Anisotropic Shells Research Articles

Low-Temperature-Induced Controllable Transversal Shell Growth of NaLnF4 Nanocrystals.

Highly controllable anisotropic shell growth is essential for further engineering the function and properties of lanthanide-doped luminescence nanocrystals, especially in some of the advanced applications such as multi-mode bioimaging, security coding and three-dimensional (3D) display. However, the understanding of the transversal shell growth mechanism is still limited today, because the shell growth direction is impacted by multiple complex factors, such as the anisotropy of surface ligand-binding energy, anisotropic core–shell lattice mismatch, the size of cores and varied shell crystalline stability. Herein, we report a highly controlled transversal shell growth method for hexagonal sodium rare-earth tetrafluoride (β-NaLnF4) nanocrystals. Exploiting the relationship between reaction temperature and shell growth direction, we found that the shell growth direction could be tuned from longitudinal to transversal by decreasing the reaction temperature from 310 °C to 280 °C. In addition to the reaction temperature, we also discussed the roles of other factors in the transversal shell growth of nanocrystals. A suitable core size and a relative lower shell precursor concentration could promote transversal shell growth, although different shell hosts played a minor role in changing the shell growth direction.

The limit forming estimation of multi-stage thin-walled vessel cold forming technological process

The multi-stage technological process of cold stamping of a thin-walled vessel made of sheet steel was evaluated taking into account technological heredity. The quality of the product is evaluated by the distance of its deformed state from the limit states on the strain diagram. To calculate the process, the model of large plastic deformations of the anisotropic shell is used, taking into account the dynamics and contact interactions with the tool, which was numerically implemented in the LS-DYNA® package. Models of plastic flow of an anisotropic sheet, associated with the Barlat criterion Yld 2000-2d, with the power law of isotropic strain hardening, the Peng - Landel potential of nonlinear elastic behavior of a polyurethane die, and the Coulomb friction law of contact interaction of the product with the tool are used from the package library. These models constants for low-carbon sheet steel DC04EK 0,7 mm and polyurethane SKU-PFL were identified from experimental data. The forming limit curve was built on the distortion of the coordinate grid near the zones of strain localization and failure of the vessel in the technological process without intermediate annealing and in the failure test under uniaxial tension. The features of the strain paths in the control points of the vessel at each stage of the technological process, including the sequence of operations of drawing, distributing and reduction, are studied. The path calculation was confirmed by an experiment using pressing equipment as a test. It is established that the operation of distributing the workpiece after its drawing quickly leads to the limit state and therefore requires a preliminary recovering the plasticity resource by annealing. There is a preference for forming the relief of the vessel by smaller degrees of distribution and greater degrees of reduction for elimination of the limit states and the operation of intermediate annealing.

Stress-strain state of thick-walled anisotropic cylindrical shells under thermal power load, protected by the functionally graded material

In the article the stress-strain state of thick-walled structurally anisotropic composite cylindrical shells under thermal power load, which are protected by a functionally graded material, are analysed. Based on the interrelations of the spatial theory of elasticity, a system of inhomogeneous differential equations in three-dimensional formulation, which describes the stress-strain state of thick-walled anisotropic cylindrical shells, was obtained. To reduce the dimensionality of this system, the Bubnov-Galerkin analytical method was used. Thus, the obtained one-dimensional system of twelve equations of normal Cauchy form was implemented using the numerical method of discrete orthogonalization. To represent the possibilities of the proposed approach, there were used stress-strain states of two, four and five-layered anisotropic cylindrical shells of fibrous composites, protected from temperature by a layer of transversely isotropic functionally graded material.

Fundamentals and Processes of Fluid Pressure Forming Technology for Complex Thin-Walled Components

• New fluid pressure forming processes for tubes, sheets and shells were developed. • Methodology of adjusting stress state was invented to solve defects of forming thin-walled structures. • Outstanding applications in aerospace and automobile industry are presented. A new generation of fluid pressure forming technology has been developed for the three typical structures of tubes, sheets, and shells, and hard-to-deform material components that are urgently needed for aerospace, aircraft, automobile, and high-speed train industries. In this paper, an overall review is introduced on the state of the art in fundamentals and processes for lower-pressure hydroforming of tubular components, double-sided pressure hydroforming of sheet components, die-less hydroforming of ellipsoidal shells, and dual hardening hot medium forming of hard-to-deform materials. Particular attention is paid to deformation behavior, stress state adjustment, defect prevention, and typical applications. In addition, future development directions of fluid pressure forming technology are discussed, including hyper lower-loading forming for ultra-large non-uniform components, precision forming for intermetallic compound and high-entropy alloy components, intelligent process and equipment, and precise finite element simulation of inhomogeneous and strong anisotropic thin shells.

Напружений стан шаруватих анізотропних оболонок і пластин з міжфазними дефектами

Напружений стан шаруватих анізотропних оболонок і пластин з міжфазними дефектами

Asymptotic stress analysis of multilayer composite thin cylindrical shells

Using the asymptotic theory, explicit analytical expressions were obtained that allow one to calculate the stress-strain state of multilayer thin cylindrical anisotropic elastic composite shells for small deformations. Forenamed expressions allow us to obtain the distribution of all components of the stress-strain state without any assumptions about their nature of the distribution over the thickness. An algorithm was proposed that makes it possible to obtain the total stress tensor in the shell, and all components of the stress tensor are numerically calculated for the case of a cylindrical composite shell with axisymmetric bending by pressure. The character of the distribution of characteristics of the stress-strain state of the shell was analyzed and the corresponding graphs were constructed.

Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions.

New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit.

Site- and Spatial-Selective Integration of Non-noble Metal Ions into Quantum Dots for Robust Hydrogen Photogeneration

Summary Artificial photosystems consisting of semiconductor quantum dots (QDs) and non-noble metal ions (e.g., Fe2+, Co2+, Ni2+) show intrinsic advantages in efficient and cost-effective hydrogen (H2) evolution. However, well-controlled integration of these metal ions into ultra-small QDs is a major challenge. Here, we present a two-step strategy to realize site- and spatial-selective integration of earth-abundant Fe2+ ions in CdSe QDs; i.e., CdSe QDs are modified with a thin and anisotropic ZnS shell, and partial Zn2+ ions are selectively substituted by Fe2+ via cation exchange. The anisotropic ZnS layer not only passivates CdSe core but also works as an ideal medium to intimately anchor Fe2+. The multifunctional CdSe/Zn1−xFexS QD exhibits extraordinary activity and stability toward H2 photogeneration. Specifically, more than 880 mL (∼39,300 μmol) H2 gas is produced from 6 mL of aqueous solution during a consecutive 172 h (>1 week) experiment, thus achieving a turnover number of >600,000 per QD.

The stability of anisotropic cylindrical shells under torsion in spatial position

The stability of anisotropic cylindrical shells under torsion in spatial position

Digital rock physics in four dimensions: simulating cementation and its effect on seismic velocity

SUMMARY Porosity exerts a strong control on the mechanical and hydraulic properties of rocks, but can often only be imaged indirectly from the surface using geophysical measurements, such as seismic velocity. Understanding and quantifying the relationship between seismic velocity and porosity is therefore a fundamental goal of many rock physics models. Simulating the geological processes that control porosity to generate digital rocks, and numerically modelling wave propagation to estimate their elastic properties, allows for flexible and rapid calibration of velocity–porosity trends. Here, the initial deposition of two digital carbonate sediments are simulated: grainstone (near spherical grains) and coquina (anisotropic shell fragments). The gradual precipitation of cement is then simulated, resulting in a suite of 3-D volumes of varying porosity with otherwise constant and known mineral and grain phases. These models are then used as input to a 3-D acoustic staggered-grid finite difference simulation of wavefield propagation, from which we estimate bulk seismic velocity and calculate the estimated bulk modulus. The resulting bulk modulus varies systematically with respect to porosity within the physical limits imposed by the Hashin–Shtrikman bounds. The samples exhibit anisotropy in the measured velocity consistent with structural anisotropy due to the settling of elongate grains under gravity. We use the resulting bulk velocity–porosity trends to test competing rock physics models, including one that accounts for varying effective pore-aspect ratio with porosity. The results validate the hypothesis that there is a power-law relationship between effective pore aspect ratio and porosity. This relationship is consistent with similar results obtained from a suite of natural carbonate grainstones examined in the laboratory. The results show the optimal rock physics model to be relatively insensitive to the degree of anisotropy in the fabric of the starting material, and may now be used with more confidence to link observed changes in effective pore aspect ratio to changes in porosity due to a range of geological processes, for example fracturing, dissolution and compaction, where other process-based models are available.

Propagation of Flexural Waves in Anisotropic Fluid-Conveying Cylindrical Shells

In the present article, first-order shear deformation theory (FSDT) of the shell has been employed, for the first time, in order to analyze the propagation of the flexural waves in anisotropic fluid-conveying cylindrical shells. Four various anisotropic materials are utilized and their wave propagation behavior surveyed. Viscous fluid flow has been regarded to be laminar, fully developed, Newtonian, and axially symmetric. The Navier–Stokes equation can be utilized to explore the flow velocity effect. FSDT of the shell and Hamilton’s principle have been employed in order to achieve governing equations of anisotropic fluid-conveying cylindrical shells and finally, the obtained governing equations have been solved via an analytical method. In addition, the influences of different variables such as flow velocity, radius to thickness ratio, and longitudinal and circumferential wave numbers have been investigated and indicated within the framework of a detailed set of figures.

Three-temperature nonlinear generalized magneto-thermoelastic stresses in anisotropic cylindrical shells

The main purpose of this paper is to investigate the transient three-temperature nonlinear generalized magneto-thermoelastic stresses in an anisotropic cylindrical shell. The system of governing equations is solved by means of a boundary element method (BEM) and numerical calculations are carried out for temperature and thermal stresses. The numerical results indicate that the effects of three-temperature on the thermal stresses are very pronounced, where we used two-dimensional three temperature nonlinear radiative heat conduction equations coupled with electron, ion and phonon temperatures. Also, these numerical results demonstrate the validity and accuracy of the present numerical method.

A thin-shell shape adaptable composite metamaterial

Mechanical metamaterials undergoing extreme deformations span an ever-increasing design space of mechanical performance. However, achieving selective deformability in load-carrying metamaterials remains unexplored. Anisotropic thin fiber-reinforced composite shells, which are soft in bending and stiff axially, present an attractive option for addressing this challenge but are difficult to realize in practice due to fabrication complexity. In this work, an integrated fabrication technique enabling single-step curing of complex composite mechanical metamaterials is proposed. By using 3D-printed tooling and silicone spacers, composite assemblies can be cured in an autoclave without the need for post-cure bonding of individual shells. The technique reduces manufacturing times and eliminates adhesive bonds, which add mass to the structure and can be points of failure. The proposed technique is demonstrated on a modified rotating square auxetic metamaterial geometry, with fabricated prototypes withstanding up to 60% global tensile strains elastically. The composite anisotropy is, moreover, used to control the deformation mechanism in the metamaterial, thereby delaying failure of the structure and allowing tunability of elastic properties. This work sets the stage for the use of composites as a means of expanding the design space achieved by mechanical metamaterials for shape adaptation in lightweight, load-carrying applications.

Nonlocal Anisotropic Shell Model of Linear Vibrations of Multi-walled Carbon Nanotubes

Nonlocal Anisotropic Shell Model of Linear Vibrations of Multi-walled Carbon Nanotubes

Non-stationary influence function for an unbounded anisotropic Kirchhoff-Love shell

The purpose of this article is to investigate the process of the influence of a nonstationary load on an arbitrary region of an elastic anisotropic cylindrical shell. The approach to the study of the propagation of forced transient oscillations in the shell is based on the method of the influence function, which represents normal displacements in response to the action of a single load concentrated along the coordinates. For the mathematical description of the instantaneous concentrated load, the Dirac delta functions are used. To construct the influence function, expansions in exponential Fourier series and integral Laplace and Fourier transforms are applied to the original differential equations. The original integral Laplace transform is found analytically, and for the inverse integral Fourier transform, a numerical method for integrating rapidly oscillating functions is used. The convergence of the result in the Chebyshev norm is estimated. The practical significance of the work is that the obtained results can be used by scientists or students to solve new problems of dynamics of cylindrical shells on an elastic basis under pulse loads. The found non-stationary influence function opens up possibilities for studying the stress-strain state, solving nonstationary inverse and contact problems for anisotropic shells, studying nonstationary dynamics in the case of nonzero initial conditions, and also when constructing integral equations of the boundary element method.

Analytical and Numerical Investigation of Radiation Enhancement by Anisotropic Metamaterial Shells

This paper presents analytical and numerical investigations of a 3D cylindrical metamaterial shell possessing a cylindrically anisotropic permeability that is excited by a finite-sized electric line source. A comprehensive field analysis of the system reveals that the compact metamaterial shell exhibits resonances akin to those observed in isotropic 2D cylindrical metamaterial structures, which may be used to enhance the radiated power of a nearby antenna. An analytical resonance condition that relates the dimensions of the cylindrical shell to its anisotropic effective-medium parameters is shown to be accurate in predicting the resonances of 2D and 3D metamaterial shells obtained using full-wave simulations. The effects of anisotropy and finite shell/antenna height on the system's near-fields, radiation patterns, and power-ratio enhancements are explored. It is shown through both theory and simulations that the condition for resonance is largely independent of shell/antenna height but that the quality factor reduces dramatically as these heights approach electrically small values. Also, a dispersion and loss analysis assuming Lorentz model is carried out, which indicates that practical metamaterial losses do not significantly degrade the power enhancement.

Асимптотическое решение одной смешанной краевой задачи анизотропной двухслойной цилиндрической оболочки

Асимптотическое решение одной смешанной краевой задачи анизотропной двухслойной цилиндрической оболочки

Toward Numerical Solution of the Problem on Stressed State of Thermoelastic Physically Orthotropic Cylindrical Shells

To investigate the stressed-strained state of thermoelastic anisotropic cylindrical shells the original system of nineteen differential equations of eighth order in partial derivatives of the general theory of shells is transformed into a system of eight differential equations of first order. It is suggested to carry out numerical realization by the method of orthogonal marching. Numerical results are presented for the case of temperature drop over the shell thickness.

Ultimate strength evaluation of multi-stage cold forming technique for manufacture of thin-walled vessels

The multi-stage process of cold forging of thin-walled steel vessels was evaluated taking into account technological heredity. The quality of the product is evaluated by the degree of deviation of its stress- strain state from the ultimate states of the forming limit diagram. The process is calculated based on the model of large plastic deformations of the anisotropic shell, which takes into account the dynamics and contact interactions of the shell with the tool. The model was numerically implemented in the LS-DYNA®package. Numerical simulation was performed using the simulation tools of the package library, such as the models of plastic flow of an anisotropic sheet with the power law isotropic strain hardening, associated with the Barlat criterion Yld 2000-2d, the Peng-Landel potential of nonlinear elastic behavior of a polyurethane die, and the Coulomb friction law of contact interaction of the product with the tool. The model constants for low-carbon sheet steel DC04EK 0.7 mm and polyurethane SKU-PFL were determined from the experimental data. The forming limit curve was plotted using as the basic data the distortions of the coordinate grid near the zones of strain localization and failure of the vessel during the technological process without intermediate annealing and the results of failure tests under uniaxial tension. The features of the strain paths are studied at thе control points of the vessel at each stage of the technological process, including the sequence of drawing, bulging and reducing operations. The calculated strain paths were verified by the experiment, in which pressing equipment was used as the test facility. It was found that the operation of work piece bulging after its rapid drawing leads to the limit state and therefore requires a preliminary recovery of the plasticity resource by annealing. The obtained results demonstrate the advantages of forming the relief of the vessel by smaller degrees of bulging and greater degrees of reducing for eliminating the limit states and intermediate annealing.

About a new approach to calculating spiral clamps

The bearing capacity of spiral clamps, which are mounted on wires (cables) for their tension, connection, repair, etc., is studied. The design of spiral clamps is formed from stretched spirals that are wound onto conductors with an interference fit, which makes it possible to obtain tensile connections practically inseparable. The general problem of the interaction of spiral clamps and overhead line conductor layers is formulated. Different asymptotic solutions are given for initial and boundary value problems, and the design parameters of spiral clamps are determined to provide their carrying capacity. A wire layer is represented by the energy approach as an equivalent anisotropic elastic cylindrical shell, and wire construction as a whole is considered as a system of cylindrical shells inserted each other and interacting by forces of pressure and friction. The equivalence of the elastic properties of the shell to the properties of the wire layer is established using energy averaging. The constitutive relations obtained using the Castigliano theorem relate the generalized displacements and the corresponding forces. The matrix in these ratios is a stiffness matrix or flexibility matrix of a spiral wire structure. Such approach allows variety of interaction problems for spiral clamps with conductor layers to be solved, and the force transfer mechanism to be investigated from common positions. Static equations are written from the equilibrium of the elementary shell ring. It is considered that the length of the clamp is so great that the mutual influence of its ends can be neglected; the clamp is modeled as semi-infinite shell. This model allows the different initial and boundary value problems to be formulated, depending on the boundary conditions and clamp mounting methods on a conductor.