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Layer-wise shell theory for postbuckling of laminated circular cylindrical shells
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Laboratory Measurements of the K-Shell Transition Energies in L-Shell Ions of Si and S
We have measured the energies of the strongest 1s-2 ℓ (azimuthal quantum number) (ℓ = s, p (s, p are angular momentum states)) transitions in He- through Ne-like silicon and sulfur ions to an accuracy of less than 1 electronvolt using the Lawrence Livermore National Laboratory's electron beam ion traps, EBIT-I and SuperEBIT, and the NASA/GSFC EBIT Calorimeter Spectrometer (ECS). We identify and measure the energies of 18 and 21 X-ray features from silicon and sulfur, respectively. The results are compared to new Flexible Atomic Code calculations and to semi-relativistic Hartree-Fock calculations by Palmeri et al. (2008). These results will be especially useful for wind diagnostics in high-mass X-ray binaries, such as Vela X-1 and Cygnus X-1, where high-resolution spectral measurements using Chandraʼs high-energy transmission grating has made it possible to measure Doppler shifts of 100 kilometers per second. The accuracy of our measurements is consistent with that needed to analyze Chandra observations, exceeding Chandraʼs 100 kilometers per second limit. Hence, the results presented here not only provide benchmarks for theory, but also accurate rest energies that can be used to determine the bulk motion of material in astrophysical sources. We show the usefulness of our results by applying them to redetermine Doppler shifts from Chandra observations of Vela X-1.
MCNP calculations for inner-shell radiography of double-shell implosions on the NIF
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Advanced Pt-Based Core–Shell Electrocatalysts for Fuel Cell Cathodes
Proton-exchange membrane fuel cells (PEMFCs) are highly efficient energy storage and conversion devices. Thus, the platinum group metal (PGM)-based catalysts which are the dominant choice for the PEMFCs have received extensive interest during the past couple of decades. However, the drawbacks in the existing PGM-based catalysts (i.e., high cost, slow kinetics, poor stability, etc.) still limit their applications in fuel cells. The Pt-based core–shell catalysts potentially alleviate these issues through the low Pt loading with the associated low cost and the high corrosion resistance and further improve the oxygen reduction reaction’s (ORR’s) activity and stability. This Account focuses on the synthetic strategies, catalytic mechanisms, factors influencing enhanced ORR performance, and applications in PEMFCs for the Pt-based core–shell catalysts. We first highlight the synthetic strategies for Pt-based core–shell catalysts including the galvanic displacement of an underpotentially deposited non-noble metal monolayer, thermal annealing, and dealloying methods, which can be scaled-up to meet the requirements of fuel cell operations. Subsequently, catalytic mechanisms such as the self-healing mechanism in the Pt monolayer on Pd core catalysts, the pinning effect of nitrogen (N) dopants in N-doped PtNi core–shell catalysts, and the ligand effect of the ordered intermetallic structure in L10-Pt/CoPt core–shell catalysts and their synergistic effects in N-doped L10-PtNi catalysts are described in detail. Additionally, the core–shell structure in the Pt-based catalysts have two main effects for enhanced ORR performance: (i) the interaction between Pt shells and core substrates can tune the electronic state of the surface Pt, thus boosting the ORR activity and stability, and (ii) the outer Pt shell with modest thickness can enhance the oxidation and dissolution resistance of the core, resulting in improved durability. We then review the recent attempts to optimize the ORR performance of the Pt-based core–shell catalysts by considering the shape, composition, surface orientation, and shell thickness. The factors influencing the ORR performance can be grouped into two categories: the effect of the core and the effect of the shell. In the former, PtM core–shell catalysts which use different non-PGM element cores (M) are summarized, and in the latter, Pt-based core–shell catalysts with different shell structures and compositions are described. The modifications of the core and/or shell structure can not only optimize the intermediate-binding energetics on the Pt surface through tuning the strain of the surface Pt, which increases the intrinsic activity and stability, but also offer a significantly decreased catalyst cost. Finally, we discuss the membrane electrode assembly performance of Pt-based core–shell catalysts in fuel cell cathodes and evaluate their potential in real PEMFCs for light-duty and heavy-duty vehicle applications. Even though some challenges to the activity and lifetime in the fuel cells remain, the Pt-based core–shell catalysts are expected to be promising for many practical PEMFC applications.
High-Fidelity Nonlinear Analysis of Compression-Loaded Composite Shells
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have four different shell-wall laminates and two different shell-radius-to-thickness ratios. The shell-wall laminates include two different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios include shell-radius-to-thickness ratios equal to 100 and 200. The results identify the effects of traditional and nontraditional initial imperfections on the nonlinear response characteristics and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these traditional and nontraditional imperfections on the nonlinear response characteristics and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. The results of a local shell-wall stress analysis used to estimate failure stresses are also described.
Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory
Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.
Sound Transmission through Two Concentric Cylindrical Sandwich Shells
This paper solves the problem of sound transmission through a system of two infinite concentric cylindrical sandwich shells. The shells are surrounded by external and internal fluid media and there is fluid (air) in the annular space between them. An oblique plane sound wave is incident upon the surface of the outer shell. A uniform flow is moving with a constant velocity in the external fluid medium. Classical thin shell theory is applied to the inner shell and first-order shear deformation theory is applied to the outer shell. A closed form for transmission loss is derived based on modal analysis. Investigations have been made for the impedance of both shells and the transmission loss through the shells from the exterior into the interior. Results are compared for double sandwich shells and single sandwich shells. This study shows that: (1) the impedance of the inner shell is much smaller than that of the outer shell so that the transmission loss is almost the same in both the annular space and the interior cavity of the shells; (2) the two concentric sandwich shells can produce an appreciable increase of transmission loss over single sandwich shells especially in the high frequency range; and (3) design guidelines may be derived with respect to the noise reduction requirement and the pressure in the annular space at a mid-frequency range.
Comparison of tungsten versus molybdenum for double shell capsules using machine learning design optimization
Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.
Clumped isotope thermometry of modern and fossil snail shells from the Himalayan-Tibetan Plateau: Implications for paleoclimate and paleoelevation reconstructions
Carbonate clumped isotope thermometry has been applied to fossil mollusk shells from Tibet to reconstruct the paleoclimate and paleoelevation of the region. However, inferred paleoelevation and climatic conditions from this proxy are inconsistent with paleontological evidence. Here, we report new clumped isotope data from both modern and fossil (5–4 Ma) freshwater mollusk shells with the results of X-ray diffraction (XRD) analyses of fossil shells from the Himalayan-Tibetan Plateau. Although all of the fossil shells analyzed in this study appeared pristine based on visual inspection, XRD data reveal that more than half of these apparently “pristine” fossil shells contain trace amounts of calcite. Clumped isotope temperatures derived from the fossil shells display a large range of variation (>22 °C). Among the fossil shells analyzed, those containing traces of calcite have yielded temperatures that are on average ~10 °C lower than those with no detectable calcite from the same strata. These observations suggest that clumped isotope alteration can occur in aragonite shells in low-temperature environments and even in shells with no visible signs of alteration that contain only traces of calcite. The temperatures derived from fossil shells with no detectable calcite are on average 4 °C higher than those derived from modern shells, indicating that southwest Tibet was warmer 4–5 Ma than today. After accounting for temperature change due to global cooling, the difference in clumped isotope temperatures between pristine fossil shells and modern shells suggests that the paleoelevation of the southwestern Tibetan Plateau in the Pliocene was similar to its present-day elevation.
Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics
Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.
Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach
Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.
A survey of ultraviolet circumstellar absorption lines in the spectra of early Be and shell stars
Copernicus UV data are used to examine the rich shell absorption spectra between 1120 and 1140 A in 17 Be and shell stars. Previous observations of the program stars are reviewed, the general appearance of the shell spectra between 1120 and 1140 A is described, and the shell spectra are compared with the spectra of four bright B-type supergiants in the same wavelength region. The line strengths are analyzed to determine quantitative shell strengths and shell column densities; the shell line velocities are discussed in the context of different models. It is shown that UV shell lines can exist in stars with no visible-wavelength shell features, that Fe III shell lines dominate the spectra between 1120 and 1140 A in Be and shell stars with circumstellar absorption features, and that the spectra of Be and shell stars in this region strongly resemble those of supergiants of similar effective temperature.
Crack problems in cylindrical and spherical shells
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Buckling and Damage Resistance of Transversely-Loaded Composite Shells
Experimental and numerical work was conducted to better understand composite shell response to transverse loadings which simulate damage-causing impact events. The quasi-static, centered, transverse loading response of laminated graphite/epoxy shells in a [+/-45(sub n)/O(sub n)](sub s) layup having geometric characteristics of a commercial fuselage are studied. The singly-curved composite shell structures are hinged along the straight circumferential edges and are either free or simply supported along the curved axial edges. Key components of the shell response are response instabilities due to limit-point and/or bifurcation buckling. Experimentally, deflection-controlled shell response is characterized via load-deflection data, deformation-shape evolutions, and the resulting damage state. Finite element models are used to study the kinematically nonlinear shell response, including bifurcation, limit-points, and postbuckling. A novel technique is developed for evaluating bifurcation from nonlinear prebuckling states utilizing asymmetric spatial discretization to introduce numerical perturbations. Advantages of the asymmetric meshing technique (AMT) over traditional techniques include efficiency, robustness, ease of application, and solution of the actual (not modified) problems. The AMT is validated by comparison to traditional numerical analysis of a benchmark problem and verified by comparison to experimental data. Applying the technique, bifurcation in a benchmark shell-buckling problem is correctly identified. Excellent agreement between the numerical and experimental results are obtained for a number of composite shells although predictive capability decreases for stiffer (thicker) specimens which is attributed to compliance of the test fixture. Restraining the axial edge (simple support) has the effect of creating a more complex response which involves unstable bifurcation, limit-point buckling, and dynamic collapse. Such shells were noted to bifurcate into asymmetric deformation modes but were undamaged during testing. Shells in this study which were damaged were not observed to bifurcate. Thus, a direct link between bifurcation and atypical damage could not be established although the mechanism (bifurcation) was identified. Recommendations for further work in these related areas are provided and include extensions of the AMT to other shell geometries and structural problems.
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
The results of an experimental and numerical study of the effects of imperfections on the buckling response of unstiffened thin-walled composite cylindrical shells are presented. Results that identify the individual and combined effects of traditional initial geometric shell-wall imperfections and non-traditional shell-wall thickness variations, shell-end geometric imperfections and variations in loads applied to the ends of the shells on the shell buckling response are included. In addition, results illustrating the effects of manufacturing flaws in the form of gaps between adjacent pieces of graphite-epoxy tape in some of the laminate plies are presented in detail. The shells have been analyzed with a nonlinear finite-element analysis code that accurately accounts for these effects on the buckling and nonlinear responses of the shells. The numerical results indicate that traditional and nontraditional initial imperfections can cause a significant reduction in the buckling load of a compression-loaded composite shell. Furthermore, the results indicate that the imperfections couple in a nonlinear manner. The numerical results correlate well with the experimental results. The nonlinear analysis results are also compared to the results from a traditional linear bifurcation buckling analysis. The results suggest that the nonlinear analysis procedure can be used for determining accurate, high-fidelity design knockdown factors for shell buckling and collapse. The results can also be used to determine the effects of manufacturing tolerances on the buckling response of composite shells.
Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts
Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.
Pressure Shell Approach to Integrated Environmental Protection
The next generation of exploration mission human systems will require environmental protection such as radiation protection that is effective and efficient. In order to continue human exploration, habitat systems will require special shells to protect astronauts from hostile environments. The Pressure Shell Approach to integrated environmental (radiation) protection is a multi-layer shell that can be used for multifunctional environmental protection. Self-healing, self-repairing nano technologies and sensors are incorporated into the shell. This shell consists of multiple layers that can be tailored for specific environmental protection needs. Mainly, this innovation focuses on protecting crew from exposure to micrometeorites, thermal, solar flares, and galactic cosmic ray (GCR) radiation. The Pressure Shell Approach consists of a micrometeoroid and secondary ejecta protection layer; a thin, composite shell placed in between two layers that is non-structural; an open cavity layer that can be filled with water, regolith, or polyethylene foam; a thicker composite shell that is a structural load bearing that is placed between two layers; and a bladder coating on the interior composite shell. This multi-layer shell creates an effective radiation protection system. Most of its layers can be designed with the materials necessary for specific environments. In situ materials such as water or regolith can be added to the shell design for supplemental radiation protection.