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At least 199 records · Page 11

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NASA NTRS1947

Determination of elastic stresses in gas-turbine disks

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Manson, S S↗

NASA NTRS1950

The longitudinal stability of elastic swept wings at supersonic speed

The longitudinal stability characteristics of elastic swept wings of high aspect ratio experiencing bending and torsional deformations are calculated for supersonic speed by the application of linearized lifting-surface theory. A parabolic wing deflection curve is assumed and the analysis is simplified by a number of structural approximations. The method is thereby limited in application to wings of high aspect ratio for which the root effects are small. Expressions for the lift, pitching-moment, and span load distribution characteristics are derived in terms of the elastic properties of the wing; namely, the design stress, the modulus of elasticity, the shearing modulus, and the maximum design load factor. The analysis applies to wings with leading edges swept behind the Mach lines. In all cases, however, the trailing edge is sonic or supersonic. Application of the method of analysis to wings with leading edges swept ahead of the Mach lines is discussed.

Frick, C W↗

NASA NTRS1993

Elastic plastic fracture mechanics methodology for surface cracks

The Elastic Plastic Fracture Mechanics (EPFM) Methodology has evolved significantly in the last several years. Nevertheless, some of these concepts need to be extended further before the whole methodology can be safely applied to structural parts. Specifically, there is a need to include the effect of constraint in the characterization of material resistance to crack growth and also to extend these methods to the case of 3D defects. As a consequence, this project was started as a 36 month research program with the general objective of developing an EPFM methodology to assess the structural reliability of pressure vessels and other parts of interest to NASA containing defects. This report covers a computer modelling algorithm used to simulate the growth of a semi-elliptical surface crack; the presentation of a finite element investigation that compared the theoretical (HRR) stress field to that produced by elastic and elastic-plastic models; and experimental efforts to characterize three dimensional aspects of fracture present in 'two dimensional', or planar configuration specimens.

Ernst, Hugo A.↗

NASA NTRS1993

Effective elastic thickness of the Venusian lithosphere with lateral viscosity variations in the mantle

Both the Earth and Venus have a convecting mantle at the top of which is a relatively strong, mechanical boundary layer. The surface topography and gravity signals which result from the convection within the viscous mantle are modified by the elastic properties of this lithospheric boundary layer. In particular the ability of the lithosphere to support loads and transmit stresses from below is a function of the wavelength of the load--the lithosphere is strong to loading at shorter wavelengths. As a consequence it is usual to expect that long wavelength topography cannot be supported by the mechanical strength of the lithosphere and must be compensated--isostatically or dynamically--within the uppermost mantle or the crust. The flexural rigidity of the lithosphere can therefore be determined by estimating the greatest wavelength at which uncompensated surface topography can be supported, usually by measuring the admittance as a function of wavelength. In fact this procedure for determining the elastic thickness relies upon being able to distinguish topography with underlying support from that supported by the brittle lithosphere on the basis of their each having a characteristic value of the admittance. However, in the presence of lateral viscosity variations in the mantle, it is possible for topography to be generated which is NOT compensated by density anomalies in the underlying mantle at the same wavelength. Although this effect is not likely to be important for the Earth, on Venus, where the high surface temperatures would be expected to give a weaker lithosphere, lateral viscosity variations in the mantle can give a misleadingly large apparent elastic thickness for the lithosphere.

Moresi, Louis↗

NASA NTRS1994

Dynamic analysis of pretwisted elastically-coupled rotor blades

The accuracy of using a one-dimensional analysis to predict frequencies of elastically-coupled highly-twisted rotor blades is addressed. Degrees of freedom associated with shear deformation are statically condensed from the formulation, so the analysis uses only those degrees of freedom associated with classical beam theory. The effects of cross section deformation (warping) are considered, and are shown to become significant for some types of elastic coupling. Improved results are demonstrated for highly-coupled blade structures through account of warping in a local cross section analysis, without explicit inclusion of these effects in the beam analysis. A convergence study is also provided which investigates the potential for improving efficiency of elastically-coupled beam analysis through implementation of a p-version beam finite element.

Nixon, Mark W.↗

NASA NTRS1994

Scaling, elasticity, and CLPT

The first few viewgraphs describe the general solution properties of linear elasticity theory which are given by the following two statements: (1) for stress B.C. on S(sub sigma) and zero displacement B.C. on S(sub u) the altered displacements u(sub i)(*) and the actual stresses tau(sub ij) are elastically dependent on Poisson's ratio nu alone: thus the actual displacements are given by u(sub i) = mu(exp -1)u(sub i)(*); and (2) for zero stress B.C. on S(sub sigma) and displacement B.C. on S(sub u) the actual displacements u(sub i) and the altered stresses tau(sub ij)(*) are elastically dependent on Poisson's ratio nu alone: thus the actual stresses are given by tau(sub ij) = E tau(sub ij)(*). The remaining viewgraphs describe the minimum parameter formulation of the general classical laminate theory plate problem as follows: The general CLT plate problem is expressed as a 3 x 3 system of differential equations in the displacements u, v, and w. The eighteen (six each) A(sub ij), B(sub ij), and D(sub ij) system coefficients are ply-weighted sums of the transformed reduced stiffnesses (bar-Q(sub ij))(sub k); the (bar-Q(sub ij))(sub k) in turn depend on six reduced stiffnesses (Q(sub ij))(sub k) and the material and geometry properties of the k(sup th) layer. This paper develops a method for redefining the system coefficients, the displacement components (u,v,w), and the position components (x,y) such that a minimum parameter formulation is possible. The pivotal steps in this method are (1) the reduction of (bar-Q(sub ij))(sub k) dependencies to just two constants Q(*) = (Q(12) + 2Q(66))/(Q(11)Q(22))(exp 1/2) and F(*) - (Q(22)/Q(11))(exp 1/2) in terms of ply-independent reference values Q(sub ij); (2) the reduction of the remaining portions of the A, B, and D coefficients to nondimensional ply-weighted sums (with 0 to 1 ranges) that are independent of Q(*) and F(*); and (3) the introduction of simple coordinate stretchings for u, v, w and x,y such that the process is neatly completed.

Brunelle, Eugene J.↗

NASA NTRS1995

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.↗

NASA NTRS1996

Determination of Elastic Moduli of Fiber-Resin Composites Using an Impulse Excitation Technique

The elastic moduli of graphite/epoxy and graphite/cyanate ester composite specimens with various laminate lay-ups was determined using an impulse excitation/acoustic resonance technique and compared to those determined using traditional strain gauge and extensometer techniques. The stiffness results were also compared to those predicted from laminate theory using uniaxial properties. The specimen stiffnesses interrogated ranged from 12 to 30 Msi. The impulse excitation technique was found to be a relatively quick and accurate method for determining elastic moduli with minimal specimen preparation and no requirement for mechanical loading frames. The results of this investigation showed good correlation between the elastic modulus determined using the impulse excitation technique, strain gauge and extensometer techniques, and modulus predicted from laminate theory. The flexural stiffness determined using the impulse excitation was in good agreement with that predicted from laminate theory. The impulse excitation/acoustic resonance interrogation technique has potential as a quality control test.

Viens, Michael J.↗

NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗

NASA NTRS1995

An Experimental Study of Incremental Surface Loading of an Elastic Plate: Application to Volcano Tectonics

Models of surface fractures due to volcanic loading an elastic plate are commonly used to constrain thickness of planetary lithospheres, but discrepancies exist in predictions of the style of initial failure and in the nature of subsequent fracture evolution. In this study, we perform an experiment to determine the mode of initial failure due to the incremental addition of a conical load to the surface of an elastic plate and compare the location of initial failure with that predicted by elastic theory. In all experiments, the mode of initial failure was tension cracking at the surface of the plate, with cracks oriented circumferential to the load. The cracks nucleated at a distance from load center that corresponds the maximum radial stress predicted by analytical solutions, so a tensile failure criterion is appropriate for predictions of initial failure. With continued loading of the plate, migration of tensional cracks was observed. In the same azimuthal direction as the initial crack, subsequent cracks formed at a smaller radial distance than the initial crack. When forming in a different azimuthal direction, the subsequent cracks formed at a distance greater than the radial distance of the initial crack. The observed fracture pattern may explain the distribution of extensional structures in annular bands around many large scale, circular volcanic features.

Williams, K. K.↗

NASA NTRS2001

Stress Formulation in Three-Dimensional Elasticity

The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation: differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function. This Completed Beltrami-Michell Formulation (CBMF) can be specialized to derive the traditional methods, but the reverse is not possible. Elasticity solutions must be verified for the compliance of the new equation because the boundary compatibility conditions expressed in terms of displacement are not trivially satisfied. This paper presents the variational derivation of the stress formulation, illustrates the method, examines attributes and benefits, and outlines the future course of research.

Patnaik, Surya N.↗

NASA NTRS2003

An Airline-Based Multilevel Analysis of Airfare Elasticity for Passenger Demand

Price elasticity of passenger demand for a specific airline is estimated. The main drivers affecting passenger demand for air transportation are identified. First, an Ordinary Least Squares regression analysis is performed. Then, a multilevel analysis-based methodology to investigate the pattern of variation of price elasticity of demand among the various routes of the airline under study is proposed. The experienced daily passenger demands on each fare-class are grouped for each considered route. 9 routes were studied for the months of February and May in years from 1999 to 2002, and two fare-classes were defined (business and economy). The analysis has revealed that the airfare elasticity of passenger demand significantly varies among the different routes of the airline.

Castelli, Lorenzo↗

NASA NTRS2006

Modeling the Elastic Modulus of 2D Woven CVI SiC Composites

The use of fiber, interphase, CVI SiC minicomposites as structural elements for 2D-woven SiC fiber reinforced chemically vapor infiltrated (CVI) SiC matrix composites is demonstrated to be a viable approach to model the elastic modulus of these composite systems when tensile loaded in an orthogonal direction. The 0deg (loading direction) and 90deg (perpendicular to loading direction) oriented minicomposites as well as the open porosity and excess SiC associated with CVI SiC composites were all modeled as parallel elements using simple Rule of Mixtures techniques. Excellent agreement for a variety of 2D woven Hi-Nicalon(TradeMark) fiber-reinforced and Sylramic-iBN reinforced CVI SiC matrix composites that differed in numbers of plies, constituent content, thickness, density, and number of woven tows in either direction (i.e, balanced weaves versus unbalanced weaves) was achieved. It was found that elastic modulus was not only dependent on constituent content, but also the degree to which 90deg minicomposites carried load. This depended on the degree of interaction between 90deg and 0deg minicomposites which was quantified to some extent by composite density. The relationships developed here for elastic modulus only necessitated the knowledge of the fractional contents of fiber, interphase and CVI SiC as well as the tow size and shape. It was concluded that such relationships are fairly robust for orthogonally loaded 2D woven CVI SiC composite system and can be implemented by ceramic matrix composite component modelers and designers for modeling the local stiffness in simple or complex parts fabricated with variable constituent contents.

Morscher, Gregory N.↗

NASA NTRS2007

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.

Patnaik, Surya N.↗

NASA NTRS2007

Local Elastic Constants for Epoxy-Nanotube Composites from Molecular Dynamics Simulation

A method from molecular dynamics simulation is developed for determining local elastic constants of an epoxy/nanotube composite. The local values of C11, C33, K12, and K13 elastic constants are calculated for an epoxy/nanotube composite as a function of radial distance from the nanotube. While the results possess a significant amount of statistical uncertainty resulting from both the numerical analysis and the molecular fluctuations during the simulation, the following observations can be made. If the size of the region around the nanotube is increased from shells of 1 to 6 in thickness, then the scatter in the data reduces enough to observe trends. All the elastic constants determined are at a minimum 20 from the center of the nanotube. The C11, C33, and K12 follow similar trends as a function of radial distance from the nanotube. The K13 decreases greater distances from the nanotube and becomes negative which may be a symptom of the statistical averaging.

Frankland, S. J. V.↗

NASA NTRS2002

Remote magneto-elastic analyte, viscosity and temperature sensing apparatus and associated methods of sensing

An analyte, viscosity, or temperature sensing apparatus for operative arrangement within a time-varying magnetic field, including a sensor with an outer surface that is chemically, frictionally, or thermally responsive and adhered to a base magnetostrictive element, and a receiver to measure a first and second value for magneto-elastic emission intensity of the sensor taken at, respectively, a first and second interrogation frequency. A change in mass or a change in material stiffness of the sensor due to the responsiveness, the viscosity and mass density of a fluid therearound, or the temperature, can be identified. The receiver, alternatively, measures a plurality of successive values for magneto-elastic emission intensity of the sensor taken over an operating range of successive interrogation frequencies to identify a value for the sensor's magneto-elastic resonant frequency (a fundamental frequency or harmonic thereof). Several sensors in an ordered array will provide a package of information.

Grimes, Craig A.↗

NASA NTRS2009

Tailoring Elastic Properties of Silica Aerogels Cross-Linked with Polystyrene

The effect of incorporating an organic linking group, 1,6-bis(trimethoxysilyl)hexane (BTMSH), into the underlying silica structure of a styrene cross-linked silica aerogel is examined. Vinyltrimethoxysilane (VTMS) is used to provide a reactive site on the silica backbone for styrene polymerization. Replacement of up to 88 mol 1 of the silicon from tetramethoxyorthosilicate with silicon derived from BTMSH and VTMS during the making of silica gels improves the elastic behavior in some formulations of the crosslinked aerogels, as evidenced by measurement of the recovered length after compression of samples to 251 strain. This is especially true for some higher density formulations, which recover nearly 100% of their length after compression to 251 strain twice. The compressive modulus of the more elastic monoliths ranged from 0.2 to 3 MPa. Although some of these monoliths had greatly reduced surface areas, changing the solvent used to produce the gels from methanol to ethanol increased the surface area in one instance from 6 to 220 sq m2/g with little affect on the modulus, elastic recovery, porosity, or density.

Nguyen, Baochau N.↗

NASA NTRS2010

Turbofan Volume Dynamics Model for Investigations of Aero-Propulso-Servo-Elastic Effects in a Supersonic Commercial Transport

A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model

Connolly, Joseph W.↗