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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Analytical results for postbuckling behavior of plates in compression and shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗
NASA NTRS1985

Analytical results for post-buckling behaviour of plates in compression and in shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗
NASA NTRS1986

Upwind Navier-Stokes solutions for separated periodic flows

The application of an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using both the thin-layer and complete forms of the Navier-Stokes equations, the low Reynolds number laminar flow around a circular cylinder with periodic shedding is solved. The effect of grid density, grid extent, and time step on the Strouhal number is shown. Results from both sets of equations agree within the experimental data band. Unsteady, laminar flow computations around inclined plates and separated airfoils are also described. Strouhal numbers agree to within 5 percent of experiments for inclined plates. Differences between the complete equations and the thin-layer approximation for separated periodic flows are discussed. Computations of an impulsively started circular cylinder and airfoil yield time-accurate flowfield shapes in good agreement with experimental flow visualizations. The turbulent computation of an airfoil at a high angle-of-attack is massively separated, but shows no evidence of periodicity.

Rumsey, C. L.↗
NASA NTRS1975

Non-linear resonances in the forced responses of plates. I - Symmetric responses of circular plates

The dynamic analogue of the von Karman equations is used to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies. It is shown that, in general, when there is no internal resonance (i.e., the natural frequencies are not commensurable), only the mode having a frequency near that of the excitation is strongly excited (i.e., is needed to represent the response in the first approximation). A clamped, circular plate is used as a numerical example to show that, when there is an internal resonance, more than one of the modes involved in this resonance can be strongly excited; moreover, when more than one mode is strongly excited, the lower modes can dominate the response, even when the frequency of the excitation is near that of the highest mode. This possibility was not revealed by any of the earlier studies which were based on the same governing equations.

Sridhar, S.↗
NASA NTRS1973

A general conclusion regarding the large amplitude flexural vibration of beams and plates.

Use is made of the two coupled partial differential equations that govern the large amplitude flexural vibration of flat plates. On the basis of an assumed vibration mode taken to be separable in the space coordinates and time, the modal equation is obtained. In the case of a one-term solution, it is shown that the modal equation is the same as the dynamic equation of a mass-spring combination where the restoring force of the nonlinear spring is a cubic and an odd function of the displacement. Since the modal equation is a nonlinear, ordinary differential equation with positive coefficients, it is shown that the nonlinearity associated with the large amplitude flexural vibration of beams and plates is of the hardening type, that is, the frequency increases with amplitude.

Pandalai, K. A. V.↗
NASA NTRS1974

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

Wang, N. N.↗
NASA NTRS2005

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.

Qin, Zhanming↗
NASA NTRS1975

Flutter of laminated plates in supersonic flow

A solution procedure was developed using linear small deflection theory for the flutter of simply supported laminated plates. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. An extended Galerkin method is used to obtain approximate solutions to the governing equations, and the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angle. A limited parametric study was conducted for typical laminated composite plates. The calculations show that both the bending-extensional coupling and the cross-stiffness terms have a large destabilizing effect on flutter. Since classical plate theory does not consider bending-extensional coupling and cross stiffness terms, it usually gives inaccurate and nonconservative flutter boundaries for laminated plates.

Sawyer, J. W.↗
NASA NTRS1972

Vibrations of circular elastic plates due to sonic boom.

The problem of transient axisymmetric vibrations of thin circular elastic plates due to sonic boom excitation is investigated. The equation of motion for a solid circular plate is solved by applying the modified finite Hankel transform and the Laplace transform, and the numerical results are obtained with the help of the digital computer. From the analysis of the data, obtained for the dynamic deflections of the plates for the boom duration, it is concluded that for a normal flight the boom duration has a significant effect on the vibrations of plates as compared to the overpressure of the boom.

Pavagadhi, L. J.↗
NASA NTRS1985

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Stein, M.↗
NASA NTRS1991

Variational finite element-tensor formulation for the large deflection random vibration of composite plates

A numerical integration routine is derived from a set of unified single step integration algorithms using a weighted satisfaction of the equilibrium equation governing the large deflection random response of laminated composite plates. The equilibrium equation is derived using a constant matrix large deflection finite-element formulation. In-plane inertia terms are considered in the formulation, however, rotary inertia terms are assumed negligible. Probability density, spectral density and autocorrelation functions of the maximum displacement and strain responses are presented for three acoustic excitation levels. Classical thin plate boundary conditions and pseudo white noise excitation are used in this investigation.

Robinson, Jay H.↗
NASA NTRS1972

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Carter, J. E.↗
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.↗