner, T. R.↗

NASA NTRS1974

Elastic and inelastic electron scattering at 20 and 60 eV from atomic Cu

Normalized differential and integral electron-impact cross sections are presented for elastic scattering and for specified excitation levels of atomic copper at 20 and 60 eV. For some excitation levels, an unexpectedly large cross section was found, which at certain angular and energy ranges surpasses the cross section for elastic scattering.

Williams, W.↗

NASA NTRS1974

Elastic moduli of precompressed pyrophyllite used in ultrahigh pressure research

The propagation of ultrasonic pulses in pyrophyllite specimens was studied to determine the effect of specimen precompression on the measured elastic moduli. Measurements were made at room pressure and, for the precompressed specimens, to pressures of 3 kbar. Pyrophyllite was found to be elastically anisotropic, apparently the result of the fabric present in our material. The room pressure adiabatic bulk modulus as measured on specimens made of isostatically compacted powered pyrophyllite was determined to be 96.1 kbar. The wave speeds of ultrasonic pulses in pyrophyllite were found to decrease with increasing specimen precompression. A limiting value of precompression was found, above which no further decrease in wave speed was observed. For the shear wave speeds this occurs at 10 kbar while for the longitudinal wave at 25 kbar. In the limit, the shear waves propagate 20% slower than in the unprecompressed samples; for the longitudinal wave the difference is 30%.

Sachse, W.↗

NASA NTRS1975

Elastic-plastic analysis of an infinite sheet having a circular hole under pressure

An exact elastic-plastic solution for the stresses in an infinite sheet having a circular hole subject to pressure is obtained on the basis of J2 deformation theory together with a modified Ramberg-Osgood law. The sheet is orthotropic but isotropic in its plane. The results are assessed on the basis of Budiansky's criterion for the acceptability of J2 deformation theory. By using exact elastic-plastic stresses, the function connecting the pressure at the hole with the radial enlargement is obtained. Upon release of the pressure, residual stresses around the hole are produced.

Hsu, Y. C.↗

NASA NTRS1974

The design, analysis and experimental evaluation of an elastic model wing

An elastic orbiter model was developed to evaluate the effectiveness of aeroelasticity computer programs. The elasticity properties were introduced by constructing beam-like straight wings for the wind tunnel model. A standard influence coefficient mathematical model was used to estimate aeroelastic effects analytically. In general good agreement was obtained between the empirical and analytical estimates of the deformed shape. However, in the static aeroelasticity case, it was found that the physical wing exhibited less bending and more twist than was predicted by theory.

Cavin, R. K., III↗

NASA NTRS1975

The effect of adhesive layer elasticity on the fracture mechanics of a blister test specimen

An analytical model of a blister type specimen for evaluating adhesive bond strength was developed. Plate theory with shear deformation was used to model the deformation of the plate, and elastic deformation of the adhesive layer is taken into account. It is shown that the inclusion of the elastic deformation of the adhesive layer can have a significant influence in the energy balance calculations of fracture mechanics.

Updike, D. P.↗

NASA NTRS1975

Flutter analysis of two parallel elastically coupled flat plates

Flutter of two parallel elastically coupled flat plates was investigated analytically. A closed-form solution including both aerodynamic and structural damping is presented for flutter of flat orthotropic plates coupled by an elastic medium. Both plates are simply supported along the side edges but are supported by deflectional, rotational, and torsional springs of arbitrary stiffness at the leading and trailing edges. Two-dimensional quasi-steady aerodynamics was utilized in the solution. Since the large number of variables present in the problem precludes extensive parametric studies, results are presented to indicate the basic flutter characteristics of coupled two-plate systems and to assess the validity of previously published modal solutions for similar problems.

Shore, C. P.↗

NASA NTRS1976

Absolute elastic differential electron scattering cross sections in the intermediate energy region. III - SF6 and UF6

A recently developed technique has been used to measure the ratios of elastic differential electron scattering cross sections (DCS) for SF6 and UF6 to those of He at electron impact energies of 5, 10, 15, 20, 30, 40, 50, 60, and 75 eV and at scattering angles of 20 to 135 deg. In order to obtain the absolute values of DCS from these ratios, He DCS of McConkey and Preston have been employed in the 20 to 90 deg range. At angles in the 90 to 135 deg range the recently determined cross sections of Srivastava and Trajmar have been utilized. From these DCS, elastic integral and momentum transfer cross sections have been obtained.

Srivastava, S. K.↗

NASA NTRS1977

Elastic distortion of flanged inner ring of high-speed cylindrical roller bearing

The elastic distortion of the inner ring of an experimental roller bearing is investigated analytically. The geometry of the experimental bearing is unusually complex, and for this reason a bearing with an axially symmetric inner ring is also analyzed. Only the inner ring and shaft are considered using a two dimensional finite element program that can accommodate interference between these components. The results suggest that the elastic distortions are modest in relation to the design clearances associated with the experimental bearing. The variation of the radial deflection of the raceway may, however, be significant in some circumstances.

Taylor, C. M.↗

NASA NTRS1977

Constitutive acoustic-emission elastic-stress behavior of magnesium alloy

Repeated laoding and unloading of a magnesium alloy below the macroscopic yield stress result in continuous acoustic emissions which are generally repeatable for a given specimen and which are reproducible between different specimens having the same load history. An acoustic emission Bauschinger strain model is proposed to describe the unloading emission behavior. For the limited range of stress examined, loading and unloading stress delays of the order of 50 MN/sq m are observed, and they appear to be dependent upon the direction of loading, the stress rate, and the stress history. The stress delay is hypothesized to be the manifestation of an effective friction stress. The existence of acoustic emission elastic stress constitutive relations is concluded, which provides support for a previously proposed concept for the monitoring of elastic stresses by acoustic emission.

Williams, J. H., Jr.↗

NASA NTRS1976

The nonlinear transient response of thin, rectangular elastic plates

The results of experiments and theoretical analysis of the nonlinear, transient response of thin, rectangular, elastic, simply supported plates are presented. In the experiments, a plane wave tube with a special pulse generator at one end and a thin glass plate mounted at the other end was used to subject the glass plate to pressure pulses of different magnitudes. Whole-field measurements of the response of the plate were obtained by the reflected moire grid technique. The largest ratio of center deflection to thickness of the plate during the experiments was 5.6. The theoretical response of the glass plate to the pressure pulses was computed by solving the von Karman equations governing large deflections in elastic plates by two methods - (1) the finite-difference method, and (2) Galerkin's method. Good agreement was found between theoretically predicted and experimentally measured response.

Rajagopal, G.↗

NASA NTRS1976

Effect of friction in wedging of elastic solids

In this paper the contact problem for an elastic wedge of arbitrary angle is considered. It is assumed that the external load is applied to the medium through a rigid wedge and the coefficient of friction between the loading wedge and the elastic solid is constant. The problem is reduced to a singular integral equation of the second kind with the contact pressure as the unknown function. An effective numerical solution of the integral equation is described and the results of three examples are presented. The comparison of these results with those obtained from the frictionless wedge problem indicates that generally friction has the tendency of reducing the peak values of the stress intensity factors calculated at the wedge apex and at the end points of the contact area.

Erdogan, F.↗

NASA NTRS1977

Biaxial load effects on the crack border elastic strain energy and strain energy rate

The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.

Eftis, J.↗

NASA NTRS1978

The elastic distortion of the flanged inner ring of a high-speed cylindrical roller bearing

The elastic distortion of the inner ring of an experimental 3,000,000 DN roller bearing is investigated analytically. The geometry of this bearing is unusually complex and for this reason a bearing with an axially symmetric inner ring and shaft is also analyzed. Only the inner ring and shaft are considered using a two-dimensional finite element computer program which enables interference between these components to be accommodated. The results for the experimental bearing suggest that elastic distortions are modest in relation to the design clearances. However, the variation of the radial deflection of the raceway may be significant for some circumstances and the interference fit adopted between the ring and shaft appears to be questionably low.

Taylor, C. M.↗