Inhomogeneous Shells Research Articles

Scattering of Acoustic Waves by an Inhomogeneous Elastic Cylindrical Shell of Finite Length in a Half-Space

An analytical solution to the problem of diffraction of a plane acoustic wave on a radially inhomogeneous thick-walled elastic cylindrical shell of finite length is obtained. The cylindrical shell is located in an acoustic half-space filled with an ideal liquid. The boundary of the half-space is an acoustically rigid or acoustically soft surface. The results of calculations of the acoustic field in the far zone are presented.

Free Vibrations of Thin-Walled Gas Pipelines Taking into Account the Influence of Longitudinal Force During Trench Laying

A numerical experiment was carried out to determine the frequencies of free oscillations of an inhomogeneous pipeline at various mechanical and geometric parameters.This made it possible to establish the influence of factors such as longitudinal force, thickness of the reinforced concrete shell, internal working pressure and the coefficient of the soil bed on the system’s own vibrations. For calculations, a model of an inhomogeneous cylindrical two-layer shell of finite length consisting of a steel pipe and a protective reinforced concrete layer was chosen.

Are monodisperse phospholipid-coated microbubbles “mono-acoustic?”

Phospholipid-coated microbubbles with a uniform acoustic response are a promising avenue for functional ultrasound sensing. A uniform acoustic response requires both a monodisperse size distribution and uniform viscoelastic shell properties. Monodisperse microbubbles can be produced in a microfluidic flow focusing device. Here, we investigate whether such monodisperse microbubbles have uniform viscoelastic shell properties and thereby a uniform “mono-acoustic” response. To this end, we visualized phase separation of the DSPC and DPPE-PEG5000 lipid shell components and measured the resonance curves of nearly 2000 single and freely floating microbubbles using a high-frequency acoustic scattering technique. The results demonstrate inhomogeneous phase-separated shell microdomains across the monodisperse bubble population, which may explain the measured inhomogeneous viscoelastic shell properties. The shell viscosity varied over an order of magnitude and the resonance frequency by a factor of two indicating both a variation in shell elasticity and in initial surface tension despite the relatively narrow size distribution.

Bending and reverse bending during the fabrication of novel GaAs/(In,Ga)As/GaAs core–shell nanowires monitored by in situ x-ray diffraction

We report on the fabrication of a novel design of GaAs/(In,Ga)As/GaAs radial nanowire heterostructures on a Si 111 substrate, where, for the first time, the growth of inhomogeneous shells on a lattice mismatched core results in straight nanowires instead of bent. Nanowire bending caused by axial tensile strain induced by the (In,Ga)As shell on the GaAs core is reversed by axial compressive strain caused by the GaAs outer shell on the (In,Ga)As shell. Progressive nanowire bending and reverse bending in addition to the axial strain evolution during the two processes are accessed by in situ by x-ray diffraction. The diameter of the core, thicknesses of the shells, as well as the indium concentration and distribution within the (In,Ga)As quantum well are revealed by 2D energy dispersive x-ray spectroscopy using a transmission electron microscope. Shell(s) growth on one side of the core without substrate rotation results in planar-like radial heterostructures in the form of free standing straight nanowires.

Universal three-dimensional finite element for analyzing of elastic inhomogeneous shells under thermomechanical loads

The work is devoted to the development of a new modification of the finite element intended for the calculation of inhomogeneous composite shells of thin and medium thickness. The element is constructed on the basis of a universal three-dimensional isoparametric 8-node multilayer finite element of a continuous medium. The layers of the modified finite element are made of composite materials reinforced with continuous unidirectional fibers. Within the framework of a finite element model of a multilayer shell of stepwise variable thickness, a technique for modeling the properties of a unidirectional fibrous composite material has been developed, based on a method for structuring material inhomogeneities iby thickness and by plan. The shell can consist of an arbitrary number of layers of varying thickness bonded into a single piece. Each layer can have its own type of material: traditional or composite. Effective physical and mechanical characteristics of the layer material are determined using known micromechanical methods for predicting the thermoelastic constants of a fiber composite through the known physical characteristics of the matrix and fiber. The fibrous material of the layer is presented as homogeneous transversely isotropic with planes of isotropy normal to the direction of reinforcement. Additional variable parameters of the "basic" universal finite element are supplemented with new attributes that determine the thermoelastic properties of the composite components. The new parameters are related to the choice of the type of fibrous composite material in the layer of the finite element, to the setting of structural micromechanical parameters of its components, and to the setting of the reinforcement orientation angle. This allows the calculations to use both traditional and fiber-composite materials in layers of inhomogeneous shells. Numerical examples demonstrate the effectiveness of the developed approach.

The influence of geometrical shape on the buckling of thin-walled axisymmetric shells

The most economical for long span structures are thin-walled covering consisting of shell elements. These include shells of cylindrical, spherical, conical and other shapes. Buckling analysis of thinwalled structures is important in the design of buildings and structures. In this case, the geometric shape of the shell used has a great effect on the critical load. A comparative analysis of the geometrically nonlinear deformation, buckling, and postbuckling behavior of rotation panels of the same v olume under static thermomechanical loading is carried out. Spherical and conical shells having the same thickness, rise and weight are considered. Preheated shells are loaded with uniform external pressure. The calculation method is based on geometrically nonlinear relations of the three-dimensional theory of thermoelasticity without the use of simplifying hypotheses of shell theory and the use of a moment finite element scheme. A universal 3D isoparametric finite element is used. The element allows you to model shells of stepwise variable thickness, with breaks in the middle surface and with other geometric features in thickness. The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton–Kantorovich method, and a procedure for automatic correction of algorithm parameters. The method has been justified numerically in the authors' articles. Research has revealed the behavioral features of the compared shallow panels.

Construction of homogeneous solutions of the torsion problem for a radially inhomogeneous transversely isotropic cylinder

The torsion problem for a radially inhomogeneous transversely isotropic cylinder of small thickness was investigated by the method of asymptotic integration of elasticity theory equations. It is assumed that the side part of the cylinder is stress-free, and boundary conditions are set at the ends of the cylinder, leaving the cylinder in equilibrium. The elastic moduli are thought to be arbitrary continuous functions of the variable along the cylinder radius. The formulated boundary value problem is reduced to a spectral problem containing a small parameter characterizing the thin-walledness of the cylinder. Homogeneous solutions are built, i.e. any solutions of the equilibrium equation satisfying the condition of no stresses on the side surfaces. It is shown that the solution of the torsion problem consists of a penetrating solution and a boundary layer character solution similar to Saint-Venant's edge effect in the theory of inhomogeneous plates. The penetrating solution determines the internal stress-strain state of a radially inhomogeneous cylinder. The stress state determined by the penetrating solution is equivalent to the torsional moments of stresses acting in the cross-section perpendicular to the cylinder axis. Solutions having the boundary layer character are localized at the ends of the cylinder and decrease exponentially with distance from the ends. These solutions are absent in applied shell theories. Asymptotic formulas for displacement and stresses are built, which make it possible to calculate the three-dimensional stress-strain state of a radially inhomogeneous transversely isotropic cylinder of small thickness. Based on the obtained asymptotic expansions, it is possible to assess the applicability of applied theories and build a refined applied theory for radially inhomogeneous cylindrical shells

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.

Finite Element Spectral Integral (FESI) Method for Scattering From an Arbitrary Number of Circular Cylinders With Inhomogeneous Shells

Finite Element Spectral Integral (FESI) Method for Scattering From an Arbitrary Number of Circular Cylinders With Inhomogeneous Shells

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.

An Amorphous Native Oxide Shell for High Bias-Stress Stability Nanowire Synaptic Transistor.

The inhomogeneous native oxide shells on the surfaces of III-V group semiconductors typically yield inferior and unstable electrical properties metrics, challenging the development of next-generation integrated circuits. Herein, the native GaOx shells are profitably utilized by a simple in-situ thermal annealing process to achieve high-performance GaSb nanowires (NWs) field-effect-transistors (FETs) with excellent bias-stress stability and synaptic behaviors. By an optimal annealing time of 5min, the as-constructed GaSb NW FET demonstrates excellent stability with a minimal shift of transfer curve (ΔVth ≈ 0.54V) under a 60min gate bias, which is far more stable than that of pristine GaSb NW FET (ΔVth ≈ 8.2V). When the high bias-stress stability NW FET is used as the chargeable-dielectric free synaptic transistor, the typical synaptic behaviors, such as short-term plasticity, long-term plasticity, spike-time-dependent plasticity, and reliable learning stability are demonstrated successfully through the voltage tests. The mobile oxygen ion in the native GaOx shell strongly offsets the trapping states and leads to enhanced bias-stress stability and charge retention capability for synaptic behaviors. This work provides a new way of utilizing the native oxide shell to realize stable FET for chargeable-dielectric free neuromorphic computing systems.

Stability Analysis of Shear Deformable Inhomogeneous Nanocomposite Cylindrical Shells under Hydrostatic Pressure in Thermal Environment

In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin’s procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment.

On the Existence of Solutions of Nonlinear Boundary Value Problems for a System of Differential Equilibrium Equations for Timoshenko-Type Shells in Isometric Coordinates

We prove the existence of solutions of a boundary value problem for a system of five nonlinear second-order partial differential equations with given nonlinear boundary conditions, which describes the equilibrium state of elastic shallow inhomogeneous isotropic shells with free edges in the Timoshenko shear model referred to isometric coordinates. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in the Sobolev space, the solvability of which is established using the contraction mapping principle.

Shock Corrugation to the Rescue of the Internal Shock Model in Microquasars: The Single-scale Magnetohydrodynamic View

Questions regarding the energy dissipation in astrophysical jets remain open to date, despite numerous attempts to limit the diversity of the models. Some of the most popular models assume that energy is transferred to particles via internal shocks, which develop as a consequence of the nonuniform velocity of the jet matter. In this context, we study the structure and energy deposition of colliding plasma shells, focusing our attention on the case of initially inhomogeneous shells. This leads to the formation of distorted (corrugated) shock fronts—a setup that has recently been shown to revive particle acceleration in relativistic magnetized perpendicular shocks. Our study shows that the radiative power of the far downstream of nonrelativistic magnetized perpendicular shocks is moderately enhanced with respect to the flat-shock cases. Based on the decay rate of the downstream magnetic field, we make predictions for multiwavelength polarization properties.

Creep of an inhomogeneous polymeric cylindrical shell under heating

The article presents the calculation of a polymer thick-walled cylindrical shell, taking into account creep under the action of a uneven temperature field. The relevance of the work lies in the widespread intro-duction of polymer pipes in the repair and construction of pipelines for heating, sewerage, and water supply systems. The problem is solved in an axisymmetric formulation under plane deformation conditions. The calculation is based on the non-linear Maxwell-Gurevich equation, which is widely used in the calculations of polymer structures. In the problem under consideration, the cylindrical shell is in a flat de-formed state. It is also believed that temperature is a function of radius and time.

Evaluation of the dynamic characteristics of complex multiply connected, structurally inhomogeneous systems

In this work, its application's theoretical and methodological foundations are developed for calculating the dynamic characteristics of shell structures that function independently or are parts of a complex mechanical system as a substructure. An important stage in the study of the dynamic behavior of the complex multiply connected shell structure under consideration is the determination of the dynamic characteristics of the structure, which include natural frequencies and modes of vibration, amplitude-phase frequency characteristics, dynamic coefficients of influence, dynamic stiffness and the coefficient of dynamicity. A solution method, an algorithm, and a program for calculating dynamic problems of structurally inhomogeneous shell systems have been developed. The developed method makes it possible to determine the dynamic characteristics of structurally inhomogeneous shell systems, numerical results are obtained, and graphs of the change in vibration frequencies depending on the inhomogeneity parameter are plotted.

Buckling analysis of shallow shells having linear-variable thickness

One way to increase the overall stiffness of a shell structure is to design shells with variable thickness. The effect of thickness change on the stability of flexible shallow panels has been little studied due to the complexity of solving such non-linear problems. Geometrically nonlinear deformation, buckling and postbuckling behavior of thin elastic shells of linearly variable thickness subjected to uniform normal pressure is investigated. The behavior of shallow axisymmetric spherical panels is compared for three laws of thickness distribution along the meridian of the shell. A more rational distribution of the material in the volume of the shell from the point of view of the stability of the structure is revealed. The same mass of material will be used more rationally if the shell is thickened in its central part. The method is based on geometrically nonlinear equations of the three-dimensional thermoelasticity without the use of simplifying hypotheses of the shell theory, and the use of the moment finite-element scheme and the 3D universal finite element. The universal finite element makes it possible to model sections of the shell with both step-variable and smooth-variable thickness, as well as shells with other geometric features. The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton–Kantorovich method, and a procedure for automatic correction of algorithm parameters. The results of calculations performed using the moment finite-element scheme are compared with the solutions obtained using the LIRA and SCAD software packages.

Vibrations of launch vehicle fairings with conical shape

Vibrations of launch vehicle conical fairings are investigated. Fairings are simulated using thin conic shells. The modal analysis of a thin elastic shell is based on the use of the developed finite element model of an inhomogeneous shell. In general, the technique makes it possible to investigate the geometrically nonlinear deformation, stability, and post-buckling behavior of a wide class of thin elastic shells. The modal analysis of the structure is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest vibration frequencies of shells of an inhomogeneous structure. The shell behavior analysis method is based on the relations of the three-dimensional theory of thermoelasticity and uses the finite element moment scheme. A thin elastic shell is simulated by a universal solid isoparametric finite element. The parameters of natural vibrations of conical shells of revolution with different thicknesses are investigated. Comparison of the calculation results obtained by the finite element moment scheme with the data of other authors shows a fairly good agreement between the solutions.

Identification of the patterns of influence the number of reinforcing elements and the inhomogeneity parameter of the shell material on frequencies of a reinforced inhomogeneous orthotropic spherical shell with a medium

Spherical shells are used in many areas of the national economy. Spherical domes are widely used in the construction of various structures (technoparks, testing laboratories, entertainment complexes, reservoirs, etc.). They are also used in aircraft, ship structures, radar antennas and other structures. It is known that coatings have sufficient strength and durability even with a small thickness. However, to increase the working life of coatings, to ensure their long-term operation, as well as to increase their hardness, it is necessary to strengthen them on the surface or inside with rods. Sometimes it is possible to reduce the weight of the structure and save material consumption by strengthening it with. One of the advantages of these structures is that they give the maximum useful volume, being both load-bearing and enclosing structures. Checking the shells for stability is a priority task, since it is known that the shells, even with an insignificant thickness, have great strength and therefore their insufficient stability can be a criterion determining the bearing capacity. This article is devoted to identifying the regularities of the influence of the number of reinforcing elements and the inhomogeneity parameter of the shell material on the frequencies supported by an inhomogeneous orthotropic spherical shell with a medium. To solve the problem under consideration, the Hamilton-Ostrogradsky variation principle is applied. The frequency equation is constructed and implemented numerically. Such studies have not been considered for a reinforced spherical shell with a no uniform filler in thickness

Numerical Analysis of Deformation Characteristics of Elastic Inhomogeneous Rotational Shells at Arbitrary Displacements and Rotation Angles

Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of “tracking” type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells.