Shell Model Research Articles

Semi-analytical vibration modeling of complex axisymmetric shells using shifted Legendre series

This paper presents a semi-analytical approach based on the shifted Legendre series for vibration modeling of complex axisymmetric shells. This method divides the structure along its generator into complex axisymmetric shells comprised solely of conical and spherical shell segments. A global cylindrical coordinate system is established to unify the coordinate system of complex axisymmetric shells. Coupling between segments and the simulation of arbitrary boundary conditions are achieved using artificial spring technology. Based on the first-order shear deformation theory (FSDT), the energy functional of each segment is derived. The circumferential displacement is expanded using Fourier series, while the meridional displacement is expanded using the shifted Legendre series at shifted Gauss-Lobatto nodes. Utilizing the inner product matrix and differential matrix of the shifted Legendre series, the integration and differentiation processes in the vibration characteristic equation are simplified into a product form, significantly enhancing computational efficiency. Through convergence analysis and comparison of the computational results of the present method with numerical simulation results, experimental results and literature results demonstrate the advantages of high convergence, high accuracy and fast solution speed of this solution method. On this basis, the vibration characteristics of ring-stiffened double-layer hemispherical shells are investigated. The results demonstrate the great applicability of this method for vibration modeling of complex axisymmetric shells in engineering.

Proteinaceous Nanoshells with Quasicrystalline Local Order

Among various proteinaceous nanocontainers and nanoparticles, the most promising ones for various applications in nano- and medical science appear to be those whose structures differ fundamentally from icosahedral viral capsids described by the paradigmatic Caspar-Klug model. By analyzing such anomalous assemblies represented in the Protein Data Bank, we identify a series of shells with square-triangular local order and find that most of them originate from short-period approximants of a dodecagonal tiling consisting of square and triangular tiles. Examining the nonequilibrium assembly of such packings, we propose a new method for obtaining periodic square-triangle approximants and then construct the simplest models of tetragonal, octahedral, and icosahedral shells based on cubic and icosahedral nets cut from the approximant structures. Since gluing the nets can change the distances between adjacent vertices of the resulting shell, we introduce an effective energy, the minimization of which equalizes these distances. While the obtained spherical polyhedra reproduce the structures of experimentally observed protein shells and nanoparticles, the principles of protein organization that we lay out, and the ensuing structural models, can help to discover and investigate similar systems in the future. Published by the American Physical Society 2024

Higher forbidden unique β− decay transitions and shell-model interpretation

In the present work, we have predicted the half-lives for the β− decay for higher forbidden unique transitions in the mass range of nuclei from A = 40-138. For these transitions, the experimental data for half-lives are not available except for a few cases. The calculations for half-lives are performed within the framework of the nuclear shell model (SM). We have used the effective interactions sdpf-mu, gxpf1a, gwbxg, G-matrix, snet, sn100pn, and jj56pnb to perform the SM calculations in different mass regions. A comprehensive discussion has been made between the SM predicted half-lives and the scaled half-lives from proton-neutron quasiparticle random-phase approximation (pnQRPA). The results of the present study will be useful to plan new experiments to measure half-lives for these higher forbidden unique β− transitions.

Effect of rib profile on critical buckling pressure of ring-stiffened composite shells under hydrostatic pressure

ABSTRACT The buckling behaviour of thin-walled composite cylindrical shells with different rib profiles under hydrostatic pressure is studied in this paper. Various models of composite shells with outer diameter of 324 mm, thickness of 8 mm, length of 800 mm, and 18 different rib profiles are designed. Ribs have same sectional area and the total height is no more than 18 mm. Finite element (FE) models are built and validated by published experimental and FE results. The results for above models are obtained and show that the critical buckling pressure of ring-stiffened composite shells can improve by 44% to 136% compared to that of unstiffened composite shells. The rib total height, web thickness, and rib profile type are three factors affecting the critical buckling pressure of ring-stiffened composite shells. The composite shell stiffened by groove shape can acquire maximum buckling-carrying capacity.

3D electro-elastic static analysis of advanced plates and shells

The proposed three-dimensional (3D) coupled electro-elastic shell model allows the static analysis of smart structures embedding classical piezoelectric and functionally graded piezoelectric layers. Plates, cylindrical and spherical panels are investigated in both sensor and actuator configurations. The primary variables of the coupled model are displacement components and the electric potential. Therefore, displacements, stresses, strains, electric potential and electric displacements are calculated for smart structures used as sensors (applied mechanical load) and smart structures used as actuators (applied electric potential). In the case of spherical shells, 3D equilibrium equations are coupled with the 3D divergence electric displacement equation. The obtained coupled system is also valid for cylindrical shells and plates thanks to the use of a mixed curvilinear orthogonal reference system. The partial differential governing equations are solved using the Navier harmonic form and the exponential matrix method for simply supported structures. Preliminary assessments are proposed to validate the model and further benchmarks are analyzed to discuss the effects connected with the thickness ratio, the lamination scheme, the load conditions, the geometry of the structures and the employed materials. The main innovation point of the proposed model is the possibility to analyze several geometries including different materials and applied loads by means of a unique and general formulation where partial differential equations are solved in closed form. The use of functionally graded piezoelectric materials allows to eliminate all stress component discontinuities at each layer interface.

Weakening of N = 28 shell gap and the nature of 02+ states

The work reports a novel application of the interacting boson model in light-mass region around 48Ca, that takes into account intruder states and configuration mixing. The model is shown to provide a reasonable description of the observed low-lying yrast and yrare states of the N = 28 even–even isotones from Si to Fe, and even–even Ca isotopes. The nature of 02+ states is addressed in terms of the competition between spherical and deformed intruder configurations, and the rigidity of the N = 28 shell gap is tested, particularly for 44S. The 02+ isomer in 44S is shown to arise from a weak mixing between the two configurations and called as shape isomer. The unresolved low-lying spectra in 46Ar is also approached using the core-excitations across N = 28 shell. The SU(3) structure in 42Si is supported by the present calculation. The nearly spherical nature of 50Ti, 52Cr, 54Fe and 42,44,46Ca isotopes is found, while the core excitations are found to be essential for the description of yrare states. Shell model calculation is also performed for comparison.

Precise neural network predictions of energies and radii from the no-core shell model

Precise neural network predictions of energies and radii from the no-core shell model

The big bang of halide perovskites: The starting point of crystallization

Hybrid halide perovskites (HHPs) are very promising absorber materials for solar cells due to their high power conversion efficiency and the low-cost solution-based processing methods. We applied small angle X-ray scattering to MAPbI3, FAPbI3 and MAPbBr3 precursor solutions in different solvents (GBL, DMF, and mixtures) to gain a deeper understanding of the building blocks during the early stage of HHP formation. We present a core–shell model where the core is formed by [PbX6] octahedra surrounded by a shell of solvent molecules, which explains the arrangement of the precursors in solution and how the solvent and the halide influence such arrangement.Graphical

Enhanced biofuel production from Sacha Inchi wastes: Optimizing pyrolysis for higher yield and improved fuel properties

Sacha inchi waste consists of residues (SR) and shells (SS) that are processed into liquid fuel using a traditional pyrolysis process. Pyrolysis was performed at a constant heating rate of 20 °C/min and nitrogen flow rate of 100 mL/min. Before the process took place, a preliminary TGA analysis was performed and the results revealed that the appropriate pyrolysis temperature and time allowed a variation of 250–450 °C and 10–50 min, respectively. The results showed that the pyrolysis oil yields of both SR and SS increased with increasing pyrolysis temperature and time. However, the pyrolysis oil yield of SR was significantly higher than that of SS because the main component of SR contains abundant carbon from saturated fatty acids. The ANOVA method shows that the SS model is more complex and examines more terms and interactions, whereas the SR model is simpler and focuses on fewer components, but still shows significant effects, especially through temperature. The nonsignificant p-value for time in the SR model suggests that time may not have the same influence as temperature on the dependent variable. The SS pyrolysis oil was consistent and resulted in a constant calorific value and flash point between 31.10 and 32.14 MJ/kg and 120 and 124 °C, respectively. However, decreasing the O/C atomic ratio of SR pyrolysis oil from 0.92 to 0.38 influenced the increasing calorific value from 36.66 to 38.75 MJ/kg, while the H/C atomic ratio of SR pyrolysis oil was close to 2.00. This suggests that its effectiveness maintains an alkene structure that can improve fuel efficiency. The molecular formulae of the SS pyrolysis oil were CH16N0.04O7 and that of SR pyrolysis oil was CH2.2N0.08O0.45.

Investigating the level structure of 206Rn: evolution from seniority regime to collective dynamics* *Supported partially by the National Natural Science Foundation of China(10975191, U1867210, 11375023, 11475014, 11575018, 12075169 , 12322506), and the National Key R&D program of China (2016YFA0400504)

Excited states of have been examined via the ( , 5n) fusion reaction at a beam energy of 78 MeV. A number of transitions and levels are identified by the γ-γ coincidence measurement, further enriching the level scheme of . The full configuration shell model and nucleon-pair approximation (NPA) were utilized to investigate the single-particle configurations and seniority structures in . The results of these two calculations suggest that and states exhibit only a 50% component of a seniority-two state associated with a broken neutron pair. The collectivity of these two states primarily arises from configuration mixing due to residual proton-neutron interactions. Furthermore, and states are predominantly characterized by a seniority-two state marked by a broken proton pair.

An Investigation of the Energy-Absorption Characteristics of Thin-Walled Polymer Composite C-Channels: Experiment and Stacked Shell Simulation.

Polymer composite materials are increasingly used in civil aircraft structures. The failure mode and energy-absorption characteristics of polymer composite structures have garnered significant attention from academia and industry. For thin-walled polymer composite C-channels with layups of [0/90]3s, [45/-45]3s, and [45/90/-45/0]3, low-speed axial compression tests were performed to investigate the failure modes, failure mechanisms, and energy-absorbing characteristics. After parametric studies using [0] and [90] single-element models, stacked shell models of thin-walled composite C-channels were established using the Lavadèze single-layer damage constitutive model, Puck 2000, and Yamada Sun failure criteria. The results show that these thin-walled composite C-channels exhibit a stable progressive crushing process with a local buckling failure mode, encompassing local buckling, fiber break-age, matrix cracks, delamination, and corner cracking. The stacked shell model demonstrates reasonable agreement with the progressive crushing process of thin-walled composites, accurately capturing interlayer matrix failure and interface delamination cracking behavior. A comparison of the specific energy absorption (SEA) and mean crushing force (Fmean) between the simulation and test results yields a difference of less than 6%, indicating a strong correlation between the simulation results and the experimental energy-absorbing characteristics. It also shows that a deep understanding of the parameters is helpful for accurate numerical modeling.

Trineutron resonances in the SS-HORSE extension of the no-core shell model

Trineutron resonances in the SS-HORSE extension of the no-core shell model

Three-dimensional vibration analysis of multilayered composite and functionally graded piezoelectric plates and shells

In the present paper, a coupled 3D exact electro-elastic shell model for Functionally Graded (FG) and composite piezoelectric structures is proposed. Primary variables of the electro-elastic model are the electric potential and the three displacement components. The model allows to evaluate the piezoelectric effect in terms of frequencies and vibration modes. Both closed and open circuit configurations are analyzed and compared. The 3D equilibrium equations and the 3D divergence electric displacement equation for spherical shells give the set of partial differential equations for the electro-elastic problem. The proposed model for spherical shells automatically degenerates into simpler models for plates and cylindrical shells via properly considerations on radii of curvature along in-plane directions. The orthogonal mixed curvilinear coordinates α, β and z are employed. The partial differential governing equations have constant coefficients considering fictitious layers and they are solved using the Navier harmonic form and the exponential matrix method. These features lead to an exact solution for simply-supported boundary conditions. Free vibration analyses are conducted and circular frequencies for the first three thickness vibration modes are computed. After a global assessment phase to verify the correctness of the developed model, new benchmarks are proposed: different thickness ratios and material configurations are investigated. The present work can be intended as a reference general solution for those scientists interested in the study of piezoelectric structures via 2D analytical and numerical formulations.

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

Predictive modeling of buckling in composite tubes: Integrating artificial neural networks for damage detection

Tubular structural composites are widely used in applications where high stiffness and low weight are required. This work proposes the study and evaluation of the influence of damage on the structural responses of thin-walled structures made of composite materials, as well as the development of a buckling prediction model using artificial intelligence. The methodology is approached on a few main fronts, namely: i) numerical modeling of the direct problem of the structure in finite elements, ii) modeling and parameterization of delamination in the elliptical shell model; iii) obtaining a database through finite element updating and iv) formulation and construction of the regression and prediction model using artificial neural networks. The numerical results showed that, as expected, the presence of delamination has a significant impact on the occurrence of buckling. The study also showed that it is possible to predict buckling values, with extremely satisfactory results - an error of around 1%, provided that more complex regression methods are used, such as regression by artificial neural networks, since the relationship between damage and buckling values is not trivial.

Intruder band mixing in an ab initio description of 12Be

The spectrum of ▪ exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate SU(3) symmetry and are qualitatively consistent with Elliott model predictions.

Sustainable removal of methylene blue dye from textile effluents by magnetized Tea waste and Peanut shells

Methylene blue finds numerous applications across various industries but its prolonged exposure to living organisms can result in significant health risks. In this study, the adsorption of magnetized Peanut shells and Tea waste for methylene blue dye removal has been reported. The biosorbents were synthesized by co-precipitation method and their suitability for methylene blue adsorption was confirmed through characterization techniques including Scanning Electron Microscope, Fourier Transfer Infrared Spectroscopy and X-Ray Diffraction analysis. After optimizing for pH (8.0), temperature (312 k), biosorbents dosage 25 mg/L with contact periods (35 min for Tea waste@Fe3O4 and 40 min for Peanut shells@Fe3O4), and initial methylene blue concentrations (5 ppm), the removal percentages of 95.88 % for Tea waste@Fe3O4 and 84.11 % for Peanut shells@Fe3O4 were achieved effectively. The equilibrium data for MB dye adsorption fitted well with the Langmuir model (R2 = 0.99) for Tea waste@Fe3O4 which indicated the formation of monolayer formation of adsorbate at the surface of adsorbent and the Freundlich model (R2 = 0.98) for Peanut shells@Fe3O4 confirmed the multilayers formation of MB dye at the material surface. Kinetic studies specified that both Tea waste@Fe3O4 (R2 = 0.99) and Peanut shells@Fe3O4 (R2 = 0.99) followed the pseudo-second order. Thermodynamic analysis showed that the adsorption process on Tea waste@Fe3O4 and Peanut shells@Fe3O4 was spontaneous (−ΔG) and endothermic. Tea waste@Fe3O4 exhibited ΔH (27.97 kJ/mol) and entropy ΔS (93.69 kJ/mol) while ΔH = 208.9 kJ/mol and ΔS 62 kJ/mol were found for Peanut shells@Fe3O4. The performance of the proposed biosorbent in industrial effluent demonstrated their effectiveness, highlighting their potential as a cost effective and sustainable solution for wastewater treatment.

Topology optimization of curved thick shells using level set method and non-conforming multi-patch isogeometric analysis

We present a novel framework for topological shape optimization of curved non-conforming multi-patch and trimmed thick-shells subjected to external loads. Our method integrates the level set method (LSM) with a diffuse interface, a Hadamard shape derivative, and multi-patch isogeometric analysis (IGA) into a gradient descent algorithm to systematically capture the evolution of the shape. This integration enables us to directly manipulate CAD-compatible geometries and analysis techniques and to obtain the results as a CAD surface. The novelty lies in the utilization of multi-patch IGA models based on NURBS functions, which allows us to simultaneously maximize the stiffness and minimize the volume of the shell by searching for an optimal material distribution within its middle surface. The material is modeled under a small strain assumption in linear elasticity using a Reissner–Mindlin kinematic shell model in plane stress. The effectiveness of our approach is demonstrated on several curved conforming and non-conforming multi-patch geometries in 3D.

Machine Learning in the Problem of Extrapolating Variational Calculations in Nuclear Physics

A modified machine learning method is proposed, utilizing an ensemble of artificial neural networks for the extrapolation of energies obtained in variational calculations, specifically in the No-core Shell Model (NCSM), to the case of the infinite basis. A new neural network topology is employed, and criteria for selecting both the data used for training and the trained neural networks for statistical analysis of the results are formulated. The approach is tested by extrapolating the deutron ground state energy in calculations with the Nijmegen II NN interaction and provides statistically significant results. This technique is applied to obtain extrapolated ground state energies of 6Li and 6He nuclei based on the NCSM calculations with Daejeon16 NN interaction.

Davidson basis in the shell model for 2p, 2h, and pn nuclei

In this study, we replace the widely used harmonic oscillator basis with the Davidson basis for the shell model computation. The new foundation was introduced and its application to the shell model computation was explained. A detailed discussion is given on the method of calculation and utilization. Then, three cases two-particle, 18O, and two-hole, 38Ar, and proton-neutron nuclei, 6Li, and 18F, that illustrate various scenarios are examined. In these two scenarios, both Davidson bases and harmonic oscillator are used to replicate energy levels and a few electric transition probabilities. We assess each case’s accuracy by comparing the theoretical predictions with the experimental data.