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At least 127 records · Page 7

Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

Patnaik, Surya N.

Sensitivity analysis for the dynamic response of viscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric response of viscoplastic shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. Spatial discretization is performed using finite elements, with discontinuous stress resultants across element interfaces. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) with an implicit constitutive update. The sensitivity coefficients are evaluated using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading, and a circular plate subjected to impulsive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to thickness, mass density, Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of these quantities at selected times.

Kulkarni, Makarand

Experimental confirmation of a PDE-based approach to design of feedback controls

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

Banks, H. T.

Bubble Formation at a Submerged Orifice in Reduced Gravity

The dynamic regime of gas injection through a circular plate orifice into an ideally wetting liquid is considered, when successively detached bubbles may be regarded as separate identities. In normal gravity and at relatively low gas flow rates, a growing bubble is modeled as a spherical segment touching the orifice perimeter during the whole time of its evolution. If the flow rate exceeds a certain threshold value, another stage of the detachment process takes place in which an almost spherical gas envelope is connected with the orifice by a nearly cylindrical stem that lengthens as the bubble rises above the plate. The bubble shape resembles then that of a mushroom and the upper envelope continues to grow until the gas supply through the stem is completely cut off. Such a stage is always present under conditions of sufficiently low gravity, irrespective of the flow rate. Two major reasons make for bubble detachment: the buoyancy force and the force due to the momentum inflow into the bubble with the injected gas. The former force dominates the process at normal gravity whereas the second one plays a key role under negligible gravity conditions. It is precisely this fundamental factor that conditions the drastic influence on bubble growth and detachment that changes in gravity are able to cause. The frequency of bubble formation is proportional to and the volume of detached bubbles is independent of the gas flow rate in sufficiently low gravity, while at normal and moderately reduced gravity conditions the first variable slightly decreases and the second one almost linearly increases as the flow rate grows. Effects of other parameters, such as the orifice radius, gas and liquid densities, and surface tension are discussed.

Buyevich, Yu A.

Estimation of ZnSe Slow-Crack-Growth Properties for Design of the Flow Enclosure Accommodating Novel Investigations in Combustion of Solids (FEANICS) Windows

This report reviews some of the literature on the fracture strength, fracture toughness, and crack growth properties of chemical-vapor-deposited ZnSe. The literature was reviewed to determine if the existing data on ZnSe is adequate to design windows for the Flow Enclosure Accommodating Novel Investigations in Combustion of Solids (FEANICS) project. Unfortunately, most of the published reports do not give all of the necessary design parameters despite having measured the data to do so. Further, the original data is not available. The data tabulated herein was determined by digitizing plots in original reprints of the publications. Based on the published data, an estimate of the slow-crack-growth parameters for small cracks in 100 percent humidity was made. For 100 percent humidity, the slow-crack-growth parameters n and A for small crack (or single crystal) failure were estimated. Weibull moduli estimated from bending of beams and circular plates ranged from 4 to 9, while fracture strengths ranged from 29 MPa in water to 72 MPa in dry nitrogen. Fracture toughness measurements yielded ranges, with the lower values representing failure from small flaws within grains and the larger values representing macroscopic cracks. Much of the data analyzed exhibited significant scatter, and the standard deviations were very large.

Salem, Jonathan A.

Analysis of a Circular Composite Disk Subjected to Edge Rotations and Hydrostatic Pressure

The structural analysis results for a graphite/epoxy quasi-isotropic circular plate subjected to a forced rotation at the boundary and pressure is presented. The analysis is to support a specialized material characterization test for composite cryogenic tanks. Finite element models were used to ensure panel integrity and determine the pressure necessary to achieve a predetermined equal biaxial strain value. The displacement results due to the forced rotation at the boundary led to a detailed study of the bending stiffness matrix [D]. The variation of the bending stiffness terms as a function of angular position is presented graphically, as well as, an illustrative technique of considering the laminate as an I-beam.

Oliver, Stanley T.

Resolving the Issues with Flywheel Position Sensors

For the past few years, the Advanced Electrical Systems Branch here at NASA Glenn has been pursuing research in the area of flywheels. The purpose of these pursuits has been t o explore the potential for flywheels to replace current battery-powered systems in space. So far it has been learned that flywheels offer large momentum storage capacity, comparatively small volume, high durability, and near- complete discharge capabilities, all of which are advancements over the existing nickel hydrogen and nickel cadmium batteries. Another significant advantage of flywheels is the potential they offer for combining the function of attitude control with energy storage. During the summer of 2004, I worked with Dr. Barbara Kenny in the Advanced Electrical Systems Branch, supporting the work she is doing by analyzing and testing some new components for the new Generation-2 flywheel. To monitor the speed and angular position of the flywheel rotor, a once-around (OAR) signal along with a sensorless algorithm is used. The OAR signal is used for the magnetic bearings that keep the flywheel suspended for frictionless operation. The sensorless algorithm is used for the flywheel motor/generator control. The OAR is generated from position sensors that monitor a circular plate. The plate has a cut down the middle such that one half of the circle is on a slightly lower level than the other. Every half-turn, or 180, the sensors detect the "cut" on the plate, and trigger the OAR, telling the computer that the rotor has made half a revolution. This, however, doesn't provide needed detailed information about the angular position of the rotor, since it only provides a signal alert every half- revolution. This is enough information for the magnetic bearing control but is insufficient for the motor/generator control. A new resolver was designed such that it would give continuous angle information rather than the 180 degree information of the OAR. The new resolver has two separate observable pieces: a flat middle section to monitor vertical motion, and an angled section around the circumference, which, when observed from above, produces a sine-wave displacement through the entire 360" revolution. My first job when I arrived this summer was to calibrate the sensors that would be mounted on the inside of the flywheel casing to monitor the position (angular and vertical) of the shaft. After calibration, I used the sensors to evaluate voltage outputs created by position differences between two pairs of sensors on the angled portion of the resolver for eight different angular positions, moving the resolver vertically and laterally through its entire potential range of motion. The results of these tests will be used to determine the rotor angular (and axial) position from the sensor readings once the new flywheel unit is assembled. The sensorless algorighm mentioned above consists of two operations: the signal injection method and the back electro-motive force (EMF). The signal injection is meant to work at low speeds, while the back EMF algorithm is meant to work at higher speeds. Both work together to determine the correct estimate of rotor position and speed based on the measured motor/generator current. It was determined that we wanted to know exactly how accurate our estimation methods were, and so a resolver (a commercially available mechanical sensor mounted to the motor/generator shaft to measure rotor position and speed) and a "Resolver to Digital" (R2D) circuit board was purchased to make the comparison to the existing estimation. My work related to the R2D board has included the following: creating two connector cables (one to power the circuit and one to get readable output off the board), writing Simulink code to process the board's output, and building a dSpace panel to control and monitor the circuit. The next step in the process will be to perform tests to compare the estimated rotor position and speed from the sensorless algorithm to the actual rotor and speed from the resolver signal.

Fehrmann, Elizabeth A.

Mechanical Characterization of ZnSe Windows for Use With the Flow Enclosure Accommodating Novel Investigations in Combustion of Solids (FEANICS) Module

Mechanical and physical properties of ZnSe windows to be used with the FEANICS (Flow Enclosure Accommodating Novel Investigations in Combustion of Solids) experiments were measured in order to determine design allowables. The average Young s modulus, Poisson's ratio, equibiaxial fracture strength, flaw size, grain size, Knoop hardness, Vicker s hardness, and branching constant were 74.3 +/- 0.1 GPa, 0.31, 57.8 +/- 6.5 MPa, 21 +/- 4 mm, 43 +/- 9 microns, 0.97 +/- 0.02 GPa, 0.97 +/- 0.02 GPa, and 1.0 +/- 0.1 MPa(square root of)m, respectively. The properties of current ZnSe made by chemical vapor deposition are in good agreement with those measured in the 1970 s. The hardness of CVD ZnSe windows is about one-twentieth of the sapphire window being replaced, and about one-sixth of that of window glass. Thus the ZnSe window must be handled with great care. The large grain size relative to the inherent crack size implies the need to use single crystal crack growth properties in the design process. In order to determine the local failure stresses in one of the test specimens, a solution for the stresses between the support ring and the edge of a circular plate load between concentric rings was derived

Salem, Jonathan A.

Mechanical Properties of ZnSe for the FEANICS Module

Mechanical and physical properties of ZnSe windows to be used with the FEANICS (Flow Enclosure Accommodating Novel Investigations in Combustion of Solids) experiments were measured in order to determine design allowables. In addition, the literature on crack growth properties was summarized. The average Young's modulus, Poisson's ratio, equibiaxial fracture strength, flaw size, grain size, Knoop hardness, Vicker's hardness, and branching constant were 74.3 +/- 0.1 GPa, 0.31, 57.8 +/- 6.5 MPa, 21 4 mm, 43 +/- 9 micron, 0.97 +/- 0.02 GPa, 0.97 +/- 0.02 GPa, and 1.0 +/- 0.1 MPam(exp 0.5), respectively. The properties of current ZnSe made by chemical vapor deposition are in good agreement with those measured in the 1970's. The hardness of CVD ZnSe windows is about one twentieth of the sapphire window being replaced, and about one-sixth of that of window glass. Thus the ZnSe window must be handled with great care. The large grain size relative to the inherent crack size implies the need to use single crystal crack growth properties in the design process. In order to determine the local failure stresses in one of the test specimens, a solution for the stresses between the support ring and the edge of a circular plate load between concentric rings was derived.

Salem, Jon

Air Coupled Acoustic Thermography (ACAT) Inspection Technique

The scope of this effort is to determine the viability of a new heating technique using a noncontact acoustic excitation source. Because of low coupling between air and the structure, a synchronous detection method is employed. Any reduction in the out of plane stiffness improves the acoustic coupling efficiency and as a result, defective areas have an increase in temperature relative to the surrounding area. Hence a new measurement system, based on air-coupled acoustic energy and synchronous detection is presented. An analytical model of a clamped circular plate is given, experimentally tested, and verified. Repeatability confirms the technique with a measurement uncertainty of plus or minus 6.2 percent. The range of frequencies used was 800-2,000 Hertz. Acoustic excitation and consequent thermal detection of flaws in a helicopter blade is examined and results indicate that air coupled acoustic excitation enables the detection of core damage in sandwich honeycomb structures.

Zalameda, Joseph

Comparing Two Weather-Robust Microphone Configurations for Outdoor Measurements

This paper discusses comparisons made between two ground-based outdoor microphone configurations. The first is known as the Compact Outdoor Unit for Ground-based Acoustical Recordings (COUGAR) and consists of an inverted microphone placed above a convex circular plate and covered by a large dome windscreen. The second configuration is the COUGARxt, where the “xt” simultaneously refers to an extra thick windscreen and an extra thin ground plate. COUGAR and COUGARxt were subjected to laboratory testing where their responses to sound were recorded at several different elevation and azimuthal angles. At almost all shown elevation angles, both configurations recorded levels that were within ±3 dB of a baseline measurement between 50 Hz – 20 kHz. At all shown azimuthal angles and over the same frequency range, both recorded levels within ±2 dB of the levels reported at an azimuthal angle of 0°, with COUGARxt having less variation than COUGAR. The configurations were also subjected to wind noise testing, where COUGARxt demonstrated superior wind noise rejection at low frequencies. The conclusion is that both configurations are suitable for outdoor acoustical measurements and that COUGARxt is the superior configuration, especially when measuring low-frequency noise.

sonic boom

Tailoring the Stiffness of Large Mirrors to Reduce Specific Optical Aberrations

Presented is a method that tailors the geometry of a mirror’s core structure as well as the mounting interface such that a desired set of aberrations is reduced. It will be shown that targeting specific aberrations as opposed to reducing overall surface figure error (SFE) is a valid method to reduce weight or improve performance. Analyzed first is the self-weight deflection of a thin circular plate of uniform thickness continuously supported along its outer edge. The Kirchhoff-Love plate bending equations are related to the radially symmetric Zernike polynomials of piston, defocus, and primary spherical aberration. Next, the mirror’s radial thickness is optimized to eliminate primary and secondary spherical aberrations when the outer edge is simply supported. As an example, the method is demonstrated using a 2-meter diameter aluminum mirror where surface deflections can have an appreciable effect at mid-to-near infrared wavelengths

mirror stiffness optimization

Numerical Simulation of Inlet Bleed with Circular Holes on Plate Under Shock-Wave/Boundary-Layer Interactions

A numerical study was performed to investigate the shock-wave/boundary-layer interactions on a flat plate with bleed through one or more circular holes that vent into a plenum. The bleed-hole patterns considered for the study include in-line multiple holes and staggered multiple-row holes that are configured to simulate the patterns used in inlet bleed systems of high performance aircraft. The focus of the study was to examine how the bleed through multiple holes affect bleed rate and the pressure and Mach number distributions. Since the bleed performance was found sensitive to the change in bleed conditions, a computational procedure was developed to give a good turnaround computational time for parametric studies involving changes in bleed hole geometry and the structure of shock-wave/boundary-layer flowfield. The procedure includes the grid-generation methodology and the flow simulation with solutions from the Navier-Stokes equations. The computational techniques permit analysis of complex bleed systems and make possible the investigation of a broader range of design variables associated with inlet bleed operation.

Chyu, Wei J.

The use of curvilinear fiber format to improve buckling resistance of plates with central circular holes

The potential gain in buckling resistance is explored by using the curvilinear format with a plate containing a centrally located circular hole and subjected to a uniaxial compressive load. The buckling loads for a uniform stress loading and simple support boundary conditions were examined. The method of analysis is outlined for the buckling improvement study. Several designs that represent an improvement over a baseline quasi-isotropic design (a design that is quite good for buckling resistance) are discussed. The tensile load of these designs is examined. A recommended design is presented that not only shows an improved buckling capacity, but also shows improved tensile performance. Follow-on activities are also discussed.

Lee, H. H.

Stress concentration factors for cylindrically orthotropic plates

Stress concentration factors are presented for circular holes in circular composite plates of cylindrical orthotropy when the outer edge of the plate is subjected to uniform uniaxial traction. The values that can be calculated from the formulas presented and the values shown in the diagrams are valid rigorously only for the circular plate but they can be used as approximation for differently shaped (for instance, rectangular) finite plates also.

Hoff, N. J.

Failure mechanisms of uni-ply composite plates with a circular hole under static compressive loading

The objective of the study was to identify and study the failure mechanisms associated with compressive-loaded uniply graphite/epoxy square plates with a central circular hole. It is found that the type of compressive failure depends on the hole size. For large holes with the diameter/width ratio exceeding 0.062, fiber buckling/kinking initiated at the hole is found to be the dominant failure mechanism. In plates with smaller hole sizes, failure initiates away from the hole edge or complete global failure occurs. Critical buckle wavelengths at failure are presented as a function of the normalized hole diameter.

Khamseh, A. R.

Compression failure mechanisms of uni-ply composite plates with a circular cutout

The effect of circular-hole size on the failure mode of uniply graphite-epoxy composite plates is investigated experimentally and analytically for uniaxial compressive loading. The test specimens are sandwiched between polyetherimide plastic for nondestructive evaluations of the uniply failure mechanisms associated with a range of hole sizes. Finite-element modeling based on classical lamination theory is conducted for the corresponding materials and geometries to reproduce the experimental results analytically. The type of compressive failure is found to be a function of hole size, with fiber buckling/kinking at the hole being the dominant failure mechanism for hole diam/plate width ratios exceeding 0.062. The results of the finite-element analysis supported the experimental data for these failure mechanisms and for those corresponding to smaller hole sizes.

Khamseh, A. R.