Shell Model Research Articles

Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model

Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales ℓn such that each structure transfers its energy to two substructures of scale ℓn+1=ℓn/λ. For this model, we construct exact inertial range solutions that display intermittency, i.e., absence of self-similarity. Using a large ensemble of these solutions, we investigate how the probability distributions of the velocity modes change with scale. It is demonstrated that, while velocity amplitudes are not scale-invariant, their ratios are. Furthermore, using large deviation theory, we show how the probability distributions of the velocity modes can be re-scaled to collapse in a scale-independent form. Finally, we discuss the implications the present results have for real turbulent flows.

Vibration characteristics analysis of flexible helical gear system with multi-tooth spalling fault: Simulation and experimental study

Gear systems operating at high speeds and under heavy loads are susceptible to continuous multiple tooth surface spalling. The time-varying meshing stiffness (TVMS) model of helical gear pair with multi-tooth spalling fault is established by combining image recognition method and loaded tooth contact analysis (LTCA) method to target the actual form of the spalling fault, and its effectiveness was verified through finite element method (FEM). The flexible helical gear dynamic model is established by utilizing 8-node shell model and Timoshenko beam model to simulate the gear foundations and shafts, the TVMS in multi-tooth spalling fault condition is introduced as the excitation. The mapping relationship between the meshing process, TVMS and vibration response under the influence of rotational speed, spalling surface morphology scale, spalling depth and location of spalling occurrence is analyzed by combining simulation and experimental results. As the rotational speed increases, the specific meshing frequency coincides with the natural frequency of the gear system, leading to the phenomenon of superharmonic resonance. Continuous multi-tooth spalling fault results in continuous time-domain shocks and the meshing frequency modulation of the rotational frequency of the gear with spalling fault. In the absence of bottoming out, the increase in spalling surface morphology scale exerts a more pronounced influence on the vibration characteristics of the helical gear system compared to the increase in spalling depth. The research results can provide theoretical basis for gear system fault diagnosis.

Vibration and damping of carbon fiber reinforced polymer orthogonal lattice truss sandwich panels manufactured by a new manufacturing process

A new method of fabricating carbon fiber reinforced polymer (CFRP) orthogonal lattice truss sandwich panels is proposed. Inner trusses are inserted into outer trusses. Three structures are prepared using different adhesives: epoxy resin, ethylene–vinyl acetate copolymer (EVA), and nitrile butadiene rubber (NBR). The mode shapes, natural frequencies, and loss factors of the structures are tested and predicted using the finite element modal strain energy method with a solid model and two shell models, respectively. The shell stiffness matrixes are calculated using representative volume element (RVE) method and analytical method. The results show that these three theories can accurately predict the sandwich panels with epoxy or EVA adhesive, while the sandwich panel with rubber layer cannot be accurately predicted. The strain energy composition, shell stiffness matrices, influence of node offset and influence of adhesive layer thicknesses are studied. The EVA adhesive improves the loss factors of the structure within an acceptable reduction of natural frequency.

Ab initio calculations of mirror energy difference in sd-shell nuclei* *Supported by the National Natural Science Foundation of China (12205340, 11975282); the Gansu Natural Science Foundation (22JR5RA123); the Special Research Assistant Project of the Chinese Academy of Sciences; the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000); the Key Research Program of the Chinese Academy of Sciences (XDPB15);

Mirror energy difference is a key observable in isospin symmetry breaking, containing rich information about nuclear structure. Understanding the mechanisms underlying mirror energy difference is important in nuclear physics. In the present work, we extensively investigated mirror energy difference using ab initio valence-space in-medium similarity renormalization group approach, focusing specifically on -shell nuclei. The low-lying spectra of Al isotopes and isotones, together with their mirror nuclei, were calculated, followed by a systematic analysis of the evolution of the mirror energy difference. The results suggest that the large mirror energy difference is mainly caused by the weakly-bound effects and large average occupations of the orbit. Lastly, we compare the results of our ab initio calculations with shell model results, elucidating the relationship and coherence between these two models.

Effect of different material on the folding of composite ultrathin tape spring hinges via unifed 2D shell models

The aim of this work is to analyze the effect of different materials on the folding of ultrathin tape spring hinges. This mechanism is modeled using the Finite Element Method (FEM) combined with the Carrera Unified Formulation (CUF) for the development of refined 2D shell models. These models can deal with different materials and different theoretical approximations can be introduced in an automatic way thanks to the hierarchical capability of the CUF formalism, according to which the degree of refinement of the mathematical model is an input to the analysis. The nonlinear governing equations are developed using a Total Lagrangian formulation and solved via a Newton-Raphson linearization technique with arc-length type constraints. A validation of the proposed model is carried out by comparing the results with those available in the literature involving a cured T300-1k/913 tow and HexPly 913 resin. After a convergence analysis, the mathematical model proves to ensure a good fit. This model is used for the final analysis with different materials, i.e. isotropic metallic with hardened steel tape spring and unidirectional T300 graphite fibre/epoxy prepreg with 34% resin content by weight. The results, in the form of moment angle curves, are reported for two different values of the thickness of the structure.

Numerical and Theoretical Study on Failure Characteristics and Damage Assessment Model of Curved Steel-Concrete-Steel Sandwich Shells Subjected to Impact Load

In this study, damage assessment model of curved steel–concrete–steel (CSCS) sandwich shells subjected to impact loads was investigated. A numerical simulation method was applied to obtain failure modes of CSCS sandwich shells under impact load by changing the impact velocity as well as the mass and diameter of the hammer. From the 108 finite element (FE) models, three failure modes were found: local deformation, top steel plate fracture, and penetration. The failure mechanism for each failure mode was analyzed based on numerical simulation results, such as impact force and displacement-time histories, varying internal energy, and deformation modes of the structures. The law of failure mode distribution of the CSCS sandwich shell was also summarized. Moreover, the impact force–displacement relationship was obtained using an analytical method, and the FE results were in acceptable agreement with experiments. Finally, damage assessment model of the CSCS sandwich shells was obtained by comparing the hammer initial kinetic energy with the maximum absorbed energy of the CSCS sandwich shell. This model can be used as a quick tool to judge the failure status of the CSCS sandwich shell. The work presented in this paper is of significance and can fill the gap of the damage assessment model of CSCS sandwich shells subjected to impact loads.

The s-p Nonhybrid Nature Causes Adaptive Superatomic States of Bismuth Clusters.

We report a joint experimental and theoretical study on the stability and reactivity of Bin+ (n = 5-33) clusters. The alternating odd-even effect on the reaction rates of Bin+ clusters with NO is observed, and Bi7+ finds the most inertness. First-principles calculation results reveal that the lowest energy structures of Bi6-9+ exhibit quasi-spherical geometry pertaining to the jellium shell model; however, but the Bin+ (n ≥ 10) clusters adopt assembly structures. The prominent stability of Bi7+ is associated with its highly symmetric structure and superatomic states with a magic number of 34e closed shell. For the first time, we demonstrate that the unique s-p nonhybrid feature in bismuth rationalizes the stability of Bi6-9+ clusters within the jellium model, by filling the 6s electrons into the superatomic orbitals (forming "s-band"). Interestingly, the stability of 18e "s-band" coincides with the compact structure for Bin+ at n≤9 but assembly structures for n ≥10, showing an accommodation of the s electrons to the geometric structure. The atomic p-orbitals also allow to form superatomic orbitals at higher energy levels, contributing to the preferable structures of tridentate binding units. We illustrate the s-p nonhybrid nature accommodates the structure and superatomic states of bismuth clusters.

Fatigue Performance of Rib-to-Deck Double-Sided Weld Joint of Orthotropic Steel Deck on Plate Girder Railway Bridges

This research work presents the stress behavior of rib-deck weld joints in Orthotropic Steel Deck (OSD) railway bridges. It is essential to determine the most vulnerable load mode of the wheels for fatigue failure of OSD bridges and to improve the fatigue resistance of the welded rib-deck connection. Fatigue performance largely depends on the weld stress. Double-sided welds for rib-deck welds improve fatigue performance. The fatigue behavior of the rib-deck double-sided weld joint has been compared with the single-sided one. This study used Abaqus software to create the global shell model and the solid submodel of the OSD. The results of the structural stress-based finite element analysis indicated that when the center line of the front axle pair of a locomotive coincides with the center line of the midspan of the bridge, the most severe loading condition occurs. The rib near the main girder experiences the maximum structural stress in the weld toe of the rib-deck joint. Moreover, the rib-deck double-sided weld joints have 43.7% less structural stress compared to single-sided weld joints at the root of the weld, and this improves the performance during fatigue of OSDs.

A novel model for buckling of composite shell: Ring stiffened shell and stiffened shell with cutout under hydrostatic pressure

Focusing on buckling problem under hydrostatic pressure of ring stiffened shells and shells with stiffened cutout fabricated by filament winding process, a new form of equilibrium equations is given in this paper based on high-order shear deformation theory (HSDT). A novel theoretical model is proposed based on Messager's model of geometrical imperfection. The model contains both ring stiffened shell model (RSSM) and stiffened shell with cutout model (SSCM). In this model, changes in the shells' thickness z˜k(x,y),k=1,2,…,n are described using a Fourier series representation, which is included in HSDT stiffness matrix A, B, D, E, F, H. To evaluate the critical buckling pressure pcr, the model is applied and compared with the conventional stiffened cylindrical shell (SCS) model. The results demonstrate a significant reduction in error, ranging from 71.08% to 81.22%, when using the proposed model for shells stiffened by a ring stiffener in the middle, as compared to the SCS model. This highlights the enhanced accuracy provided by the proposed model. The results indicate that small stiffened cutouts in thin shells and large stiffened cutouts in moderately thick shells have relatively small influence on the critical buckling pressure. Conversely, the presence of a ring stiffener in the middle has a more pronounced effect.

Ultrasound measurements of particle shells in magnetic Pickering emulsions

A magnetic Pickering emulsion is an emulsion stabilized by magnetic nanoparticles that accumulate at the droplet interface to form a shell. The physical characterization of a Pickering emulsion, particularly the size of the stabilizing layer and the size of Pickering droplets, is essential for many applications. This report presents the findings of a theoretical and experimental study of ultrasound attenuation involving magnetic Pickering emulsions. Specifically, the ultrasound scattering theory based on the so-called core–shell model was utilized to interpret data obtained from ultrasonic measurements. In this model, the additional phase, i.e., the particle shell covering the oil core of a Pickering droplet, was considered for acoustic wave propagation in emulsions. The attenuation of an ultrasonic wave in the function of wavenumber multiplied by core radius (kb), wavenumber multiplied by shell thickness (kc), and frequency was numerically calculated for different concentrations of the droplets. The theoretical results and measurements were compared using a novel approach based on ultrasound spectroscopy to determine the stability and the size of the magnetic Pickering droplets.

On the Discussions of Nonlinear Terms in the Large Deformation Model of Thin-Walled Cylindrical Shells

On the Discussions of Nonlinear Terms in the Large Deformation Model of Thin-Walled Cylindrical Shells

Sizes of the Neutron–Proton Halo in Nucleon-Stable States of the 6Li Nucleus

The matter, neutron, and proton radii of nucleon-stable 1+ and 0+ states of the 6Li nucleus are studied theoretically within the no-core shell model. The results have been comparatively analyzed with the radii of the 0+ state of the 6He nucleus. To increase the accuracy of calculations, we have developed an extrapolation procedure. A new definition of the quantitative measure has been proposed and justified to describe the properties of a halo formed by loosely bound neutrons and protons in the A-nucleon problem. The sizes of the halo in the indicated states of 6Li have been calculated for the first time. It has been demonstrated that the sizes of their halos are close to those of the two-neutron halo in 6He. Thus, additional reliable evidence of the existence of the neutron–proton halo in the discussed states of 6Li has been obtained.

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

Microscopic study of normal deformed bands in 167,169,171Lu

The normal deformed bands of [Formula: see text]Lu isotopes have been studied by using projected shell model approach. The band head spins, configurations and energies of all the normal deformed bands are reproduced well by the above said approach. The present calculations have predicted [Formula: see text] band head spin for [523]7/2− bands of [Formula: see text]Lu. The observed systematics of aligned angular momenta and the experimental differences in frequencies around the backbends for all the normal deformed bands are reproduced well by the theoretical results. Besides this, the observed backbends or upbends in these isotopes may be ascribed to the alignment of a pair of neutrons in the neutron [Formula: see text] orbital. Although the theoretical [Formula: see text] values obtained from the projected shell model wavefunctions overestimate the experimental [Formula: see text] values in [Formula: see text]Lu, yet they are close to the measured values, considering the precision of measurement. The reduction in the theoretical [Formula: see text] values around the band crossing region may be ascribed to change in nuclear structure of yrast bands due to neutron pair alignment in [Formula: see text] orbital.

A high-latitude coronal mass ejection observed by a constellation of coronagraphs: Solar Orbiter/Metis, STEREO-A/COR2, and SOHO/LASCO

Context. A few days before the first perihelion of the Solar Orbiter nominal mission, which occurred on 2022 March 26, the Metis coronagraph on board Solar Orbiter detected a coronal mass ejection (CME) that was moving away from the far side of the Sun (with respect to Solar Orbiter) at high northern latitudes. The eruption was also seen by other spacecraft, in particular, by STEREO-A, which was in quadrature configuration with Solar Orbiter. Aims. We analyse the different views of the CME by a constellation of spacecraft with the purpose to determine the speed and acceleration of the CME, and to identify the source region of the CME. Methods. Considering the positions of various spacecraft on 2022 March 22, this CME happened to be within the field of view of STEREO-A/SECCHI, and it was visible over the limb from SOHO/LASCO. We present the results of the 3D reconstruction of the CME based on the graduated cylindrical shell model and of the identification of the possible origin of the CME using extreme-ultraviolet (EUV) observations by Solar Orbiter/EUI, STEREO-A/EUVI, and SDO/AIA. The observations in EUV are compared with the coronal magnetic structure obtained by the potential field source surface method. Results. The 3D reconstruction of the CME derives a central latitude of 29° N, a Stonyhurst longitude of −125°, and an average radial speed at the apex of 322 ± 33 km s−1 between 4 and 13 R⊙, which is probably not high enough to generate a shock wave. The estimated average acceleration of the CME is 16 ± 11 m s−2 in the same range of distances from the Sun. This CME may be associated with the disappearance of a coronal cloud prominence, which is seen in the EUV by STEREO-A/EUVI and SDO/AIA, and is also associated with rapidly evolving emerging magnetic flux.

Experimental and numerical studies on mechanical properties of TPMS structures

Due to their exceptional lightweight and mechanical properties, triply periodic minimal surface (TPMS) based lattice structures have been widely studied. In this paper, the energy absorption performance of eight TPMS structures under large deformation was thoroughly studied, and five meshing strategies were evaluated comprehensively for the first time. The research objectives include three parts. First, the mechanical properties of eight TPMS structures, namely Primitive (P), Gyroid (G), Diamond (D), I-Wrapped Package (I-WP), Fischer-Kock (F-K), Neovius (N), I2-Y⁎⁎ and F-Rhombic Dodecahedra (F-RD) lattices, were investigated by utilizing experimental and numerical methods. These TPMS structures were fabricated using 316 L stainless steel powder by selective laser melting (SLM) and compared experimentally under compression in terms of the stress-strain curve, deformation and energy absorption. The results showed that F-RD and D lattice structures exhibit the best energy absorption capacity at relative densities less and greater than 30%, respectively. Second, to evaluate different meshing strategies for these complex structures, five finite elements (FE) models based on the shell, solid, and voxel elements were compared in terms of modeling ease, computational efficiency, data management, and simulation accuracy. It was demonstrated that the quadrilateral shell model shows satisfactory results for lattice structures with low relative densities or thin walls. In contrast, the voxel model shows the best results for structures with higher relative densities or thicker walls. Last, the voxel model was applied to the F-RD and D lattice structures. The numerical results showed that the stress distribution was more uniform in the F-RD, and the internal self-contact occurred later in the D lattice structure, further confirming the experimental observation and revealing the energy absorption mechanisms of TPMS structures.

Nuclear shell-model simulation in digital quantum computers

The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.

Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics

We present a mass lumping approach based on an isogeometric Petrov–Galerkin method that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of the polynomial degree of the spline approximation. To discretize the test function space, our method uses an approximate dual basis, whose functions are smooth, have local support and satisfy approximate bi-orthogonality with respect to a trial space of B-splines. The resulting mass matrix is “close” to the identity matrix. Specifically, a lumped version of this mass matrix preserves all relevant polynomials when utilized in a Galerkin projection. Consequently, the mass matrix can be lumped (via row-sum lumping) without compromising spatial accuracy in explicit dynamics calculations. We also address the imposition of Dirichlet boundary conditions and the preservation of approximate bi-orthogonality under geometric mappings. In addition, we establish a link between the exact dual and approximate dual basis functions via an iterative algorithm that improves the approximate dual basis towards exact bi-orthogonality. We demonstrate the performance of our higher-order accurate mass lumping approach via convergence studies and spectral analyses of discretized beam, plate and shell models.

Existence theorems for nonlinear shell models of Koiter’s type

We first show that the minimization problem associated with the nonlinear shell model of W.T. Koiter becomes coercive over its natural space of admissible deformations when the third fundamental form is added to its functional. Then, under the assumption that the middle surface of the shell is a minimal surface, we approach this minimization problem by a new minimization problem that is well-posed over the same space of admissible deformations.

Optimisation of layered shell model for analysis of reinforced concrete shear walls based on machine learning

Layered shell modelling is an effective tool for the efficient simulation of two-dimensional structural members. As machine learning (ML) provides a novel alternative for the optimisation analysis of the traditional layered shell model, it has been widely used in civil engineering applications. This study focuses on the accurate numerical simulation of reinforced concrete (RC) shear wall structures using the ML method. The user subprogram interface HYPELA2 based on the implicit solver of Marc software was compiled to implement a program package to consider the precise constitutive model of concrete. Additionally, different ML methods and loss functions were compared, and the adopted optimisation method was based on the particle swarm optimisation and L1 loss function. The analysis of constitutive parameters was realised according to the optimisation of the ML algorithm. Multiple numerical models were used to verify the stability and accuracy of the proposed layered shell model and ML method. Finally, the results obtained from comprehensive experimental research and numerical simulations were used to determine the recommended values of parameters for finite element analysis of RC shear walls to produce a novel high-precision, efficient, and universal calculation model.