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At least 1,135 records · Page 63

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Casasent, D.↗

Design for temperature and thermal buckling constraints employing a noneigenvalue formulation

A numerical procedure for simultaneous consideration of structural/thermal interactions during aircraft design is presented, with an emphasis on reentry vehicles such as the Orbiter. It has been shown that sequential design is inappropriate for reentry vehicles, due to the degradation of the material properties at elevated reentry temperatures. Attention is focused on thermal buckling, using an analytical technique that involves requiring that the stability matrix be positive definite, with the diagonal terms on the Gauss-Doolittle factor of the matrix also constrained to be positive. A finite element method is employed to calculate the derivative of the diagonal matrix, with optimization achieved by minimization of the mass of the structure and thermal protection system. Sample calculations are presented in terms of the aluminum structure and insulation for a section of the Orbiter wing bay.

Haftka, R. T.↗

Numerical analysis of free vibrations of damped rotating structures

This paper is concerned with the efficient numerical solution of damped and undamped free vibration problems of rotating structures. While structural discretization is achieved by the finite element method, the associated eigenproblem solution is effected by a combined Sturm sequence and inverse iteration technique that enables the computation of a few required roots only without having to compute any other. For structures of complex configurations, a modal synthesis technique is also presented, which is based on appropriate combinations of eigenproblem solution of various structural components. Such numerical procedures are general in nature, which fully exploit matrix sparsity inherent in finite element discretizations, and prove to be most efficient for the vibration analysis of any damped rotating structure, such as rotating machineries, helicopter and turbine blades, spinning space stations, among others.

Gupta, K. K.↗

Development of a finite dynamic element for free vibration analysis of two-dimensional structures

The paper develops an efficient free-vibration analysis procedure of two-dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free-vibration analysis presented herein clearly indicate that these dynamic elements combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.

Gupta, K. K.↗

Fillers for improved graphite fiber retention by polymer matrix composites

The results of a program designed to determine the extent to which elemental boron and boron containing fillers added to the matrix resin of graphite/epoxy composites prevent the release of graphite fibers when the composites are exposed to fire and impact conditions are described. The fillers evaluated were boron, boron carbide and aluminum boride. The conditions evaluated were laboratory simulations of those that could exist in the event of an aircraft crash and burn situation. The baseline (i.e., unfilled) laminates evaluated were prepared from commercially available graphite/epoxy. The baseline and filled laminates' mechanical properties, before and after isothermal and humidity aging, also were compared. It was found that a small amount of graphite fiber was released from the baseline graphite/epoxy laminates during the burn and impact conditions used in this program. However, the extent to which the fibers were released is not considered a severe enough problem to preclude the use of graphite reinforced composites in civil aircraft structure. It also was found that the addition of boron and boron containing fillers to the resin matrix eliminated this fiber release. Mechanical properties of laminates containing the boron and boron containing fillers were lower than those of the baseline laminates. These property degradations for two systems: boron (5 micron) at 2.5 percent filler loading, and boron (5 micron) at 5.0 percent filler loading do not appear severe enough to preclude their use in structural composite applications.

House, E. E.↗

Majorana versus Dirac Constraints on the Neutrino Dipole Moments

Massive neutrinos are guaranteed to have nonzero electromagnetic moments and, since there are at least three neutrino species, these dipole moments define a matrix. Here, we estimate the current upper bounds on all independent neutrino electromagnetic moments, concentrating on Earth-bound experiments and measurements with solar neutrinos, including the very recent results reported by XENONnT. We make no simplifying assumptions and compare the hypotheses that neutrinos are Majorana fermions or Dirac fermions. In particular, we fully explore constraints in the Dirac-neutrino parameter space. Majorana and Dirac neutrinos are different; for example, the upper bounds on the magnitudes of the elements of the dipole moment matrix are weaker for Dirac neutrinos, relative to Majorana neutrinos. The potential physics reach of next-generation experiments also depends on the nature of the neutrino. We find that a next-generation experiment two orders of magnitude more sensitive to the neutrino electromagnetic moments via $\nu_{\mu}$ elastic scattering may discover that the neutrino electromagnetic moments are nonzero if the neutrinos are Dirac fermions. Instead, if the neutrinos are Majorana fermions, such a discovery is ruled out by existing solar neutrino data, unless there are more than three light neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Eigenvalue computations with the QUAD4 consistent-mass matrix

The NASTRAN user has the option of using either a lumped-mass matrix or a consistent- (coupled-) mass matrix with the QUAD4 shell finite element. At the Sixteenth NASTRAN Users' Colloquium (1988), Melvyn Marcus and associates of the David Taylor Research Center summarized a study comparing the results of the QUAD4 element with results of other NASTRAN shell elements for a cylindrical-shell modal analysis. Results of this study, in which both the lumped-and consistent-mass matrix formulations were used, implied that the consistent-mass matrix yielded poor results. In an effort to further evaluate the consistent-mass matrix, a study was performed using both a cylindrical-shell geometry and a flat-plate geometry. Modal parameters were extracted for several modes for both geometries leading to some significant conclusions. First, there do not appear to be any fundamental errors associated with the consistent-mass matrix. However, its accuracy is quite different for the two different geometries studied. The consistent-mass matrix yields better results for the flat-plate geometry and the lumped-mass matrix seems to be the better choice for cylindrical-shell geometries.

Butler, Thomas A.↗

Chemical, isotopic and mineralogical evidence for the origin of matrix in ordinary chondrites

Results are presented of a combined chemical, isotopic, and mineralogical study of fine-grained opaque matrix material from a type-3 ordinary chondrite Allan Hills A77299. It was found that the matrix of this chondrite (in contrast to chondrules) shows no siderophile element depletions and is remarkably unfractionated relative to CI chondrites. It was also found that the matrix lump has a unique oxygen isotopic composition which lies below the terrestrial fractionation line and differs markedly from the composition of fine-grained matrix lumps and chondrule rims from Semarkona chondrules (Grossman and Wasson, 1987; Grossman et al., 1987); the mineralogy and textures of the matrix lump (which consists of rare angular grains of pyroxene and olivine embedded within a ground-mass of rounded fine-grained olivines), as well as its major element composition, are typical of matrix material of other type-3 chondrites studied. It is concluded that the matrix lump in these chondrites consists largely of material that formed by annealing of amorphous presolar dust or nebular condensates.

Brearley, Adrian J.↗

Microwave Cavity Simulation Using Ansys HFSS

The design of microwave cavity detectors for axion dark matter research is often accomplished using advanced full-wave electromagnetic simulation software tools. These tools provide a cost-effective approach to evaluate a wide variety of cavity configurations, frequency tuning mechanisms, and conductive or dielectric materials and coatings. One simulation software package used for this application is Ansys High Frequency Structure Simulator (HFSS), which is based upon the well-established finite element method. HFSS includes numerous features useful for microwave cavity design such as parametric geometry modeling, adaptive meshing algorithm, curvilinear mesh elements, driven modal and eigenmode matrix solvers, and optimization algorithms. This paper describes the use of the HFSS software to simulate microwave cavities for axion haloscope detectors, with an example tutorial for a cylindrical cavity. Excellent agreement between the simulated and analytical results is shown for the resonant frequency, quality factor, and form factor.

Ansys HFSS, Cavity simulation, finite element mode↗

Polymer matrix and graphite fiber interface study

Hercules AS4 graphite fiber, unsized, or with EPON 828, PVA, or polysulfone sizing, was combined with three different polymer matrices. These included Hercules 3501-6 epoxy, Hercules 4001 bismaleimide, and Hexcel F155 rubber toughened epoxy. Unidirectional composites in all twelve combinations were fabricated and tested in transverse tension and axial compression. Quasi-isotropic laminates were tested in axial tension and compression, flexure, interlaminar shear, and tensile impact. All tests were conducted at both room temperature, dry and elevated temperature, and wet conditions. Single fiber pullout testing was also performed. Extensive scanning electron microphotographs of fracture surfaces are included, along with photographs of single fiber pullout failures. Analytical/experimental correlations are presented, based on the results of a finite element micromechanics analysis. Correlations between matrix type, fiber sizing, hygrothermal environment, and loading mode are presented. Results indicate that the various composite properties were only moderately influenced by the fiber sizings utilized.

Adams, D. F.↗

A micromechanics analysis of the influence of the interface on the performance of polymer-matrix composites

A specially developed two-dimensional finite element micromechanics analysis was used to predict the transverse tensile response of three different carbon fiber-reinforced, polymer matrix unidirectional composites. Experimental data were available for four different fiber sizings. The composites were tested both dry and moisture-conditioned, at room and elevated temperatures. Analytical/experimental correlations are presented and discussed.

Adams, Donald F.↗

A micromechanics analysis of the influence of the interface on the performance of polymer-matrix composites

A specially developed two-dimensional finite element micromechanics analysis was used to predict the transverse tensile response of three different carbon fiber-reinforced, polymer matrix unidirectional composites. Experimental data were available for four different fiber sizings. The composites were tested both dry and moisture-conditioned, at room and elevated temperatures. Analytical/experimental correlations are presented and discussed.

Adams, Donald F.↗

Optical implementation of an iterative algorithm for matrix inversion

The incorporation of a photorefractive gain element into a confocal Fabry-Perot processor, with a photorefractive BaTiO3 crystal in the feedback path providing the coherent image amplification, is discussed. The implementation of an iterative algorithm for matrix inversion is described, and its experimental implementation is demonstrated. It is shown that the BaTiO3 amplifier provides loss compensation and coherence restoration of the feedback signal, thereby increasing the effective number of iterations in the algorithm. Thus, the technique makes it possible to implement slowly converging (as well as rapidly converging) algorithms.

Rajbenbach, Henri↗

Unsteady transonic Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented and demonstrated for 2D airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage Runge-Kutta scheme to march forward in time. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite-volume techniques. The effects of using either a lumped or consistent mass matrix are presented; the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils.

Davis, Gary A.↗

Shock Effects in the Metal-rich Chondrites QUE 94411, Hammadah al Hamra 237 and Bencubbin

We have studied the metal-rich chondrites QUE94411 (QUE), Hammadah al Hamra 237 (HH237) and Bencubbin with an emphasis on the petrographical and mineralogical effects of the shock processing that these meteorite assemblages have undergone. Iron-nickel metal and chondrule silicates are the main components in these meteorites. These high-temperature components are held together by shock melts consisting of droplets of dendritically intergrown FeNi metal/sulfide embedded in ferrous silicate glass. The silicate glass component of the shock melt is substantially more FeO-rich (FeO: 30 to 40 wt%) than the prevailing chondrule silicates (FeO less than 5 wt%). Fine-grained matrix material, which is a major component in most other chondritic assemblages, is extremely scarce in QUE4411 and HH237; it has not been observed in Bencubbin. This material occurs as rare, hydrated, and fine-grained matrix lumps with major and minor element abundances roughly similar to the ferrous silicate shock melts (and CI). We infer that hydrated, fine-grained material, compositionally similar to these matrix lumps, was originally present between the FeNi metal grains and chondrules, but was preferentially heated by the shock wave and melted. Other shock-related features in QUE94411, HH237, and Bencubbin include a distinct alignment and occasionally strong plastic deformation of metal and chondrule fragments. However, the existence of chemically zoned and metastable FeNi metal condensates condensates in direct contact with shock melts indicates that the shock did not substantially increase the average temperature of the aggregate. TEM analyses of the FeNi metal droplets embedded in the shock melts show martensitic crystal structures, indicating rapid cooling, essentially quenching, of the shock melts. These findings indicate that the preshock temperature of the assemblage was low. Because porphyritic olivine-pyroxene chondrules are absent in QUE94411, HH237, and Bencubbin, it is difficult to determine the precise shock stage of these meteorites, but the shock was probably relatively light (S2- S3; 5-20 GPa) consistent with a bulk temperature increase of the assemblages of less than 200 C. The higher pressures within this range (i.e. 15-20 GPa) are consistent with the findings of shock produced diamonds in Bencubbin. The many mineralogical, petrological and isotopic (e.g. O and N) similarities between Bencubbin, Weatherford, Gujba and QUE/HH237 have been used to argue for a common origin of these meteorites on a single asteroidal parent body. The findings of this study, which indicate similar shock processing, lend support to this view.

Meibom, A.↗

Method and apparatus for shape-based energy analysis of solids

A computer-readable medium stores instructions including storing a model of a physical structure and defining a mesh for the model. The mesh includes finite elements, each defined by a respective set of edges. The instructions include, for each finite element, identifying a governing differential equation and a set of complementary functions that exactly satisfy the governing differential equation. The instructions include determining an applied physical stimulus for the physical structure. The instructions include generating an energy optimization model that minimizes a difference between internal energy and external energy of the finite elements in response to the applied physical stimulus. The model includes a matrix of respective scalar multipliers for the complementary functions for each finite element. The instructions include transforming the matrix and calculating a physical parameter of interest. The instructions include, in response to the physical parameter not satisfying a design parameter, updating the model of the physical structure.

Spears, Robert E.↗

Hourglass control in staggered-grid hydrodynamics using virtual element stabilization techniques

Numerical simulations using the staggered-grid hydrodynamics (SGH) discretization suffer from hourglass instabilities. In this work, we develop a stabilization method to suppress the hourglass instabilities using techniques from the virtual element method (VEM). The stiffness matrix of the VEM consists of two terms: the consistency matrix which is rank deficient and the stability matrix. Here, we first show that in two dimensions and on general polygons, the stiffness matrix of the SGH is identical to the consistency matrix of the linear VEM for both the diffusion equation and the linear elasticity equation. These analyses explain the origin of the hourglass instabilities of the SGH discretization method, and establish a theoretical foundation for our proposed stabilization method by augmenting the stiffness matrix of the SGH discretization using the VEM stability matrix. Then, we present numerical examples using Lagrangian SGH simulations. The numerical experiments demonstrate that the proposed VEM stabilization method is effective at eliminating hourglass modes in the SGH discretization.

97 MATHEMATICS AND COMPUTING↗