Isotropic Shells Research Articles

Numerical simulation of nanoneedle-cell membrane collision: minimum magnetic force and initial kinetic energy for penetration

Aims and objectives: This research aims to develop a kinetic model that accurately captures the dynamics of nanoparticle impact and penetration into cell membranes, specifically in magnetically-driven drug delivery. The primary objective is to determine the minimum initial kinetic energy and constant external magnetic force necessary for successful penetration of the cell membrane. Model Development: Built upon our previous research on quasi-static nanoneedle penetration, the current model development is based on continuum mechanics. The modeling approach incorporates a finite element method and explicit dynamic solver to accurately represent the rapid dynamics involved in the phenomenon. Within the model, the cell is modeled as an isotropic elastic shell with a hemiellipsoidal geometry and a thickness of 200 nm, reflecting the properties of the lipid membrane and actin cortex. The surrounding cytoplasm is treated as a fluid-like Eulerian body. Scenarios and Results: This study explores three distinct scenarios to investigate the penetration of nanoneedles into cell membranes. Firstly, we examine two scenarios in which the particles are solely subjected to either a constant external force or an initial velocity. Secondly, we explore a scenario that considers the combined effects of both parameters simultaneously. In each scenario, we analyze the critical values required to induce membrane puncture and present comprehensive diagrams illustrating the results. Findings and significance: The findings of this research provide valuable insights into the mechanics of nanoneedle penetration into cell membranes and offer guidelines for optimizing magnetically-driven drug delivery systems, supporting the design of efficient and targeted drug delivery strategies.

Identification of excessive contact pressures under hand orthosis based on finite element analysis.

Implicit magnitudes and distribution of excessive contact pressures under hand orthoses hinder clinicians from precisely adjusting them to relieve the pressures. To address this, contact pressure under a hand orthosis were analysed using finite element method. This paper proposed a method to numerically predict the relatively high magnitudes and critical distribution of contact pressures under hand orthosis through finite element analysis, to identify excessive contact pressure locations. The finite element model was established consisting of the hand, orthosis and bones. The hand and bones were assumed to be homogeneous and elastic bodies, and the orthosis was considered as an isotropic and elastic shell. Two predictions were conducted by assigning either low (fat) or high (skin) material stiffness to the hand model to attain the range of pressure magnitudes. An experiment was conducted to measure contact pressures at the predicted pressure locations. Identical pressure distributions were obtained from both predictions with relatively high pressure values disseminated at 12 anatomical locations. The highest magnitude was found at the thumb metacarpophalangeal joint with the maximum pressure range from 13 to 78 KPa. The measured values were within the predicted range of pressure magnitudes. Moreover, 6 excessive contact pressure locations were identified. The proposed method was verified by the measurement results. It renders understanding of interface conditions underneath the orthosis to inform clinicians regarding orthosis design and adjustment. It could also guide the development of 3D printed or sensorised orthosis by indicating optimal locations for perforations or pressure sensors.

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff–Love shell patches

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document} requirement of Kirchhoff–Love-based discretizations. Weak enforcement of coupling conditions is achieved through the symmetric interior penalty method, where the fluxes are computed using their correct variationally consistent expression that was only recently proposed and is unprecedentedly adopted herein in the context of coupling conditions. The constitutive relationship accounts for generically laminated materials, although the proposed tests are conducted under the assumption of uniform thickness and lamination sequence. Numerical experiments assess the method for an isotropic and a laminated plate, as well as an isotropic hyperbolic paraboloid shell from the new shell obstacle course. The boundary conditions and domain force are chosen to reproduce manufactured analytical solutions, which are taken as reference to compute rigorous convergence curves in the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}, H1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^1$$\\end{document}, and H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^2$$\\end{document} norms, that closely approach optimal ones predicted by theory. Additionally, we conduct a final test on a complex structure comprising five intersecting laminated cylindrical shells, whose geometry is directly imported from a STEP file. The results exhibit excellent agreement with those obtained through commercial software, showcasing the method’s potential for real-world industrial applications.

Vibration of black phosphorus nanotubes via orthotropic cylindrical shell model

Black phosphorus nanotubes (BPNTs) may have good properties and potential applications. Determining the vibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designing optimized nanodevices. In this paper, the mechanical behaviour and vibration property of BPNTs are studied via orthotropic cylindrical shell model and molecular dynamics (MD) simulation. The vibration frequencies of two chiral BPNTs are analysed systematically. According to the results of MD calculations, it is revealed that the natural frequencies of two BPNTs with approximately equal sizes are unequal at each order, and that the natural frequencies of armchair BPNTs are higher than those of zigzag BPNTs. In addition, an armchair BPNTs with a stable structure is considered as the object of research, and the vibration frequencies of BPNTs of different sizes are analysed. When comparing the MD results, it is found that both the isotropic cylindrical shell model and orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of the longer BPNTs better. However, for the vibration of shorter and thinner BPNTs, the prediction of the orthotropic cylindrical shell model is obviously superior to the isotropic shell model, thereby further proving the validity of the shell model that considers orthotropic for BPNTs.

AXISYMMETRIC DYNAMIC BEHAVIOUR OF THIN OBLATE SHELLS

This paper presents a theoretical investigation of the axisymmetric free vibrations of an isotropic thin oblate spheroid shell. The analysis depends on the Rayliegh – Ritz's method. The non – shallow shell theory is used for the analysis. The analysis based on considering the oblate spheroid as a continuous system constructed from two spherical shell elements matched at the continuous boundaries.Throughout the results, it is shown that when the eccentricity reaches zero, an exact thin sphere solution is emerged and when the eccentricity equals one an exact thin circular plate solution is emerged. Therefore, the eccentricity of an oblate shell at medium value lies between these two values.It was found that the Rayleigh – Ritz's method is suitable for all eccentricities, while the literature showed that the Rayleigh's method is suitable for eccentricities less than 0.6.

On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates

The solvability of a boundary value problem for a system, which describes the equilibrium state of elastic shallow inhomogeneous isotropic shells with loose edges referred to isometric coordinates in the Timoshenko shear model and consists of five non-linear second-order partial differential equations under given non-linear boundary conditions, is studied. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of this equation is established with the help of the contraction mapping principle.

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.

Solvability of nonlinear boundary value problems for non-sloping Timoshenko-type isotropic shells of zero principal curvature

We study the solvability of boundary value problem for a system of second order partial differential equations under boundary given conditions describing the equilibrium of elastic non-sloping isotropic inhomogeneous shells with free boundary in the framework of the Timoshenko shear model. The base of the study method are the integral representations for generalized motions involving arbitrary functions, which also involve arbitrary holomorphic functions. The arbitrary functions ate determined so that the generalized motions satisfy a linear system of equations and linear boundary conditions extracted from the original boundary value problem. The holomorphic functions are sought as Cauchy type integrals with real densities. The integral representations allow us to reduce the initial boundary value problem to a nonlinear operator equations for generalized motions in the Sobolev space. While studying the solvability of this operator equation, the most essential point is to invert it with respect to the linear part. As a result, the work is reduced to an equation, the solvability of which is established on the base of the contracting mapping principle.

Electrostatic interactions and structural transformations in viral shells.

Structural transformations occurring in proteinaceous viral shells (capsids) can be induced by changing the pH of bathing solution, thus modifying the dissociation equilibrium of ionizable amino acids in proteins. To analyze the effects of electrostatic interactions on viral capsids, we construct a model of 2D isotropic elastic shells with embedded point charges located in the centers of mass of individual proteins. We find that modification of the electrostatic interactions between proteins affects not only the size and shape of capsids, but in addition induces substantial deformations of hexamers in capsid structures. Using bacteriophage P22 and Nudarelia capensis omega virus (NωV) as examples, we analyze the capsid faceting and propose an explanation as to why the hexamers in spherical procapsid are skewed, while they acquire a regular shape in the faceted state. Also, we examine the electrostatic and elastic effects that can explain different shapes of coronavirus shells decorated with spikes, which are often localized in compact areas over the shell surface. The proposed mechanism of local curvature generation is supported by the remarkable correspondence between the shell shape and the distribution of spikes in model and observed shells.

EQUATIONS OF MOTION OF AN ISOTROPIC SPHERICAL MOMENT ELASTIC SHELL*2

Using the previously obtained equations of motion of thin moment elastic shells of constant thickness with an arbitrary middle surface, the equations of motion of an isotropic moment spherical shell in terms of forces and “displacements” (kinematic parameters) are constructed. In this case, the metric of the middle spherical surface is taken into account, as the curvilinear coordinates of which two angular coordinates of the standard spherical coordinate system with the origin at the center of the middle surface are used. First, a closed system is written down, which includes the equations of motion in the physical components of the tensors of internal forces and moments, as well as additional similar characteristics corresponding to the moment properties of the model, and physical relationships. Then, by excluding physical relations, it is reduced to twelve equations of motion in kinematic parameters, written in operator form. In this case, the coefficients of partial derivative operators are simplified by neglecting terms that have a higher order of smallness relative to the thickness of the shell. Despite the bulkiness of the system, it is written in a compact form. Boundary conditions are not written, since the shell is considered closed. By introducing additional hypotheses similar to those used in the classical theory of shells (neglecting the compression of a normal fiber, the Kirchhoff – Love hypothesis about the connection between the tangential components of the rotation angle vector of a normal fiber and normal displacement, as well as the hypothesis about the connection between the normal to the middle surface part of the coordinate of the rotation angle vector and its tangential components) the number of equations and unknowns decreases. To carry out this procedure, a variational Hamilton equation is constructed, which takes into account the connections between kinematic parameters imposed by the hypotheses, and then the corresponding one is transformed using the generalized Ostrogradsky – Gauss theorem.

On the Problem of Solvability of Nonlinear Boundary Value Problems for Shallow Isotropic Shells of Timoshenko Type in Isometric Coordinates

On the Problem of Solvability of Nonlinear Boundary Value Problems for Shallow Isotropic Shells of Timoshenko Type in Isometric Coordinates

Comparative analysis of the stability and natural vibrations of shallow panels under the action of thermomechanical loads

The work is a continuation of research devoted to substantiating the reliability of solutions obtained by the finite element method for the analysis of nonlinear deformation, buckling and vibrations of thin elastic shells under the action of thermomechanical loads. The method is based on geometrically nonlinear relations of the three-dimensional theory of thermoelasticity and the principles of the moment finite element scheme. A thin elastic shell of an inhomogeneous structure is modeled by a universal spatial isoparametric finite element. The modal analysis of the shell is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest frequencies of natural vibrations of shells. A shallow spherical panel with a square plan is considered. The effect of preheating on the loss of stability and vibrations of an elastic isotropic shell under uniform pressure loading is investigated. The behavior of the shell weakened by two pairs of cross-channels is analyzed. The weakening of the panel by narrow and wide channels, which can be eccentrically located relative to the middle surface of the shell, is considered. The effectiveness and adequacy of the method is confirmed by a comparative analysis of solutions with results obtained using modern multifunctional software systems LIRA-SAPR and SCAD. The features of using the systems for solving the problems under consideration are given. Analysis of the results made it possible to evaluate the possibilities of using these software systems to substantiate the reliability of solutions to certain classes of problems of geometrically nonlinear deformation, buckling and vibrations of elastic shells.

The Strain Effects and Interfacial Defects of Large ZnSe/ZnS Core/Shell Nanocrystals.

The shell growth of large ZnSe/ZnS nanocrystals( is of great importance in the pursuit of pure-blue emitters for display applications, however, suffers from the challenges of spectral blue-shifts and reduced photoluminescence quantum yields. In this work, the ZnS shell growth on different-sized ZnSe cores is investigated. By controlling the reactivity of Zn and S precursors, the ZnS shell growth can be tuned from defect-related strain-released to defect-free strained mode, corresponding to the blue- and red-shifts of resultant nanocrystals respectively. The shape of strain-released ZnSe/ZnS nanocrystals can be kept nearly spherical during the shell growth, while the shape of strained nanocrystals evolutes from spherical into island-like after the critical thickness. Furthermore, the strain between ZnSe core and ZnS shell can convert the band alignment from type-I into type-II core/shell structure, resulting in red-shifts and improved quantum yield. By correlating the strain effects with interfacial defects, a strain-released shell growth model is proposed to obtain large ZnSe/ZnS nanocrystals with isotropic shell morphology.

The modified CUF-EFG method for the dynamic analysis of GPLs-CNTs-reinforced FG multilayer thick cylindrical shells under shock loadings: A modified meshless implementation

The main scope of this paper is to develop the Carrera unified formulation in cylindrical coordinates for two-dimensional meshless modelling of graphene platelet and carbon nanotube reinforced functionally graded multilayer thick cylindrical shells with the same accuracy of three-dimensional modelling. The cylindrical shell is composed of several homogeneous layers with uniform distribution of both GPL and CNT contents in each layer. The effective macroscopic mechanical properties of each GPLs and CNTs reinforced layer are estimated using the modified Halpin-Tsai (H-T) micromechanical model and rule of mixture. The volume fraction of nanofillers gradually changes layer to layer by nonlinear continuous function which leads to functionally graded (FG) distribution of nanofillers. Five grading patterns of layer distribution along the thickness direction of cylindrical shell are considered to investigate the effect of layer arrangement on dynamic behavior of cylindrical shells. The FG multilayer hybrid nanocomposite cylindrical shell is assumed to be under mechanical shock loading. The numerical method for dynamic analysis of multilayer cylindrical shell is based on element free Galerkin (EFG) method with radial basis shape functions in the framework of displacement-based Carrera unified formulation (CUF). The present EFG-CUF method is compared with analytical method for isotropic homogeneous shells and results available in the literature for FG multilayer cylindrical shells. Considering the results related to various expansion orders, proved accuracy and efficiency of proposed method for dynamic analysis of thin to thick FG multilayer cylindrical shells at high expansion orders ‘n > 2’. After verifying the analytical method, the effects of several key factors such as layer distribution patterns, volume fraction index, number of layers, nanofiller weight fraction, aspect ratios of cylinder, and damping ratio on static, free vibration, time history and wave propagation of cylinder are studied in detail.

On the Static Instability of FG-GNP-Reinforced Composite Cylindrical Shells Under Thermo-Mechanical Loading

The nonlinear buckling response of laminated composite cylindrical shells reinforced with graphene nanoplatelets (GNPs) is studied in this paper. The functionally graded (FG) shell reinforced by GNPs is analytically studied under external pressure and uniform temperature rise loadings. It is also assumed that the GNP-reinforced laminated composite shell is in contact with an elastic foundation. Various types of profiles are employed for the GNP distribution patterns in the shell thickness including 10 nanocomposite layers. The nonlinear strain-displacement relations of the shallow cylindrical panel are established utilizing the third-order shear deformation shell theory. Governing equilibrium equations of the laminated GNP-reinforced composite shell are formulated employing the principle of virtual displacement. The coupled system of nonlinear differential equations is solved analytically for the hinged–hinged and fixed–fixed boundaries of the shell using a perturbation-based technique. Correctness of presented formulations and obtained solutions is proved by comparisons with results from previous studies for an isotropic cylindrical shell. Novel numerical results reveal that the material properties, geometrical characteristics and load parameters significantly affect on the buckling behavior of laminated composite cylindrical shells.

Detailed analysis of banded chorus gap formation by an electron shell distribution

In a recent paper [K. Min, Phys. Plasmas 30, 012904 (2023)], the formation of the banded chorus with a gap in intensity at half the electron cyclotron frequency (Ωe/2) is demonstrated by particle-in-cell simulations including an isotropic shell distribution at an intermediate energy. This follow-up study focuses on the phase space density (PSD) hill formation process and its role in the chorus wave damping at the gap. We first show that phase-trapped particles closely follow single wave characteristics in momentum space. This means that the formation of either PSD hole or hill is primarily determined by the temperature anisotropy, T⊥/T‖, of an initial distribution function. The critical value of T⊥/T‖ increases (decreases) for a higher (lower) resonant frequency. We then revisit the recent banded chorus simulations to investigate how the presence of an isotropic shell distribution self-consistently affects chorus wave evolution at the gap. Initially, with an increasing wave frequency, more and more shell electrons get trapped and a PSD hill is formed. The enhanced PSD hill counteracts wave growth driven by phase-trapped anisotropic electrons and subsequently reduces wave amplitude. The weakened wave self-consistently feeds back to the particle trapping, ultimately suppressing both the PSD hole and hill. By the time the wave frequency reaches about 0.45Ωe, the gyro-phase structure of the electron distribution becomes much less organized. In some cases, however, the wave growth at the upstream source region can be strong enough that waves still manage to go through the gap frequency, suggesting that additional process(es) should likely be accompanied.

Numerical investigation of force and deflection of nanoneedle penetration into cell using finite element approach: Parameter study and experimental validation of results.

This paper aims to develop a numerical methodology to investigate the penetration process of nanoneedles into cells and the corresponding force and indentation length. The finite element approach via the explicit dynamic method handles convergence difficulties in the nonlinear phenomenon. The cell is modeled as an isotropic elastic hemiellipsoidal shell with a thickness of 200 nm, which represents the lipid membrane and actin cortex, encapsulating cytoplasm that is regarded as an Eulerian body because of its fluid-type behavior. Nanoneedles with diameters 400, 200, and 50 nm are considered for model development based on available experimental data. The Von Mises strain failure criterion is used for rupture detection. A parameter study using 1, 2.5, 5, 7.5, and 10 kPa shows that Young's modulus of the HeLa cell membrane is about 5 kPa. Moreover, a failure strain of 1.2 chosen among 0.2, 0.4, 0.6, 0.8, 1, and 1.2 matches best the experimental data. In addition, a diameter study shows that the relations between force-diameter and indentation length-diameter are linear and polynomial, respectively. Furthermore, regarding the experimental data and by using contour of minimum principal stress around needle and an analytical equation for calculation of buckling force of a woven fabric, we proposed that for a given cell, membrane structural stability-a function of the coupled effect of Young's modulus and actin meshwork size-contributes directly to needle insertion success rate for that type of cell.

A STUDY OF THE EFFECT OF SEMI-ANGLE OF CONE ON THE VIBRATION CHARACTERISTICS OF CYLINDRICAL-CONICAL COUPLED SHELL STRUCTURE

In this work, the effect of variation of semi-angle of the conical part on the vibration characteristics of cylindrical-conical coupled structure is investigated. The shell is made of polyester resin reinforced by continuous E-glass fibers. The case is analyzed experimentally and numerically for orthotropic shell structures. The experimental program is conducted by exciting the fabricated structure by an impact hammer and monitoring the response using an attached accelerometer for different semi-angles of the conical part.Software named SIGVIEW is used to perform the signal processing on the acquired signal in order to measure the natural frequencies and the corresponding mode shapes. The numerical investigation is achieved using ANSYS (Finite Element software) which was verified by the experimental results. Good agreement is achieved when comparing the experimental and numerical results. The maximum deviation in results was found to be (5.9%). The maximum relative nodal rotational and translational amplitudes associated with thefirst normal mode of the orthotropic and isotropic shells are noted for the structure of semi-angle of cone of 45o .

Hybrid Simulation of Proton Cyclotron Waves Upstream of Mars Generated by Pickup Ion Beam Distribution

AbstractLinear instability analysis as well as a corresponding two‐dimensional hybrid simulation are performed to examine the excitation of the proton cyclotron waves observed upstream of Mars. The waves are believed to be excited by the pickup ions produced from the ionization of the Martian hydrogen exosphere. And previous statistical analysis of wave observations suggested that the waves are mostly related to pickup ion beam velocity distributions. While earlier linear instability analysis of pickup ion beam distributions has mainly been focused on the parallel unstable modes, our analysis reveals that the maximum growth rate occurs at very oblique propagation. The corresponding hybrid simulation confirms the linear analysis results and further demonstrates that the pickup ions are scattered toward an isotropic shell velocity distribution by the waves excited. Interestingly, the waves at oblique propagation gradually damp out and the system is eventually dominated by waves of quasi‐parallel propagation.