Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EQUATIONS - STRESSES PLATES”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Vibration of thermally buckled composite plates with initial deflections using triangular elements

A consistent finite element formulation is presented for the analysis of thermal postbuckling and free vibration of thermally buckled thin, laminated composite plates subjected to large temperature change. The influence of moderately large initial imperfections in deflection on the thermal postbuckling deflection and the vibration characteristics of the buckled plate is also investigated. The finite element equations of motion are derived from the principle of virtual work. These equations can be mathematically separated into two sets and solved in sequence. The first set of equations yields the particular solution of static thermal postbuckling deflection, and the second set of equations gives the homogeneous solution of vibration characteristics on the buckled plate. The first set of static equations is solved by using Newton-Raphson iteration method. The tangent stiffness matrix in the final iteration is equal to the total stiffness matrix of the second set of dynamic equations. This feature saves tremendous computation time in comparing with using the conventional approach. The influence of lamination angle, temperature distribution, plate planform of arbitrary shape, and boundary support conditions on postbuckling and vibration behavior are investigated.

Zhou, R. C.↗
NASA NTRS1994

Non-Reflecting Regions for Finite Difference Methods in Modeling of Elastic Wave Propagation in Plates

Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.

Kishoni, Doron↗
NASA NTRS2000

Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models

Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.

Liuo, William W.↗
NASA NTRS1960

Effect on Gaseous Film Cooling of Coolant Injection Through Angled Slots and Normal Holes

A study was made to determine the effect of coolant injection angularity on gaseous film-cooling effectiveness. In the correlation of experimental data an effective injection angle was defined by a vector summation of the coolant and mainstream gas flows. The cosine of this angle was used as a parameter to empirically develop a corrective term to qualify a correlating equation presented in Technical Note D-130 that was limited to tangential injection of the coolant. Data were also obtained for coolant injection through rows of holes normal to the test plate. The slot correlating equation was adapted to fit these data by the definition of an effective slot height. An additional corrective term was then determined to correlate these data.

Papell, S. Stephen↗
NASA NTRS1991

Finite element analysis of nonlinear flutter of composite panels

A finite element formulation is developed to analyze large-amplitude panel flutter of arbitrary laminated plates. The plates considered are anisotropic composite, thin rectangular panels. The equations of motion for an oscillating plate are determined and solved by linearizing the nonlinear stiffness matrices. The solution procedure is presented to determine the limit-cycle motions which are caused by the large deflections and vibrations induced by the areodynamic load. The aerodynamic load is defined by the first-order piston theory. Examples studied include cross-ply laminates with various numbers of layers and three-layer angle-ply laminates with different lamination angles. The effects of simply supported and clamped boundary conditions of a cross-ply laminate are also examined.

Dixon, Iain R.↗
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.↗
DOE OSTI2023

Expanded verification and validation studies of hypersonic aerodynamics with multiple physics-fidelity models

Hypersonic aerothermodynamics is an important domain of modern multiphysics simulation. The Multi-Fidelity Toolkit is a simulation tool being developed at Sandia National Laboratories to predict aerodynamic properties for compressible flows from a range of physics fidelities and computational speeds. These models include the Reynolds-averaged Navier–Stokes (RANS) equations, the Euler equations with momentum-energy integral technique (MEIT), and modified Newtonian aerodynamics with flat-plate boundary layer (MNA+FPBL) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities, as well as model validation with uncertainty considerations. Code verification activities on the MNA+FPBL model build on previous work by focusing on the viscous portion of the model. Viscous quantities of interest are compared against those from an analytical solution for flat-plate, inclined-plate, and cone geometries. The code verification methodology for the MEIT model is also presented. Test setup and results of code verification tests on the laminar and turbulent models within MEIT are shown. Solution-verification activities include grid-refinement studies on simulations that model the HIFiRE-1 wind tunnel experiments. These experiments are used for validation of all model fidelities. A thorough validation comparison with prediction error and uncertainty is also presented. Three additional HIFiRE-1 experimental runs are simulated in this study, and the solution verification and validation work examines the effects of the associated parameter changes on model performance. Finally, a study is presented that compares the computational costs and fidelities from each of the different models.

42 ENGINEERING↗
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.↗