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At least 199 records · Page 11

Lattice QED in an external magnetic field: Evidence for dynamical chiral symmetry breaking

We simulate quantum electrodynamics (QED) in a strong constant homogeneous external magnetic field on a Euclidean space-time lattice using the rational hybrid Monte Carlo method, developed for simulating lattice quantum chromodynamics (QCD). Our primary goal is to measure the chiral condensate in the limit when the input electron mass m is zero. We observe a nonzero value, indicating that the external magnetic field catalyzes chiral symmetry breaking as predicted by approximate truncated Schwinger-Dyson methods. Such behavior is associated with dominance by the lowest Landau level which causes the effective dimensional reduction from 3 + 1 dimensions to 1 + 1 dimensions for charged particles (electrons and positrons) where the attractive forces of QED can produce chiral symmetry breaking with a dynamical electron mass and associated chiral condensate. Since our lattice simulations use bare (lattice) parameters, while the Schwinger-Dyson analyses work with renormalized quantities, direct numerical comparison will require renormalization of our lattice results. Published by the American Physical Society 2024

Kogut, J. B. (ORCID:000000030151548X)↗

Stability of Goertler vortices in boundary layers

A formal analysis of Goertler-type instability is presented. The boundary-layer and disturbance equations are formulated in a general, orthogonal, curvilinear system of coordinates constructed from the inviscid flow over a curved surface. Effects of curvature on the boundary-layer flow are analyzed. The basic approximation for the disturbance equations is presented and solved numerically. Previous analyses are discussed and compared with our analysis. It is shown that the general system of coordinates developed in this analysis and the correct order-of-magnitude analysis of the disturbance velocities with two velocity scales leads to a rational foundation for future work in Goertler vortices.

Floryan, J. M.↗

Combined effects of space flight factors and radiation on humans

The probability that a dose of ionizing radiation kills a cell is about 10,000 times the probability that the cell will be transformed to malignancy. On the other hand, the number of cells killed required to significantly impact health is about 10,000 times the number that must be transformed to cause a late malignancy. If these two risks, cell killing and malignant transformation, are about equal, then the risk that occurs during a mission is more significant than the risk that occurs after a mission. The latent period for acute irradiation effects (cell killing) is about 2-4 weeks; the latent period for malignancy is 10-20 years. If these statements are approximately true, then the impact of cell killing on health in the low-gravity environment of space flight should be examined to establish an estimate of risk. The objective of this study is to synthesize data and conclusions from three areas of space biology and environmental health to arrive at rational risk assessment for radiations received by spacecraft crews: (1) the increased physiological demands of the space flight environment; (2) the effects of the space flight environment on physiological systems; and (3) the effects of radiation on physiological systems. One physiological system has been chosen: the immune response and its components, consisting of myeloid and lymphoid proliferative cell compartments. Best-case and worst-case scenarios are considered. In the worst case, a doubling of immune-function demand, accompanied by a halving of immune capacity, would reduce the endangering dose to a crew member to around 1 Gy.

Non-NASA Center↗

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C–C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C–C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH–CHO, *COH–*COH, and *OCH–*OCH. The most kinetically favorable path forms *COH–CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C–C coupling paths produce only *COH–*COH and *CO–*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C 2+ product formation via CO 2 RR electrocatalysts.

30 DIRECT ENERGY CONVERSION↗

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

Cosentino, G. B.↗

The Favre-Reynolds Average Distinction and a Consistent Gradient Transport Expression for the Dissipation

Two equation and higher order closures for compressible turbulence fail to capture the compressible wall layers' log scaling. Accounting for the distinction between Favre and Reynolds averaged variables in the compressible moment equations indicate that turbulent transport expressions obtained using the 'variable density approximation' are in error. The error is related to the enstrophy, a Reynolds averaged variable appearing in the equation for the Favre averaged k; recognizing this fact an expression for the transport of dissipation consistent with simple mixing length arguments is obtained. Within the (limited) context of a gradient transport hypothesis a rational form for the turbulent transport of the dissipation is found. Modestly better agreement with the well established compressible Van Driest log scaling is found in k - epsilon calculation.

Ristorcelli, J. R.↗

Orbital, Rotational and Climatic Interactions: Energy Dissipation and Angular Momentum Exchange in the Earth-Moon System

A numerical ocean tide model has been developed and tested using highly accurate TOPEX/Poseidon (T/P) tidal solutions. The hydrodynamic model is based on time stepping a finite difference approximation to the non-linear shallow water equations. Two novel features of our implementation are a rigorous treatment of self attraction and loading (SAL), and a physically based parameterization for internal tide (IT) radiation drag. The model was run for a range of grid resolutions, and with variations in model parameters and bathymetry. For a rational treatment of SAL and IT drag, the model run at high resolution (1/12 degree) fits the T/P solutions to within 5 cm RMS in the open ocean. Both the rigorous SAL treatment and the IT drag parameterization are required to obtain solutions of this quality. The sensitivity of the solution to perturbations in bathymetry suggest that the fit to T/P is probably now limited by errors in this critical input. Since the model is not constrained by any data, we can test the effect of dropping sea-level to match estimated bathymetry from the last glacial maximum (LGM). Our results suggest that the 100 m drop in sea-level in the LGM would have significantly increased tidal amplitudes in the North Atlantic, and increased overall tidal dissipation by about 40%. However, details in tidal solutions for the past 20 ka are sensitive to the assumed stratification. IT drag accounts for a significant fraction of dissipation, especially in the LGM when large areas of present day shallow sea were exposed, and this parameter is poorly constrained at present.

Egbert, Gary D.↗

Interior and its implications for the atmosphere

The bulk composition and interior structure of Titan required to explain the presence of a substantial methane atmosphere are shown to imply the presence of solid CH4 - 7H2O in Titan's primitive material. Consideration of the possible composition and structure of the present atmosphere shows plausible grounds for considering models with total atmospheric pressures ranging from approximately 20 mb up to approximately 1 kb. Expectations regarding the physical state of the surface and its chemical composition are strongly conditioned by the mass of atmosphere believed to be present. A surface of solid CH4, liquid CH4 solid, CH4 hydrate, H2O ice, aqueous NH3 solution, or even a non-surface of supercritical H2O-NH3-CH4 fluid could be rationalized.

Lewis, J. S.↗

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Mengshoel, Ole J.↗

Rational Design of Nanoplasmonic Array Geometries for Biosensing

Background: Molecular diagnostics provide early and accurate diagnosis, which is essential for the prevention and treatment of infectious as well as chronic diseases. These tests are designed to detect disease-specific bioanalytes such as nucleic acid (DNA or RNA) or protein (antigens, antibodies) biomarkers. In the context of infectious disease diagnosis, nucleic acid-based detection methods are known to provide more specific and sensitive results. Here, the presence of a unique sequence belonging to the pathogenic genomic material is targeted to identify species, organism, genera and/or antimicrobial resistant gene markers. The majority of the common nucleic acid based diagnostic techniques require amplification (polymerase chain reaction, isothermal amplification etc.) of the pathogenic genetic material prior to detection impacting diagnostic speed, complexity, and cost thereby limiting ease of use. Thus, the development of simplified nucleic acid-based diagnostics that can be even used in resource-poor settings may hugely benefit patients across the globe. Nanopath is a molecular diagnostics company utilizing a solid-state nanosensor to enable sequence-specific detection of target nucleic acids without the need of amplification. These nanostructures enable ultra-sensitive biomarker detection using geometric, feature-dependent properties highly dependent on the local dielectric environment, allowing them to be sensitive to low concentration binding events. This paper describes an application of this approach to provide highly relevant clinical information within a single doctor’s office visit. Intro: The Nanopath team is in collaboration with NASA (National Aeronautics and Space Administration) and NIST (National Institute of Standards and Technology) to push the bounds of the fundamental physics associated with their biosensing platform. The ability of metals to support electromagnetic surface waves gives rise to surface plasmons when optically illuminated. This property, and its strong sensitivity to changes in the local refractive index, allows for the use of metal nanoparticles as ultra-sensitive transducers. In prior work by members of this team, ensembles of randomly oriented nanoparticles (i.e., colloidal nanorods dispersed on chip) were employed for sequence-specific nucleic acid sensing (1-3). While these particle sensors have the advantage of rapid fabrication, they suffer from low sensitivity and quality factor due to the random particle dispersity. In contrast, in this study we employ ordered array nanoparticle ensembles which can be used to improve sensor sensitivity and figure-of-merit. Study Methods Overview: In this talk, we detail the results of sensing experiments and computational simulations to outline a rational design of the structure of these plasmonic nanoparticle arrays for biomolecular sensing. Through simulation and experiment, we iteratively tailor nanostructure dimension to provide high quality signal and large resonance shifts upon modeled nucleic acid binding. In particular, full-wave electromagnetic simulations were conducted using Lumerical photonic simulation software in which periodic boundary conditions were applied in the x- and y- dimensions for each of the nanoplasmonic sensor geometries. To simulate the resonance response to changes in the bulk solution in contact with the sensor surface, the refractive index of the surrounding media was changed appropriately. Nucleic acid hybridization events were modeled using either using spherical structures approximating the relevant radius of genomic material as estimated by polymer models, or as conformal layers with the known refractive indices for nucleic acids. On the basis of initial simulations, nanosensors were fabricated using traditional electron-beam lithography protocols at NIST. To evaluate consensus between simulations and experiments, bulk sensing experiments were carried out in which the resonance peaks were obtained by submerging the sensors in refractive index standards. Key nanosensor characteristics including resonance peak locations, resonance peak shifts as a function of refractive index, and figure of merit (FOM) of extinction curves were examined between the experimental and simulation results prior to proceeding with simulations on additional geometries and more complex solution conditions, and further device fabrication. This iterative process is repeated toward a rational design of nanoplasmonic array geometries for biosensing optimizing response for targeted disease detection. In summary, this study puts forth a methodology for rational design and characterization of regularly spaced nanoparticle arrays for optics-based biosensing. The results of this study will allow for more informed design of nanostructure geometries towards sequence-specific nucleic acid detection. These improved designs have the potential to improve clinical sensitivity and limit-of-detection across disease indication.

sensor↗

Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

Here, we use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile. On top of this mean shrinkage, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening. Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events. In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Unraveling the conundrum of electronic leakage in protonic ceramic cells: Operation-specific insights and rational design strategies

Electronic conduction through proton-conducting electrolytes significantly impairs the efficiency of protonic ceramic cells (PCCs). Here, in this study, we explore the electron and ion mixed transport properties of four common protonic ceramics, BaZr 0.8 Y 0.2 O 3-δ (BZY82), BaZr 0.7 Ce 0.2 Y 0.1 O 3-δ (BZCY721), BaZr 04 Ce 0.4 Y 0.1 Yb 0.1 O 3-δ (BZCYYb4411), and BaZr 0.1 Ce 0.7 Y 0.1 Yb 0.1 O 3-δ (BZCYYb1711). It marks the first instance of investigating these properties under operation-specific scenarios: fuel side of electrolysis cell, air side of electrolysis cell, fuel side of fuel cell, and air side of the fuel cell. BZCYYb1711 exhibits the highest ionic conductivity, but two to three times higher electronic leakage when exposed to oxygen-containing environments than the others. BZY82 exhibits approximately two times higher electronic leakage in a hydrogen-containing environment. BZCY721 demonstrates excellent ion transport numbers (~0.95) across these four operating conditions. BZCYYb4411 behaves quite similarly to BZCY721. The most challenging operating environment for all candidates is the air side of fuel cell mode. This mode leads to a high initial electronic leakage, followed by a significant increase with polarization. The probable cause for this behavior is a H 2 -free, polarization-induced reduction that leads to the formation of V$^•_O$. The electron small polaron associated with V$^•_O$ is released by the electrical field due to the Poole-Frenkel effect. ZnO and NiO sintering aids are found to be detrimental to the ionic conductivity of the electrolytes. In particular, NiO substantially lowers the ion transport number. The correlation of the operation-specific electronic leakage to full cells is discussed. It is suggested that a rational PCC design should synergistically couple BZCYYb1711 at fuel side with BZCY4411 at air side to deliver a well-balanced performance and faradaic efficiency simultaneously, and the high temperature sintering process with a NiO fuel electrode should be shortened or replaced by ultra-fast sintering techniques or using a fuel electrode scaffold-infiltration fabrication strategy.

42 ENGINEERING↗

An Ultrafast, Durable, and High-Loading Polymer Anode for Aqueous Zinc-Ion Batteries and Supercapacitors

Zn metal has shown promise as an anode material for grid-level energy storage, yet is challenged by dendritic growth and low Coulombic efficiency. Herein, an ultrafast, stable, and high-loading polymer anode for aqueous Zn-ion batteries and capacitors (ZIBs and ZICs) is developed by engineering both the electrode and electrolyte. The anode polymer is rationally prepared to have a suitable electronic structure and a large pi-conjugated structure, whereas the electrolyte is manufactured based on the superiority of triflate anions over sulfate anions, as analyzed and confirmed via experiments and simulations. This dual engineering results in an optimal polymer anode with a low discharge potential, near-theoretical capacity, ultrahigh-loading capability (approximate to 50 mg cm -2 ), ultrafast rate (100 A g -1 ), and ultralong lifespan (one million cycles). Further, its mechanism involves reversible Zn 2+ /proton co-storage at the carbonyl site. When the polymer anode is coupled with cathodes for both ZIB and ZIC applications, the devices demonstrate ultrahigh power densities and ultralong lifespans, far surpassing those of corresponding Zn-metal-based devices.

25 ENERGY STORAGE↗

Influence of surface static-pressure orifices on boundary-layer transition

An investigation of the interaction of a laminar boundary layer and surface static-pressure orifices was conducted on a natural laminar flow airfoil. The effects of both favorable and adverse pressure gradients were studied at Reynolds numbers based on airfoil chord from approximately 500,000 to 6,000,000 with Mach number varying accordingly from about 0.03 to 0.42. The smaller the diameter of the orifice, the less likely it will cause premature transition. Locating the orifices in a chord-wise row aligned with the flow appears to have an additive, adverse effect on transition. Tube length-to-orifice diameter ration does not seem to have a consistent influence on transition.

Somers, D. M.↗

A transport-based framework for solidification cracking in Ni-based superalloys processed by laser powder bed fusion

Solidification cracking remains a persistent barrier to laser powder bed fusion (LPBF) processing of solid-solution-strengthened (SSS) Ni-based superalloys and is commonly attributed to carbide formation, liquation-type failure, or elemental segregation. In this work, the cracking behavior of three SSS Ni-based superalloys—Inconel 625 (625), Inconel 617 (617), and Haynes 230 (230)—is examined under comparable LPBF conditions to evaluate the origins of their cracking susceptibility. Carbides were present in both 625 and 230, yet cracking behavior differed significantly. MC-type carbides in 625 remain discrete and preserve liquid connectivity, whereas Cr-rich M23C6 carbides in 230 form at cellular triple junctions that bottleneck the interdendritic liquid network, influencing cracking through liquid connectivity rather than as an independent cause. Alloy 617 exhibited anomalous segregation without resolvable secondary phases yet cracked mildly, indicating that extensive carbide formation is not a prerequisite for cracking. To rationalize these observations, a transport-limited framework is proposed in which cracking occurs when terminal-liquid feeding cannot accommodate solidification-induced strain; among the mechanisms evaluated, this framework is most consistent with the physical constraints imposed by LPBF solidification. Transport-based crack-susceptibility indexes incorporating permeability, viscosity, and solidification kinetics distinguish the alloy hierarchy; permeability ratios Krat increased from approximately 7 (625) to 11.5 (617) and 14.5 (230), with corresponding increases in the μ-weighted mushy zone risk index (CSIMZRM). These results are consistent with transport-limited liquid feeding as a rate-limiting contributor to solidification cracking in LPBF-processed SSS Ni-based superalloys, providing a physically grounded basis for alloy and process design.

Hyer, Holden [ORNL] (ORCID:0000000343915561)↗

Semimetallicity and electron-hole liquid in two-dimensional C and BN based compounds

Insulating-metallic transition mediated by substitutional atoms is predicted in a series of two-dimensional carbon-based structures. Introducing Si atoms in selected sites of tetrahexcarbon [Carbon 137 (2018) 266] according to rational chemical rules, metallicity by trivial band inversion without band gap opening is induced. Additional substitution of remaining C atoms by BN dimers introduces no changes in the metallic properties. A series of isomorphous two-dimensional materials with isoelectronic structures derived by exchanging group IV elements exhibiting various band gaps is obtained. Dynamical stability is verified with phonon analysis and beyond the harmonic approximation with molecular dynamics up to room temperature. The semi-metallic compounds have well-nested pockets of carriers and are good candidates for the formation of an excitonic insulator.

36 MATERIALS SCIENCE↗

Influence of Test Procedures on the Thermomechanical Properties of a 55NiTi Shape Memory Alloy

Over the past few decades, binary NiTi shape memory alloys have received attention due to their unique mechanical characteristics, leading to their potential use in low-temperature, solid-state actuator applications. However, prior to using these materials for such applications, the physical response of these systems to mechanical and thermal stimuli must be thoroughly understood and modeled to aid designers in developing SMA-enabled systems. Even though shape memory alloys have been around for almost five decades, very little effort has been made to standardize testing procedures. Although some standards for measuring the transformation temperatures of SMA s are available, no real standards exist for determining the various mechanical and thermomechanical properties that govern the usefulness of these unique materials. Consequently, this study involved testing a 55NiTi alloy using a variety of different test methodologies. All samples tested were taken from the same heat and batch to remove the influence of sample pedigree on the observed results. When the material was tested under constant-stress, thermal-cycle conditions, variations in the characteristic material responses were observed, depending on test methodology. The transformation strain and irreversible strain were impacted more than the transformation temperatures, which only showed an affect with regard to applied external stress. In some cases, test methodology altered the transformation strain by 0.005-0.01mm/mm, which translates into a difference in work output capability of approximately 2 J/cu cm (290 in!lbf/cu in). These results indicate the need for the development of testing standards so that meaningful data can be generated and successfully incorporated into viable models and hardware. The use of consistent testing procedures is also important when comparing results from one research organization to another. To this end, differences in the observed responses will be presented, contrasted and rationalized, in hopes of eventually developing standardized testing procedures for shape memory alloys.

Padula, Santo A., II↗

Continuation of tailored composite structures of ordered staple thermoplastic material

The search for the cost effective composite structure has motivated the investigation of several approaches to develop composite structure from innovative material forms. Among the promising approaches is the conversion of a planar sheet to components of complex curvature through sheet forming or stretch forming. In both cases, the potential for material stretch in the fiber direction appears to offer a clear advantage in formability over continuous fiber systems. A framework was established which allows the simulation of the anisotropic mechanisms of deformation of long discontinuous fiber laminates wherein the matrix phase is a viscous fluid. Predictions for the effective viscosities of a hyper-anisotropic medium consisting of collimated, discontinuous fibers suspended in viscous matrix were extended to capture the characteristics of typical polymers including non-Newtonian behavior and temperature dependence. In addition, the influence of fiber misorientation was also modeled by compliance averaging to determine ensemble properties for a given orientation distribution. A design tool is presented for predicting the effect of material heterogeneity on the performance of curved composite beams such as those used in aircraft fuselage structures. Material heterogeneity can be induced during manufacturing processes such as sheet forming and stretch forming of thermoplastic composites. This heterogeneity can be introduced in the form of fiber realignment and spreading during the manufacturing process causing radial and tangential gradients in material properties. Two analysis procedures are used to solve the beam problems. The first method uses separate two-dimensional elasticity solutions for the stresses in the flange and web sections of the beam. The separate solutions are coupled by requiring that forces and displacements match section boundaries. The second method uses an approximate Rayleigh-Ritz technique to find the solutions for more complex beams. Analyses are performed for curved beams of various cross-sections loaded in pure bending and with a uniform distributed load. Preliminary results show that the geometry of the beam dictates the effect of heterogeneity on performance. The role of heterogeneity is larger in beams with a small average radius-to-depth ration, R/t, where R is the average radius of the beam and t is the difference between the inside and outside radii. Results of the anlysis are in the form of stresses and displacements and are compared to both mechanics of materials and numerical solutions obtained using finite element analysis.

Santare, Michael H.↗