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At least 1,297 records · Page 72

Tungsten wire/FeCrAlY matrix turbine blade fabrication study

The objective was to establish a viable FRS monotape technology base to fabricate a complex, advanced turbine blade. All elements of monotape fabrication were addressed. A new process for incorporation of the matrix, including bi-alloy matrices, was developed. Bonding, cleaning, cutting, sizing, and forming parameters were established. These monotapes were then used to fabricate a 48 ply solid JT9D-7F 1st stage turbine blade. Core technology was then developed and first a 12 ply and then a 7 ply shell hollow airfoil was fabricated. As the fabrication technology advanced, additional airfoils incorporated further elements of sophistication, by introducing in sequence bonded root blocks, cross-plying, bi-metallic matrix, tip cap, trailing edge slots, and impingement inserts.

Melnyk, P.↗

Modes of interconnected lattice trusses using continuum models, part 1

This represents a continuing systematic attempt to explore the use of continuum models--in contrast to the Finite Element Models currently universally in use--to develop feedback control laws for stability enhancement of structures, particularly large structures, for deployment in space. We shall show that for the control objective, continuum models do offer unique advantages. It must be admitted of course that developing continuum models for arbitrary structures is no easy task. In this paper we take advantage of the special nature of current Large Space Structures--typified by the NASA-LaRC Evolutionary Model which will be our main concern--which consists of interconnected orthogonal lattice trusses each with identical bays. Using an equivalent one-dimensional Timoshenko beam model, we develop an almost complete continuum model for the evolutionary structure. We do this in stages, beginning only with the main bus as flexible and then going on to make all the appendages also flexible-except for the antenna structure. Based on these models we proceed to develop formulas for mode frequencies and shapes. These are shown to be the roots of the determinant of a matrix of small dimension compared with mode calculations using Finite Element Models, even though the matrix involves transcendental functions. The formulas allow us to study asymptotic properties of the modes and how they evolve as we increase the number of bodies which are treated as flexible. The asymptotics, in fact, become simpler.

Balakrishnan, A. V.↗

Deleterious Phase Formation in Next- Generation Nickel-Base Superalloys Predicted

Nickel- (Ni-) base superalloy single crystals represent the state-of-the-art for turbine engine airfoil applications because they offer the best balance of properties under the high operating temperatures required for efficient engine operation. Current trends in alloy design take advantage of improved creep rupture strength with the addition of higher levels of refractory elements. In particular, the addition of significantly higher levels of rhenium in third-generation superalloys is key for both microstructural stability and creep rupture strength. Although refractories provide strength benefits, alloys tend to be unstable when their refractory content is high because of topologically close-packed (TCP) phases. The formation of these phases in sufficient amount is detrimental to the performance of these alloys because of their brittle nature and because they deplete the Nirich matrix of potent solid-solution strengthening elements.

Ritzert, Frank J.↗

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗

Particle Identification in the ACCESS Mission

ACCESS (Assembly Concept for Construction of Erectable Space Structures) is a planned Space Station mission to measure the elemental energy spectra of Galactic cosmic rays at energies above 100 GeV/nuc. ACCESS consists of a transition radiation detector (TRD) mounted on top of an ionization calorimeter (IC). A silicon matrix detector placed on top of the IC determines the elemental identity of each cosmic ray measured by the IC. The silicon matrix must be designed to identify each cosmic ray in the presence of backscatter from the calorimeter. Because the TRD is mounted above the IC, the matrix must also recognize cosmic rays that have interacted within the TRD before reaching the IC. We will report the results of detailed GEANT simulations of the silicon matrix in ACCESS. Results will be presented on backscatter interference with charge identification and the ability of the matrix to recognize cosmic rays that interacted in the TRD.

Wang, J. Z.↗

Incorporation of Damage and Failure into an Orthotropic Elasto-Plastic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in LS-DYNA(Registered Trademark) is under development. In particular, the material model, which is being implemented as MAT 213 into a tailored version of LS-DYNA being jointly developed by the FAA and NASA, incorporates both plasticity and damage within the material model, utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength), and is able to analyze the response of composites composed with a variety of fiber architectures. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The onset of material failure, and thus element deletion, is being developed to be a function of the stresses and plastic strains in the various coordinate directions. Systematic procedures are being developed to generate the required input parameters based on the results of experimental tests.

Finite Element Method↗

Modeling Optics For Analyses Of Dynamics And Controls

Method of computing optical sensitivities of single- and multiple-element optical trains developed for analyses of dynamics of optoelectro-mechanical systems, including controlled optics (lenses, mirrors, prisms, and/or gratings mounted on electromechanical actuators) supported by flexible structure. Based on techniques of ray tracing and on matrix representation of each surface of each optical element.

Breckenridge, William C.↗

Brittle failure analysis and modeling of high-burnup PWR fuel cladding alloys

The aim of this research is the development of methods for predicting mechanical behavior and identification of limiting conditions to prevent brittle failure of high-burnup (HBU) pressure water reactor (PWR) fuel cladding alloys. A finite element (FE) model of the ring compression test (RCT) was created to analyze the failure behavior of zirconium-based alloys with radial hydrides during the RCT. An elastic-plastic material model describes the zirconium alloy. The stress-strain curve needed for the elastic-plastic material model was derived by inverse finite element analyses. Cohesive zone modeling is used to reproduce sudden load drops during RCT loading. Based on the failure mechanism in non-irradiated ZIRLO (R) claddings, a micro-mechanical model was developed that distinguishes between brittle failure along hydrides and ductile failure of the zirconium matrix. Two different cohesive laws representing these types of failure are present in the same cohesive interface. The key differences between these constitutive laws are the cohesive strength, the stress at which damage initiates, and the cohesive energy, which is the damage energy dissipated by the cohesive zone. Statistically generated matrix-hydride distributions were mapped onto the cohesive elements and simulations with focus on the first load drop were performed. Computational results are in good agreement with the RCT results conducted on high-burnup M5 (R) samples. It could be shown that crack initiation and propagation strongly depend on the specific configuration of hydrides and matrix material in the fracture area.

Simbruner, Kai↗

Analysis of liquid petroleum using a laser-induced breakdown spectroscopy instrument

Here, a prototype analyzer for the direct LIBS analysis of nebulized liquid samples was developed and tested, particularly for the analysis of petroleum, organic solvents and aqueous solutions. The LIBS analyzer requires about 750 µl of liquid sample, 1 liter of N 2 gas, and 10 s of the analysis time to record 100 spectra. The limits of detection in oil and solvent are as low as 0.01–0.04 ppm for Li, Mg, and Cu. They increase for the difficult elements, such as Pb and Hg (7-10 ppm), Cl (250 ppm), and S (~0.7%). The relative standard deviation of measuring 100 ppm vanadium in oil and solvent was 1.5%. The LIBS detection limits and repeatability are better than required by the standard method ASTM D5185 for the analysis of lubricating oils in ICP-OES. Several petroleum samples were analyzed by LIBS and the quantitative results for V, Ni, and Fe compared to the ICP-OES data. Light crude oils can be nebulized and analyzed directly. Medium crude oils require minimal dilution at least 1:1, otherwise errors of determination become large. Presumably, utilization of the internal standard and chemometrics can be useful to correct for the matrix effects. In addition to the trace element analysis, the LIBS prototype demonstrated ability to measure the hydrogen-to-carbon ratio in organic liquid samples. Several unidentified features were observed in the carbon spectrum. Their possible origin is discussed.

02 PETROLEUM↗

Investigation of Micro-Scale Architectural Effects on Damage of Composites

This paper presents a three-dimensional, energy based, anisotropic, stiffness reduction, progressive damage model for composite materials and composite material constituents. The model has been implemented as a user-defined constitutive model within the Abaqus finite element software package and applied to simulate the nonlinear behavior of a damaging epoxy matrix within a unidirectional composite material. Three different composite microstructures were considered as finite element repeating unit cells, with appropriate periodicity conditions applied at the boundaries. Results representing predicted transverse tensile, longitudinal shear, and transverse shear stress-strain curves are presented, along with plots of the local fields indicating the damage progression within the microstructure. It is demonstrated that the damage model functions appropriately at the matrix scale, enabling localization of the damage to simulate failure of the composite material. The influence of the repeating unit cell geometry and the effect of the directionality of the applied loading are investigated and discussed.

damage↗

Data compression and covariance matrix inspection: Cosmic shear

Covariance matrices are among the most difficult pieces of end-to-end cosmological analyses. In principle, for two-point functions, each component involves a four-point function, and the resulting covariance often has hundreds of thousands of elements. We investigate various compression mechanisms capable of vastly reducing the size of the covariance matrix in the context of cosmic shear statistics. This helps identify which of its parts are most crucial to parameter estimation. We start with simple compression methods, by isolating and “removing” 200 modes associated with the lowest eigenvalues, then those with the lowest signal-to-noise ratio, before moving on to more sophisticated schemes like compression at the tomographic level and, finally, with the massively optimized parameter estimation and data compression (MOPED). We find that, while most of these approaches prove useful for a few parameters of interest, like Ω m , the simplest yield a loss of constraining power on the intrinsic alignment (IA) parameters as well as S 8 . For the case considered—cosmic shear from the first year of data from the Dark Energy Survey—only MOPED was able to replicate the original constraints in the 16-parameter space. Finally, we apply a tolerance test to the elements of the compressed covariance matrix obtained with MOPED and confirm that the IA parameter A IA is the most susceptible to inaccuracies in the covariance matrix.

79 ASTRONOMY AND ASTROPHYSICS↗

A piecewise continuous Timoshenko beam model for the dynamic analysis of tapered beam-like structures

Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.

Shen, Ji Yao↗

Low-Order Preconditioning for the High-Order Finite Element de Rham Complex

Here, we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div) and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart–Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for high-order interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any “black-box” preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, based on an implementation in the finite element library MFEM. A range of challenging three-dimensional problems are used to corroborate the theoretical properties and demonstrate the flexibility and scalability of the method.

97 MATHEMATICS AND COMPUTING↗

Solid Freeform Fabrication of Composite-Material Objects

Composite solid freeform fabrication (C-SFF) or composite layer manufacturing (CLM) is an automated process in which an advanced composite material (a matrix reinforced with continuous fibers) is formed into a freestanding, possibly complex, three-dimensional object. In CLM, there is no need for molds, dies, or other expensive tooling, and there is usually no need for machining to ensure that the object is formed to the desired net size and shape. CLM is a variant of extrusion-type rapid prototyping, in which a model or prototype of a solid object is built up by controlled extrusion of a polymeric or other material through an orifice that is translated to form patterned layers. The second layer is deposited on top of the first layer, the third layer is deposited on top of the second layer, and so forth, until the stack of layers reaches the desired final thickness and shape. The elements of CLM include (1) preparing a matrix resin in a form in which it will solidify subsequently, (2) mixing the fibers and matrix material to form a continuous pre-impregnated tow (also called "towpreg"), and (3) dispensing the pre-impregnated tow from a nozzle onto a base while moving the nozzle to form the dispensed material into a patterned layer of controlled thickness. When the material deposited into a given layer has solidified, the material for the next layer is deposited and patterned similarly, and so forth, until the desired overall object has been built up as a stack of patterned layers. Preferably, the deposition apparatus is controlled by a computer-aided design (CAD) system. The basic CLM concept can be adapted to the fabrication of parts from a variety of matrix materials. It is conceivable that a CLM apparatus could be placed at a remote location on Earth or in outer space where (1) spare parts are expected to be needed but (2) it would be uneconomical or impractical to store a full inventory of spare parts. A wide variety of towpregs could be prepared and stored on spools until needed. Long-shelf-life towpreg materials suitable for such use could include thermoplastic-coated carbon fibers and metal-coated SiC fibers. When a spare part was needed, the part could be fabricated by CLM under control by a CAD data file; thus, the part could be built automatically, at the scene, within hours or minutes.

Wang, C. Jeff↗

Computation and sensitivity considerations of the Ricatti equation in spacecraft CMG steering laws

The steady-state matrix Ricatti equation is studied with respect to sensitivity and computational burden for a linear regulator controller in spacecraft. The class of systems studied use control moment gyros (CMGs) as the torque driver, assuming that the CMGs are free of gimbal stops. Different solution techniques are evaluated relative to computation time and accuracy to determine which solution method is most acceptable with respect to the prescribed requirements. It is shown that it is not feasible to eliminate off-diagonal Ricatti equation terms in the relevent updata equation due to their high sensitivity, that Potter's algebraic technique requires the least computation time of the methods studied, and that the simple Euler method yields the best results when accuracy and computation time are equally weighted. If an optimal linear regulator formulation is employed, a full Ricatti equation solution of n(n + 1)2 elements of the symmetric positive definite gain matrix which is the solution to the matrix Ricatti equation must be computed at each update cycle.

Colburn, B. K.↗

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗

Development of a laminate fatigue analysis

A fatigue analysis technique developed to predict damage growth in notched laminates is described. Features of the analysis include: criteria to relate matrix failure to cyclic stresses in and between plies; correlation of delamination growth with strain-release rate; and in-plane shear modulus change is related to cyclic shear stresses. A simplified finite element model is used to determine stresses in laminates that contain matrix damage. Failure criteria are integrated with the finite element model to form the fatigue analysis.

Roderick, G. L.↗