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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 649 records · Page 36

A Low-Rank QTT-based Finite Element Method for Elasticity Problems

We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.

97 MATHEMATICS AND COMPUTING↗

Application of NASTRAN in nonlinear analysis of a cartridge case neck separation malfunction

The problem of case neck separation malfunction in the field of ammunition structural analysis is investigated. The axi-symmetric solid of revolution RING element was utilized in the manual piecewise linear analysis to obtain the expansion of the wall of the cartridge case and barrel chamber by the pressure of propellant gases and the stresses in the structure. The analysis included the varying material properties along the wall of the case and the chamber. Additional instructions were provided to change the element material ID's without recomputing the entire stiffness matrix.

Yang, J. C. S.↗

Problems encountered with conventional fiber-reinforced composites

Preparational, computational, and operational problems associated with fiber-reinforced composites (FRC) are reviewed. Initial preparation of FRCs is shown to involve consideration of the type of prepreg, the setting time, cure conditions and cycles, and cure temperatures. The effects of the choice of bonding agents, the fiber transfer length, and individual fiber responses to bonding agents are noted to have an impact on fiber strength, moisture uptake, and fatigue resistance. The deformation prior to failure and the failure region are modeled through models of mini-, micro- and macro mechanics formulations employing a stiffness matrix, failure criterion, or fracture mechanics. The detection, evaluation, and repair of defects comprises the operational domain, and it is stressed that no good repair techniques exist for FRCs.

Landel, R. F.↗

Inclusion of elastically connected members in exact buckling and frequency calculations

A standard stiffness matrix procedure which permits any combination of rigid, elastic, pinned or sliding connections of the degrees of freedom at the ends of a member to the nodes of its parent structure is described, in order to show how easily it can be extended to allow an existing algorithm to be used to ensure that no eigenvalues of the parent structure can be missed even when 'exact' member theory is used. The eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The method preserves the exactness of the member theory and an efficient method for computer application is indicated. The theory also permits any combination of rigid, elastic, pinned or sliding connections between the freedoms of a substructure and those of its parent structure.

Williams, F. W.↗

Hydromechanical impact of basement rock on injection-induced seismicity in Illinois Basin

Abstract The common explanation of observed injection-induced microseismicity is based on the measured stress state at the injection interval and the assumption that it remains the same in the vicinity. We argue here that representing the stress state in different geologic formations over the injection site with the single Mohr’s circle is insufficient due to local stratigraphic features and contrast in compressibilities of the involved formations. The role of hydromechanical coupling in the microseismic response is also crucial for the proper assessment of the problem. Thoroughly monitored Illinois Basin Decatur Project revealed the majority of CO 2 injection-associated microseismic events being originated in the crystalline basement. Even though basement faults can serve as the conduits for fluid flow—the predicted pressure increase seems to be insufficient to trigger seismicity. To address this issue, accurate laboratory measurements of rock properties from the involved formations are conducted. The pre-injection stress state and its evolution are evaluated with the hydromechanically coupled numerical model. It appears that the presence of an offset in a stiff competent layer affects the stress state in its vicinity. Therefore, both the pre-injection stress state and its evolution during the fluid injection should be addressed during the induced seismicity assessment.

54 ENVIRONMENTAL SCIENCES↗

The effects of pin elasticity, clearance, and friction on the stresses in a pin-loaded orthotropic plate

The effects of pin elasticity, clearance, and friction on the stresses in a pin loaded orthotropic plate are studied. The effects are studied by posing the problem as a planar contact elasticity problem, the pin and the plate being two elastic bodies which interact through contact. Coulomb friction is assumed, the pin loads the plate in one of its principal material directions, and the plate is infinite in extent. A collocation scheme and interaction, in conjunction with a complex variable series solution, are used to obtain numerical results. The contact region between the plate and pin is unknown and must be solved for as part of the solution. The same is true of the region of friction induced no slip. Two pin stiffnesses, two clearance levels, two friction levels and two laminates, a (0/+ or - 45/90)s and a (02/+ or - 45)s, are studied. The effects of pin elasticity, clearance, and friction on the load capacity of the plate are assessed by comparing the load capacity of the plate with the capacity when the pin is rigid, perfectly fitting, and frictionless.

Hyer, M. W.↗

Asynchronous τ-leaping

Stochastic simulation of cell signaling pathways and genetic regulatory networks has contributed to the understanding of cell function; however, investigation of larger, more complicated systems requires computationally efficient algorithms. τ-leaping methods, which improve efficiency when some molecules have high copy numbers, either use a fixed leap size, which does not adapt to changing state, or recalculate leap size at a heavy computational cost. We present a hybrid simulation method for reaction-diffusion systems which combines exact stochastic simulation and τ-leaping in a dynamic way. Putative times of events are stored in a priority queue, which reduces the cost of each step of the simulation. For every reaction and diffusion channel at each step of the simulation the more efficient of an exact stochastic event or a τ-leap is chosen. This new approach removes the inherent trade-off between speed and accuracy in stiff systems which was present in all τ-leaping methods by allowing each reaction channel to proceed at its own pace. Both directions of reversible reactions and diffusion are combined in a single event, allowing bigger leaps to be taken. This improves efficiency for systems near equilibrium where forward and backward events are approximately equally frequent. Comparison with existing algorithms and behaviour for five test cases of varying complexity shows that the new method is almost as accurate as exact stochastic simulation, scales well for large systems, and for various problems can be significantly faster than τ-leaping.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Scott, R. K.↗

Effects of transverse shearing flexibility on the postbuckling of plates loaded by inplane shear

This paper presents buckling and postbuckling results for plates loaded by inplane shear. The buckling results have been plotted to show the effects of thickness on the stress coefficient for aluminum plates. Results are given for various length-to-width ratios. Postbuckling results for thin plates with transverse shearing flexibility are compared to results from classical theory. The problems considered are the postbuckling response of plates in shear made of aluminum and of a + or - 45 deg graphite-epoxy laminate. Thus the materials are isotropic and orthotropic, respectively. The plates are considered to be long with side edges simply supported, with various inplane edge conditions, and the plates are subject to a constant shearing displacement along the side edges. Characteristic curves presenting the average shear stress resultant as a function of the applied displacement are given. These curves indicate that change in inplane edge conditions influence plate postbuckling stiffness and that transverse shearing is important in some cases.

Stein, Manuel↗

Dynamic Reconstruction and Multivariable Control for Force-Actuated, Thin Facesheet Adaptive Optics

The Multiple Mirror Telescope (MMT) under development at the University of Arizona takes a new approach in adaptive optics placing a large (0.65 m) force-actuated, thin facesheet deformable mirror at the secondary of an astronomical telescope, thus reducing the effects of emissivity which are important in IR astronomy. However, The large size of the mirror and low stiffness actuators used drive the natural frequencies of the mirror down into the bandwidth of the atmospheric distortion. Conventional adaptive optics takes a quasi-static approach to controlling the, deformable mirror. However, flexibility within the control bandwidth calls for a new approach to adaptive optics. Dynamic influence functions are used to characterize the influence of each actuator on the surface of the deformable mirror. A linearized model of atmospheric distortion is combined with dynamic influence functions to produce a dynamic reconstructor. This dynamic reconstructor is recognized as an optimal control problem. Solving the optimal control problem for a system with hundreds of actuators and sensors is formidable. Exploiting the circularly symmetric geometry of the mirror, and a suitable model of atmospheric distortion, the control problem is divided into a number of smaller decoupled control problems using circulant matrix theory. A hierarchic control scheme which seeks to emulate the quasi-static control approach that is generally used in adaptive optics is compared to the proposed dynamic reconstruction technique. Although dynamic reconstruction requires somewhat more computational power to implement, it achieves better performance with less power usage, and is less sensitive than the hierarchic technique.

Grocott, Simon C. O.↗

Analysis of Neural Networks as Random Dynamical Systems

In this report we present our findings and outcomes of the NNRDS (analysis of Neural Networks as Random Dynamical Systems) project. The work is largely motivated by the analogy of a large class of neural networks (NNs) with a discretized ordinary differential equation (ODE) schemes. Namely, residual NNs, or ResNets, can be viewed as a discretization of neural ODEs (NODEs) where the NN depth plays the role of the time evolution. We employ several legacy tools from ODE theory, such as stiffness, nonlocality, autonomicity, to enable regularization of ResNets thus improving their generalization capabilities. Furthermore, armed with NN analysis tools borrowed from the ODE theory, we are able to efficiently augment NN predictions with uncertainty overcoming wellknown dimensionality challenges and adding a degree of trust towards NN predictions. Finally, we have developed a Python library QUiNN (Quantification of Uncertainties in Neural Networks) that incorporates improved-architecture ResNets, besides classical feed-forward NNs, and contains wrappers to PyTorch NN models enabling several major classes of uncertainty quantification methods for NNs. Besides synthetic problems, we demonstrate the methods on datasets from climate modeling and materials science.

97 MATHEMATICS AND COMPUTING↗

Identify Structural Flaw Location and Type with an Inverse Algorithm of Resonance Inspection

To evaluate the fitness-for-service of a structural component and to quantify its remaining useful life, aging and service-induced structural flaws must be quantitatively determined in service or during scheduled maintenance shutdowns. Resonance inspection (RI), a non-destructive evaluation (NDE) technique, distinguishes the anomalous parts from the good parts based on changes in the natural frequency spectra. Known for its numerous advantages, i.e., low inspection cost, high testing speed, and broad applicability to complex structures, RI has been widely used in the automobile industry for quality inspection. However, compared to other contemporary direct visualization-based NDE methods, a more widespread application of RI faces a fundamental challenge because such technology is unable to quantify the flaw details, e.g. location, dimensions, and types. In this study, the applicability of a maximum correlation-based inverse RI algorithm developed by the authors is further studied for various flaw cases. It is demonstrated that a variety of common structural flaws, i.e. stiffness degradation, voids, and cracks, can be accurately retrieved by this algorithm even when multiple different types of flaws coexist. The quantitative relations between the damage identification results and the flaw characteristics are also developed to assist the evaluation of the actual state of health of the engineering structures.

non-destructive evaluation, resonance inspection, ↗

On the problem of stress singularities in bonded orthotropic materials

The problem of stress singularities at the leading edge of a crack lying in the neighborhood of a bimaterial interface in bonded orthotropic materials is considered. The main objective is to study the effect of material orthotropy on the singular behavior of the stress state when the crack touches or intersects the interface. The results indicate that, due to the large number of material constants involved, in orthotropic materials, the power of stress singularity as well as the stress intensity factor can be considerably different than that found in the isotropic materials with the same stiffness ratio perpendicular to the crack.

Erdogan, F.↗

NASA Langley's Approach to the Sandia's Structural Dynamics Challenge Problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the behavior of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although this type of analysis is routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing uncertain interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on target configurations. Moreover, it is typical to have multiple data sets from experiments conducted at the subsystem level, but often samples sizes are not sufficient to compute high confidence statistics. In this challenge problem additional constraints are placed as ground rules for the participants. One such rule is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these models and the multiple data sets to make predictions about the target system response under completely different input conditions. Our approach involved initially the screening of several different methods. Three of the ones considered are presented herein. The first one is based on the transformation of the modal data to an orthogonal space where the mean and covariance of the data are matched by the model. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnesses and damping coefficients; one matches confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on all the approaches, lessons learned, validation 1 metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach. Keywords: Probabilistic modeling, model validation, uncertainty quantification, kernel density

Horta, Lucas G.↗

Toward Molecular Engineering of Polymer Glasses

Glass formation has been central to fabrication technologies since the dawn of civilization. Glasses not only encompass window panes, the insulation in our homes, the optical fibers supplying our cable TV, and vessels for eating and drinking, but they also include a vast array of ‘‘plastic’’ polymeric materials. Glasses find applications in high technology (e.g., producing microelectronic materials, etc., amorphous semiconductors), and recent advances have created ‘‘plastic metallic glasses’’ that are promising for fabricating everyday structural materials. Many commercially relevant systems, such as microemulsions and colloidal suspensions, have complex molecular structures and thus solidify by glass formation. Despite the importance of understanding the fundamental nature of glass formation for the synthesis of new materials, a predictive molecular theory has been lacking. Much of our understanding of glass formation derives from the analysis of experimental data, a process that has uncovered a number of interesting universal behaviors, namely, relations between properties that are independent of molecular details. However, these empirically derived relations and their limitations remain to be understood on the basis of theories, and, more importantly, there is strong need for theories of the explicit variation with molecular system to enable the rational design and tailoring of new materials. We have recently developed the generalized entropy theory, the only analytic, theory that enables describing the dependence of the properties of glass-formation on monomer molecular structures. These properties include the two central quantities of glass formation, the glass transition temperature and the glass fragility parameter, material dependent properties that govern how a material may be processed (e.g., by extrusion, ink jet, molding, etc.) Our recent works, which are further described below, extend the studies of glass formation in polymer systems to test the theory by directly comparing between the predictions of our generalized entropy theory with experiment and with simulations and to expand the vistas of the theory to describe a wider range of important systems (e.g. glass formation in binary blends and systems with specific interactions) and phenomena that are describable by the generalized entropy theory. In addition, we have addressed longstanding fundamental problems associated with the validity of the Adam-Gibbs theory, one of the underpinnings of the general entropy theory. Theoretical advances to enable describing the properties of glass-formation over a wider class of important polymeric systems, included semi-flexible systems, the more general situation of specific interactions, and more. Our recent work removes the simplest approximation uses the simplest model in which the interaction is approximated by a single, monomer average. Thus, the theory has been extended to allow some variations of the energy parameters between the atoms within the monomers. The theory has also been extended to include all the contributions from chain semi-flexibility. Both projects are extremely difficult, but the payback is that the process of solving the problems developed strong theoretical skills in Dr. Xu, who has recently begun a postdoc position at ORNL. The theory has also been extended to describe glass formation in partially miscible blends, with good general agreement with experiment. Again, the development of the theory presented an extremely difficult problem, but the payback is the development of a theory for a very important class of systems. Another project provides an extremely simple approximation for certain properties of glass formation in polymer melts and should make the theory more accessible to everyone.

36 MATERIALS SCIENCE↗

Structural optimization of rotor blades with straight and swept tips subject to aeroelastic constraints

The main conclusions obtained in the present study are summarized. Their application to the structural optimization of a helicopter blade should be limited by the assumptions used in obtaining the numerical results presented here. The optimum design procedure described here is very efficient, and can produce improved designs with a very limited number of precise analyses. The method of constructing the approximate problem is such that previously conducted aeroelastic analyses can be reused in a new optimization problem. For example, if an optimization study is preceded by a parametric study in which the effect of various combinations of blade design parameters is examined, all the aeroelastic analyses performed for the parametric study can be reutilized in the optimization study. This is not possible when the approximate problem is built from Taylor series expansions. The results of the optimization are quite sensitive to the aeroelastic stability margins required of the blade. In the optimization of case 2, changing the aeroelastic stability constraints from simply requiring that the blade be stable in hover, to requiring that the stability margins be maintained during the course of the optimization, reduced the gains in n/rev vibration levels by more than 50 percent. The introduction of tip sweep can reduce the n/rev vertical hub shears beyond the level that can be obtained by just modifying the mass and stiffness distributions of the blade.

Friedmann, Peretz P.↗

Dissipative magnetohydrodynamics for nonresistive relativistic plasmas: An implicit second-order flux-conservative formulation with stiff relaxation

Based on a 14-moment closure for nonresistive (general-) relativistic viscous plasmas, here we describe a new numerical scheme that is able to handle all first-order dissipative effects (heat conduction, bulk and shear viscosities), as well the anisotropies induced by the presence of magnetic fields. The latter is parametrized in terms of a thermal gyrofrequency or, equivalently, a thermal Larmor radius and allows to correctly capture the thermal Hall effect. By solving an extended Israel-Stewart-like system for the dissipative quantities that enforces algebraic constraints via stiff-relaxation, we are able to cast all first-order dissipative terms in flux-divergence form. This allows us to apply traditional high-resolution shock capturing methods to the equations, making the system suitable for the numerical study of highly turbulent flows. We present several numerical tests to assess the robustness of our numerical scheme in flat spacetime. The 14-moment closure can seamlessly interpolate between the highly collisional limit found in neutron star mergers, and the highly anisotropic limit of relativistic Braginskii magnetohydrodynamics appropriate for weakly collisional plasmas in black-hole accretion problems. We believe that this new formulation and numerical scheme will be useful for a broad class of relativistic magnetized flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sensitivity of Hingeless Rotor Blade Flap-lag Stability in Hover to Analytical Modelling Assumptions

Prediction of flap-lag stability using a single bending mode for each degree-of-freedom is examined in the case in which the bending modes are assumed to be the same in the flap and lag directions and are independent of pitch angle and stiffness distribution. It is shown that this model gives results analogous to those obtained by Ormiston employing a rigid blade model with the blade and hub stiffness represented by springs in the limiting cases of the elastic coupling parameter R = 0 and 1. For intermediate values of R the results are shown to be quite different. The mode shape assumptions are shown to result in what is referred to as the parallel spring model in contrast to Ormiston's model which is referred to as a series spring model. The similarities and differences between these two models are developed in some details. The differences between these two models are examined for various typical rotor blade characteristics. Other aspects of the sensitivity of this problem are also considered.

Curtiss, H. C., Jr.↗