Anisotropic Shells Research Articles

Quantum Tunneling of the Magnetization in Systems with Anisotropic 4f Ion Pairs: Rates from Low-Temperature Zero-Field Relaxation.

Anisotropic open shell 4f ions have magnetic moments that can be read and written as atomic bits. If it comes to quantum applications where the phase of the wave function has to be written, controlled, and read, it is advantageous to rely on more than one atom that carries the quantum information on the system because states with different susceptibilities may be addressed. Such systems are realized for pairs of lanthanides in single-molecule magnets, where four pseudospin states are found and mixed in quantum tunneling processes. For the case of endohedral fullerenes like Dy2S@C82 or Tb2ScN@C80, the quantum tunneling of the magnetization is imprinted in the magnetization lifetimes at sub-Kelvin temperatures. A (4 × 4) Hamiltonian that includes quantum tunneling of the magnetization and the dipole and exchange interaction between the two lanthanide magnetic moments predicts the lifting of the zero-field ground state degeneracy and nonlinear coupling to magnetic fields in such systems.

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

Optical manipulation of anisotropic spherical shell particles in a dual-beam trap

In this paper, based on the generalized Lorenz-Mie theory (GLMT), expressions for the scattering coefficient and the shape factor of the beam are derived for a uniaxial anisotropic spherical shell (UASS) particle illuminated by standing laser beams. Through a comprehensive analysis involving the Maxwell stress tensor equations and conservation law of electromagnetic momentum, explicit expressions for both the transverse and axial radiation force (RF) acting upon UASS particles have been analytically derived. The current theories are shown to be valid by comparison with the existing reference. To achieve a more stable capture of UASS particles, the influence of the corresponding parameters of the particle and the dual laser beams on the capture and manipulation is investigated in detail. These investigations could provide an effective way to achieve improvements in optical tweezers and can become an encouraging approach to realize the high accuracy operation of UASS particles.

A health monitoring technique for spherical structures based on multi-acoustic source localization

Multi-acoustic source localization (MASL) technique has important applications in the early warning and maintenance of spherical structures. Without solving complex nonlinear equations and without knowing the wave velocity distribution a priori, this work demonstrates the feasibility of MASL on the surface of spherical structures using L-shaped sensor clusters. The positions of multiple acoustic sources can be localized using only time difference of arrival values. Relative location determination and relative probability density analysis have been presented and verified to eliminate two types of pseudo-sources. Simulations are performed for isotropic and anisotropic spherical shells. The proposed technique is validated experimentally for stainless steel spherical shells. Simulation and experimental results show that the proposed technique can enable MASL in spherical structures without knowing the wave velocity in the material.

Effect of porosity on the modal response of doubly-curved laminated shell structures made of functionally graded materials employing higher order theories

The manuscript investigates the modal response of laminated anisotropic doubly-curved shell structures of variable thickness made of Functionally Graded Materials (FGM), according to an efficient equivalent single layer strategy where the displacement field is described employing a condensed unified formulation, accounting for a higher order through-the-thickness expansion. A generalized power law distribution is adopted for the assessment of the FGM layers, whereas the presence of voids is considered starting from different homogenization assumptions. Unlike previous works which presented a variation of the homogenized material properties within the shell solid, in this paper the problem of material porosity is addressed, therefore a general distribution of the volume fraction of the constituent materials is considered, along with the presence of voids. To this end, both linear and trigonometric through-the-thickness distributions are here assumed. The fundamental governing equations are derived starting from a proper set of curvilinear principal coordinates, while a generalized set of blending functions accounts for arbitrarily shaped structures. Non-conventional boundary conditions are, here, modelled with a distribution of linear springs along the shell edges. The numerical implementation of the problem is performed with the generalized differential quadrature method. A systematic set of validating examples is presented, whose results are compared to predictions based on refined models, as well as some experimental evidence. After a validation step, an extensive parametric analysis points out the sensitivity of the porosity parameters on the modal response of structures with different curvatures and external constraints, with valid findings for engineering design purposes.

Multiplexed Surface Protein Detection and Cancer Classification Using Gap-Enhanced Magnetic-Plasmonic Core-Shell Raman Nanotags and Machine Learning Algorithm.

Cancer is the second leading cause of death attributed to disease worldwide. Current standard detection methods often rely on a single cancer marker, which can lead to inaccurate results, including false negatives, and an inability to detect multiple cancers simultaneously. Here, we developed a multiplex method that can effectively detect and classify surface proteins associated with three distinct types of breast cancer by utilizing gap-enhanced Raman scattering nanotags and machine learning algorithm. We synthesized anisotropic magnetic core-gold shell gap-enhanced Raman nanotags incorporating three different Raman reporters. These multicolor Raman nanotags were employed to distinguish specific surface protein markers in breast cancer cells. The acquired signals were deconvoluted and analyzed using classical least-squares regression to generate a surface protein profile and characterize the breast cancer cells. Furthermore, computational data obtained via finite-difference time-domain and discrete dipole approximation showed the amplification of the electric fields within the gap region due to plasmonic coupling between the two gold layers. Finally, a random forest classifier achieved an impressive classification and profiling accuracy of 93.9%, enabling effective distinguishing between the three different types of breast cancer cell lines in a mixed solution. With the combination of immunomagnetic multiplex target specificity and separation, gap-enhancement Raman nanotags, and machine learning, our method provides an accurate and integrated platform to profile and classify different cancer cells, giving implications for identification of the origin of circulating tumor cells in the blood system.

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

The article presents a calculation of the stability of non-thin cylindrical anisotropic layered shells under the action of end torsional moments in a spatial formulation. The anisotropy of the used material is characterized by one plane of elastic symmetry of characteristics. This is caused by the mismatch between the main elastic directions of the composite fibrous orthotropic material and the axes of the curvilinear cylindrical coordinate system.
 A three-dimensional inhomogeneous system of partial differential equations describing the subcritical stress-strain state within the linear theory of elasticity is derived using the Hu-Washizu variational principle. Reducing the dimension of the problem under consideration from three-dimensional to one-dimensional is carried out by taking into account the axial symmetry of the deformation of the cylindrical shell and using the method of straight lines along the generatrix.
 Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous partial differential stability equations is derived within the framework of the spatial theory of elasticity. The reduction of a three-dimensional system to a one-dimensional one is carried out along the generatrix and in the circular direction - by expanding the components of stresses and displacements into double trigonometric series when applying the procedure of the Bubnov-Galorkin method, as well as taking into account the periodicity of the resolving functions.
 An algorithm has been developed, implemented in the form of application software packages for PCs. In it, in a single computational process using the numerical method of discrete orthogonalization in the direction normal to the middle surface of the shell, the establishment of the parameters of the subcritical stress-strain state and the solution on this basis of stability problems for non-thin anisotropic cylindrical shells under the influence of torsion are combined.
 The problem of the influence on the stability of an anisotropic cylindrical non-thin shell of an increase in the number of cross-reinforced layers depending on the angle of rotation of the main directions of elasticity of the material and the direction of application of torque is considered. The obtained results of stability calculations according to the proposed approach were compared with critical torsion loads calculated using an orthotropic model for calculating anisotropic shells. It is shown that for single-layer cylindrical shells the difference between the compared results reaches 69%. An increase in the number of cross-reinforced layers leads to a decrease in this discrepancy, and with seven to eight layers, the difference between the critical loads obtained using the described approach and the orthotropic model is within 5%. This result is consistent with those obtained using classical or refined theories of calculations of both thin and non-thin anisotropic cylindrical shells.

Higher order theories for the modal analysis of anisotropic doubly-curved shells with a three-dimensional variation of the material properties

The manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials employing the Generalized Differential Quadrature (GDQ) method. A higher order generalized expression of the displacement field variable is assumed following the Equivalent Single Layer (ESL) approach. The geometrical description of the structures follows the differential geometry basics, whereas arbitrarily-shaped domains are distorted by means of generalized isogeometric blending functions. A three-dimensional generally anisotropic elastic constitutive behaviour is assumed within each layer of laminates, and a smooth variation of the material properties is implemented. In particular, a two-dimensional distribution alongside the physical domain is considered, whereas a through-the-thickness dispersion of the material properties is associated to each layer, taking into account both polynomial and non-polynomial analytical expressions. The fundamental equations are derived from the Hamiltonian principle, and they are solved directly in strong form via the GDQ method taking into account a non-uniform discrete computational grid. After some preliminary validating examples, some parametric investigations are performed systematically, showing the influence of the variation of the material properties on the modal response of the structures characterized by different lamination schemes, curvatures and boundary conditions. The proposed model allows for the dynamic analysis of the structures of different curvatures characterized by very complicated dispersions of the material properties following a simple and accurate methodology.

Hierarchical lattice stiffened cylindrical shell: Design, high-order vibration theory and composite parameter identification

A carbon fiber reinforced hierarchical lattice stiffened cylindrical shell (HLSCS) was designed and manufactured. Introducing effects of bending and coupling stiffness caused by neutral plane offsetting, an improved smeared stiffener method was proposed to homogenize the HLSCS to an anisotropic continuous cylindrical shell with varying-stiffness. The transverse shear stiffness was predicted by the higher-order shear deformation theory to build a high order vibration theory. Composite parameter identification method of the HLSCS was proposed based on the experimental and theoretical results to identify the composite parameters nondestructively. The method suggests discounted fiber volume fraction and stiffness for the completed HLSCS.

The Solvation Shell of Small Solutes in Aqueous-Organic Solvent Mixtures and Its Implications for Reversed-Phase Liquid Chromatography.

Reversed-phase liquid chromatography (RPLC) operates with water-organic solvent (W-OS) mobile phases where preferential solvation (PS) of solutes is likely. To investigate the relevance of the solute solvation shell in the mobile phase for RPLC retention, we combine data from molecular dynamics simulations of small, neutral solutes (six analytes and two dead time markers) in W-methanol (MeOH) and W-acetonitrile (ACN) mixtures with corresponding retention data obtained on an RPLC column over a wide range of W/OS ratios. Data derived from Kirkwood-Buff integrals show PS by the OS for analytes vs low or negative PS for dead time markers. W-ACN mixtures generate a higher amount of PS than W-MeOH mixtures, which contributes to the higher eluent strength of ACN in RPLC. Difference spatial distribution functions reveal anisotropic solvation shells with OS excess at hydrocarbon elements and W excess at functional groups, predicting that retention by the hydrophobic stationary phase is favored by hydrocarbon elements and limited by functional groups. Analysis of solute-solvent hydrogen bonds pinpoints the hydrogen-bond requirements toward W as the retention-limiting factor. The relation between the solute solvation shell and retention confirms the importance of W-OS and solute-W hydrogen bonding for RPLC retention.

Nonlinear modal analysis of multi-walled nanotube oscillations using nonlocal anisotropic elastic shell model

Nonlinear modal analysis of multi-walled nanotube oscillations using nonlocal anisotropic elastic shell model

Light scattering from the metallic nanowires with radially anisotropic cloaks

We discuss the scattering properties of the core–shell nanowires containing metallic core with nonlocal effects and radially anisotropic shell based on the nonlocal full-wave theory. The tunable extinction spectrum could be obtained by adjusting the anisotropy parameter and geometric size of the core–shell nanowires. The main peak resulted from transverse mode would be enhanced with the optimal anisotropy parameter. The subsidiary peaks due to the longitudinal mode become dense for the coated nanowires with thin anisotropic shell. Moreover, S-shaped and Z-shaped Fano resonances in the core–shell nanowires are presented under weak dissipation. These results will have potential applications in optical communications and ultra-sensitive detections.

3D-Spatiotemporal forecasting the expansion of supernova shells using deep learning towards high-resolution galaxy simulations

ABSTRACT Supernova (SN) plays an important role in galaxy formation and evolution. In high-resolution galaxy simulations using massively parallel computing, short integration time-steps for SNe are serious bottlenecks. This is an urgent issue that needs to be resolved for future higher-resolution galaxy simulations. One possible solution would be to use the Hamiltonian splitting method, in which regions requiring short time-steps are integrated separately from the entire system. To apply this method to the particles affected by SNe in a smoothed particle hydrodynamics simulation, we need to detect the shape of the shell on and within which such SN-affected particles reside during the subsequent global step in advance. In this paper, we develop a deep learning model, 3D-Memory In Memory (3D-MIM), to predict a shell expansion after a SN explosion. Trained on turbulent cloud simulations with particle mass mgas = 1 M⊙, the model accurately reproduces the anisotropic shell shape, where densities decrease by over 10 per cent by the explosion. We also demonstrate that the model properly predicts the shell radius in the uniform medium beyond the training data set of inhomogeneous turbulent clouds. We conclude that our model enables the forecast of the shell and its interior where SN-affected particles will be present.

Vibration characteristics analysis of anisotropic metal rubber medium-thick cylindrical shells

Vibration characteristics analysis of anisotropic metal rubber medium-thick cylindrical shells

Nonlinear ultrasound propagation in liquid containing multiple microbubbles coated by shell incorporating anisotropy

Using microbubbles coated by a thin shell as ultrasound contrast agents for ultrasound diagnosis improves image resolution. Since numerous microbubbles are used in clinical practice, understanding the acoustic properties of liquids containing multiple microbubbles is important. However, interactions between ultrasound and numerous coated microbubbles have not been fully investigated theoretically. Additionally, ultrasound contrast agents with shells made of various materials have been developed. Recently, an equation of motion that considers the anisotropy of the shell was proposed [Chabouh et al., “Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy,” J. Acoust. Soc. Am. 149, 1240 (2021)], and the effect of shell anisotropy on the resonance of the oscillating bubble was reported. In this study, we derived a nonlinear wave equation describing ultrasound propagation in liquids containing numerous coated microbubbles based on the method of multiple scales by expanding Chabouh's equation of motion for the single bubble. This was achieved by considering shell anisotropy in the volumetric average equation for the liquid and gas phases. Shell anisotropy was observed to affect the advection, nonlinearity, attenuation, and dispersion of ultrasound. In particular, the attenuation effects increased or decreased depending on the anisotropic shell elasticity.

General boundary conditions implementation for the static analysis of anisotropic doubly-curved shells resting on a Winkler foundation

In the present work an Equivalent Single Layer (ESL) formulation is proposed for the static analysis of doubly-curved anisotropic structures of arbitrary geometry and variable stiffness resting on a Winkler elastic foundation. In-plane and out-of-plane general distributions of linear elastic springs are provided for the implementation of general external constraints along the edges of the structure. The structure is geometrically described accounting for the principal curvatures of the shell object of analysis. A generalized set of blending functions based on Non-Uniform Rational Basis Spline (NURBS) curves is adopted so that arbitrary shaped structures can be modelled with the same approach. The fundamental governing equations are obtained in terms of displacement field unknowns, which has been effectively described accounting for a unified formulation based on the minimum potential energy principle. General anisotropic lamination schemes are considered, setting a general orientation of each lamina, as well as all possible material symmetries. The numerical implementation is performed by means of the Generalized Differential Quadrature (GDQ) method, thus allowing a strong formulation of the structural problem. A series of validation examples is performed on shells with zero, single and double curvatures in which the static structural response provided with the proposed formulation has been compared to that obtained from a refined three-dimensional finite element model, showing a great accordance between these different approaches. The research shows that the employment of higher order theories, together with the GDQ method, allows to obtain very accurate results with a reduced computational cost, compared to finite element simulations.

Three-dimensional stability of non-thin anisotropic cylindrical shells under axial pressure

Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous linearized differential equations of stability of non-thin anisotropic cylindrical shells is obtained. The anisotropy type of shells is characterized by one plane of elastic symmetry. Reducing the system to a one-dimensional one is carried out using the Bubnov-Gal'orkin method, which approximates the functions of unknown systems of equations along the generatrix and takes into account their periodicity in the circumferential direction. The numerical solution of the obtained one-dimensional system of equations is carried out using the discrete orthogonalization method. 
 The problem of stability of a non-thin anisotropic cylindrical shell for a different number of cross-laid composite layers against the action of axial pressure is solved. The nature of the dependence of critical forces on the number of layers is analyzed.

Free vibration analysis of laminated doubly-curved shells with arbitrary material orientation distribution employing higher order theories and differential quadrature method

In the present work, the dynamic behaviour of laminated anisotropic doubly-curved shells characterized by a generalized distribution of the material orientation angle is investigated employing higher order theories. The structural problem is developed following the Equivalent Single Layer (ESL) methodology, setting up a unified approach for the assessment of the displacement field variable with higher order theories. Accordingly, a generalized three-dimensional distribution of the material orientation angle is associated to each layer of the stacking sequence, accounting for an in-plane bivariate power distribution and out-of-plane symmetric and unsymmetric profiles described with both polynomial and non-polynomial analytical expressions. The fundamental equations are derived from the Hamiltonian Principle, and they are numerically tackled employing the Generalized Differential Quadrature (GDQ) method directly in the strong form. Moreover, a generalized three-dimensional set of linear elastic springs is implemented for the assessment of con-conventional boundary conditions. Furthermore, a generalized isogeometric mapping of the physical domain accounts for arbitrarily-shaped structures. The model is validated successfully with respect to refined three-dimensional classical models, and it is, then, applied systematically to check for the sensitivity of the mechanical response to the structural curvature, external constraints, and material orientation angle distributions.

A Comparison of Shell Theories for Vibration Analysis of Single-Walled Carbon Nanotubes Based on an Anisotropic Elastic Shell Model.

In the present paper, a comparison is conducted between three classical shell theories as applied to the linear vibrations of single-walled carbon nanotubes (SWCNTs); specifically, the evaluation of the natural frequencies is conducted via Donnell, Sanders, and Flügge shell theories. The actual discrete SWCNT is modelled by means of a continuous homogeneous cylindrical shell considering equivalent thickness and surface density. In order to take into account the intrinsic chirality of carbon nanotubes (CNTs), a molecular based anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and a complex method is applied to solve the equations of motion and to obtain the natural frequencies. Comparisons with the results of molecular dynamics simulations available in literature are performed to check the accuracy of the three different shell theories, where the Flügge shell theory is found to be the most accurate. Then, a parametric analysis evaluating the effect of diameter, aspect ratio, and number of waves along the longitudinal and circumferential directions on the natural frequencies of SWCNTs is performed in the framework of the three different shell theories. Assuming the results of the Flügge shell theory as reference, it is obtained that the Donnell shell theory is not accurate for relatively low longitudinal and circumferential wavenumbers, for relatively low diameters, and for relatively high aspect ratios. On the other hand, it is found that the Sanders shell theory is very accurate for all the considered geometries and wavenumbers, and therefore, it can be correctly adopted instead of the more complex Flügge shell theory for the vibration modelling of SWCNTs.