The temperature of a plate heated by a source of arbitrary motion and strength.
Temperature distribution for thin plate heated by source of arbitrary motion and strength and governed by Sturm-Liouville boundary conditions
Cobble, M. H.↗
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Application of the TRPLT1 element to large amplitude free vibrations of plates
A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.
Mei, C.↗
Residual stresses of thin, short rectangular plates
The analysis of the residual stresses in thin, short rectangular plates is presented. The analysis is used in conjunction with a shadow moire interferometry technique by which residual stresses are obtained over a large spatial area from a strain measurement. The technique and analysis are applied to a residual stress measurement of polycrystalline silicon sheet grown by the edge-defined film growth technique.
Andonian, A. T.↗
Deposition of thin films by ion plating on surfaces having various configurations
Ion plating method for thin gold film deposition on complex surface configurations
GASEOUS IONIZATION↗
Analysis and Testing of Plates with Piezoelectric Sensors and Actuators
Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Utilizing linear piezoelectric theory results in an intrinsically coupled pair of piezoelectric constitutive equations. One equation describes the direct piezoelectric effect where strains produce an electric field and the other describes the converse effect where an applied electrical field produces strain. The purpose of this study is to compare finite element analysis and experiments of a thin plate with bonded piezoelectric material. Since an isotropic plate in combination with a thin piezoelectric layer constitutes a special case of a laminated composite, the classical laminated plate theory is used in the formulation to accommodated generic laminated composite panels with multiple bonded and embedded piezoelectric layers. Additionally, the von Karman large deflection plate theory is incorporated. The formulation results in laminate constitutive equations that are amiable to the inclusion of the piezoelectric constitutive equations yielding in a fully electro-mechanically coupled composite laminate. Using the finite element formulation, the governing differential equations of motion of a composite laminate with embedded piezoelectric layers are derived. The finite element model not only considers structural degrees of freedom (d.o.f.) but an additional electrical d.o.f. for each piezoelectric layer. Comparison between experiment and numerical prediction is performed by first treating the piezoelectric as a sensor and then again treating it as an actuator. To assess the piezoelectric layer as a sensor, various uniformly distributed pressure loads were simulated in the analysis and the corresponding generated voltages were calculated using both linear and nonlinear finite element analyses. Experiments were carried out by applying the same uniformly distributed loads and measuring the resulting generated voltages and corresponding maximum plate deflections. It is found that a highly nonlinear relationship exists between maximum deflection and voltage versus pressure loading. In order to assess comparisons of predicted and measured piezoelectric actuation, sinusoidal excitation voltages are simulated/applied and maximum deflections are calculated/measured. The maximum deflection as a function of time was determined using the linear finite elements analysis. Good correlation between prediction and measurement was achieved in all cases.
Bevan, Jeffrey S.↗
Mixed mode stress-intensity-factors in mode-3 loaded middle crack tension specimen
A three dimensional stress analysis of a middle-crack tension specimen subjected to mode-3 type loading was performed using fracture mechanics based finite element code FRAC3D. Three-dimensional stress intensity factors were calculated for a range of specimen thicknesses that represent the structures used in aerospace and nuclear industries. Calculated SIF for very thick specimen (thickness-to-crack length b/a greater than or equal to 30) agreed very well with the antiplane solution in the literature. The K(sub II) stress field exists near the intersection of the crack front and free surface in a boundary-layer region covers the complete thickness of the plate and K(sub II) dominates all through the thickness. For very thin plates (b/a is less than .1), the average K(sub II) is larger than K(sub III) (about 25% for b/a = 0.1).
Shivakumar, Kunigal N.↗
An efficient quadrilateral element for plate bending analysis
A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the follwoing considerations: (1) suppression of all kinematic deformation modes, (2) the element has a favorable value for the constraint index in the thin plate limit, and (3) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
Saleeb, A. F.↗
Phenomena after meteoroid penetration of a bumper plate
The results are presented of a study to obtain a computer program for the penetration of a thin plate of aluminum by a sphere of rock. The study was divided into two projects. One project covers the initial impact, the crushing of the sphere of rock, the break up of the aluminum sheet, and the conversion of the sufficiently shock-compressed regions of rock and aluminum into a plasma. The other project considers the ejection of a cone of plasma with entrained particles from the impact zone, its expansion as it traverses a region of free space, and its impact on a stack of paper sheets. The ablation of fragments in penetrating the stack of paper sheets is also considered.
Todd, F. C.↗
A finite element method for nonlinear forced vibrations of rectangular plates
The finite element method has been extended to determine the response of large amplitude forced vibrations of thin plates. A harmonic force matrix of a rectangular element under uniform harmonic excitation is developed for nonlinear forced vibration analysis. Inplane deformation and inertia are both considered in the formulation. Results obtained are compared with simple elliptic response, perturbation and other approximation solutions.
Mei, C.↗
Effects of transverse shearing flexibility on the postbuckling of plates loaded by inplane shear
This paper presents buckling and postbuckling results for plates loaded by inplane shear. The buckling results have been plotted to show the effects of thickness on the stress coefficient for aluminum plates. Results are given for various length-to-width ratios. Postbuckling results for thin plates with transverse shearing flexibility are compared to results from classical theory. The problems considered are the postbuckling response of plates in shear made of aluminum and of a + or - 45 deg graphite-epoxy laminate. Thus the materials are isotropic and orthotropic, respectively. The plates are considered to be long with side edges simply supported, with various inplane edge conditions, and the plates are subject to a constant shearing displacement along the side edges. Characteristic curves presenting the average shear stress resultant as a function of the applied displacement are given. These curves indicate that change in inplane edge conditions influence plate postbuckling stiffness and that transverse shearing is important in some cases.
Stein, Manuel↗
Large deflection random response of cross-ply laminated plates with elastically restrained edges and initial imperfections
The large deflection random response of symmetrically laminated cross-ply rectangular thin plates subjected to random excitation is studied. The out-of-plane boundary conditions are such that all the edges are rigidly supported against translation, but elastically restrained against rotation. The plate is also assumed to have a small initial imperfection. The assumed membrane boundary conditions are such that all the edges are free from normal and tangential forces in the plane of the plate. Mean-square deflections and mean-square strains are determined for a three-layered cross-ply laminate.
Prasad, C. B.↗
Shed Vortex Structure and Phase-Averaged Velocity Statistics in Symmetric/Asymmetric Turbulent Flat Plate Wakes
The near wake of a flat plate is investigated via direct numerical simulations (DNS). Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large theta divided by D (sub TE) values (theta is the boundary layer momentum thickness towards the end of the plate and D (sub TE) is the trailing edge thickness). In the present study the emphasis is on relatively thick plates with circular trailing edges (CTE) resulting in theta divided by D values less than one (D is the plate thickness and the diameter of the CTE), and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 x 10 (sup 6) and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor 1.27 weaker in terms of peak phase-averaged spanwise vorticity at first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x divided by D) that occurs nears the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x divided by D. Both these effects are examined in detail and the important contributors are identified.
direct numerical simulations↗
Numerical evaluation of the radiation from unbaffled, finite plates using the FFT
An iteration technique is described which numerically evaluates the acoustic pressure and velocity on and near unbaffled, finite, thin plates vibrating in air. The technique is based on Rayleigh's integral formula and its inverse. These formulas are written in their angular spectrum form so that the fast Fourier transform (FFT) algorithm may be used to evaluate them. As an example of the technique the pressure on the surface of a vibrating, unbaffled disk is computed and shown to be in excellent agreement with the exact solution using oblate spheroidal functions. Furthermore, the computed velocity field outside the disk shows the well-known singularity at the rim of the disk. The radiated fields from unbaffled flat sources of any geometry with prescribed surface velocity may be evaluated using this technique. The use of the FFT to perform the integrations in Rayleigh's formulas provides a great savings in computation time compared with standard integration algorithms, especially when an array processor can be used to implement the FFT.
Williams, E. G.↗
Distribution of wave drag and lift in the vicinity of wing tips at supersonic speeds
The point-source-distribution method of calculating the aerodynamic coefficients of thin wings at supersonic speeds was extended to include the effect of the region between the wing boundary and the foremost Mach wave from the wing leading edge. The effect of this region on the surface velocity potential has been determined by an equivalent function, which is evaluated over a portion of the wing surface. In this manner, the effect of angles of attack and yaw as well as the asymmetry of top and bottom wing surfaces may be calculated. As examples of the method, the pressure distribution on a thin plate wing of rectangular plan form as well as the lift and the drag coefficients as a function of Mach number, angle of attack, and aspect ratio are calculated. The equations for the surface velocity potential of several other plan forms are also included. (author)
AIRFOILS, FLAT-PLATE↗
Mixed mode stress intensity-factors in transversely loaded plates
An attempt is made to establish the validity of the antiplane solution and to calculate all components of the stress intensity factor (SIF) at the crack front for thin plates subjected to mode III loading. The stress analysis was performed for a range of thickness to crack length (b/a) ratio, which covered long cracks in a thin aircraft fuselage structure (b/a = 0.05).
Shivakumar, Kunigal N.↗
Finding Platinum-Coating Gaps On Titanium Anodes
Simple procedure makes gaps visible to eye. New gap-detection method consists of plating thin layer of non-silver-colored metal like copper or gold on anode. Contrast in color between plated metal and bare anode material makes gaps stand out. If anode passes inspection, copper or gold plate removable by reversal of test-plating current. Remains to be determined whether test plating and removal damages anode. New method simpler and more economical than previous attempts to identify gaps in platinum.
Bodemeijer, Ronnald↗
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.↗
A deformation analysis of flat flexible gear and its equation of original curved surfaces
The equation of the original curved surface of end harmonic gearing is determined by displacement analysis of flat flexible gear. The displacement analysis is also used to calculate the strength and rigidity of the gear. The latter is regarded as a circular plate with two concentrated loads, since its torsional rigidity is much larger than its bending rigidity. Small-deflection theory of thin plates is used to solve for the displacement of any point in the middle plane of the gear. New expressions are given for radial and tangential displacements of the middle plane under asymmetrical loading. A digital computer is used to obtain numerical values for the displacements.
Yunwen, S.↗