Elastic Shell Research Articles

Pressure effects on dynamics behavior of multiwall boron nitride nanotubes

The dynamic behavior of Multiwall boron nitride nanotubes (MWBNNTs) is investigated by employing multiple elastic shells model. The influences of van der Waals interactions on layers are shown as nonlinear functions of the interlayer distance of MWBNNTs. Governing equations are solved by using the developed finite element method and by employing time history diagrams. The radial wave speed from the outermost layer to the innermost layer is computed. The effects of geometrical factors such as diameter-to-thickness ratio on dynamic behavior of MWBNNTs are determined. The magnification aspects of MWBNNTs are computed, and the effects of surrounding pressures on wave speed and magnification aspect of MWBNNTs are discussed.

Rayleigh-Ritz Vibrational Analysis of Multiwalled Carbon Nanotubes Based on the Nonlocal Flügge Shell Theory

A nonlocal elastic shell model considering the small scale effects is developed to study the free vibrations of multiwalled carbon nanotubes subject to different types of boundary conditions. Based on the nonlocal elasticity and the Flügge shell theory, the governing equations are derived which include the interaction of van der Waals forces between adjacent and nonadjacent layers. To analytically solve the problem, the Rayleigh-Ritz method is employed. In the present analysis, different combinations of layerwise boundary conditions are taken into account. Some new intertube resonant frequencies and the associated noncoaxial vibrational modes are identified owing to incorporating circumferential modes into the shell model.

On basic problems for elastic prismatic shells with microtemperatures

In the present paper on the basis of the linear theory of thermoelasticity of homogeneous isotropic bodies with microtemperatures the zeroth order approximation of hierarchical models of elastic prismatic shells with microtemperatures in the case of constant thickness (but, in general, with bent face surfaces) is considered. The existence and uniqueness of solutions of basic boundary value problems when the projections of the bodies under consideration are bounded and unbounded domains with closed contours are established. The ways of solving boundary value problems in explicit forms and of their numerical solution are indicated.

Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

The present paper talks about the free vibration analysis of simply supported Single- and Double-Walled Carbon Nanotubes (SWCNTs and DWCNTs). Refined 2D Generalized Differential Quadrature (GDQ) shell methods and an exact 3D shell model are compared. A continuum approach (based on an elastic three-dimensional shell model) is used for natural frequency investigation of SWCNTs and DWCNTs. SWCNTs are defined as isotropic cylinders with an equivalent thickness and Young modulus. DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of van der Waals interactions. Layer wise approaches are mandatory for the analysis of van der Waals forces in DWCNTs. The effect of van der Waals interaction between the two cylinders is shown for different DWCNT lengths, diameters and vibration modes. The accuracy of beam models and classical 2D shell models in the free vibration analysis of SWCNTs and DWCNTs is also investigated.

Решение краевых задач теории тонких упругих оболочек методом Неймана

Изучаются возможности применения метода Неймана для решения краевых задач теории тонких упругих оболочек. Приводится вариационная формулировка задач статического расчета оболочек, позволяющая рассматривать проблемы в рамках пространств обобщенных функций. Доказывается сходимость процедуры Неймана для оболочек с отверстиями, когда граничный контур закреплен не полностью. Численная реализация метода Неймана обычно требует значительного времени для получения надежного результата. В статье предлагается способ, улучшающий скорость сходимости процесса, позволяющий применить параллельные вычисления и их контроль во время работы алгоритма.

Dynamic response of multiwall boron nitride nanotubes subjected to impact

Dynamic behaviours of multiwall boron nitride nanotubes (MWBNNTs) with finite length were studied by employing continuum structure. Multiple elastic shells with nonlinear model of van der Waals interactions were used for developing an inclusive and inexpensive dynamical model of MWBNNTs. The systems of coupled partial differential equations were solved by applying the finite element method. Whole or part of thin and bulky MWBNNTs were exposed to external pressure impact and dynamical treatment were investigated and precision of results were checked by evaluating the answers with those found by other methods. Both deflection and stress studies were carried out for tubes of MWBNNTs and the influences of longitudinal wave caused by external pressure impact were considered in MWBNNTs. Also, time history diagrams of MWBNNTs with impact of initial longitudinal deflection were investigated and the extension of the longitudinal waves through the length of layers were shown and so, wave speed was determined.

Microbubble oscillating in a microvessel filled with viscous fluid: A finite element modeling study

Understanding the dynamics of coated-microbubble oscillating in an elastic microvessel is important for effective and safe applications of ultrasound contrast agents (UCAs) in imaging and therapy. Numerical simulations are performed based on a two-dimensional (2D) asymmetric finite element model to investigate the influences of both acoustic driving parameters (e.g., pressure and frequency) and material properties (vessel size, microbubble shell visco-elastic parameters and fluid viscosity) on the dynamic interactions in the bubble–blood–vessel system. The results show that, the constrained effect of the blood vessel along the radial direction will induce the asymmetric bubble oscillation and vessel deformation, as well as shifting the bubble resonance frequency toward the higher frequency range. For a bubble (1.5-μm radius) activated by 1-MHz ultrasound pulses in a microvessel with a radius varying between 2 and 6.5μm, up to 26.95kPa shear stress could be generated on the vessel wall at a driving pressure of 0.2MPa, which should be high enough to damage the vascular endothelial cells. The asymmetrical oscillation ratio of the bubble can be aggravated from 0.12% to 79.94% with the increasing acoustic driving pressure and blood viscosity, or the decreasing vessel size and microbubble shell visco-elastic properties. The maximum compression velocity on the bubble shell will be enhanced from 0.19 to 22.79m/s by the increasing vessel size and acoustic pressure, or the decreasing microbubble shell visco-elasticity and blood viscosity. As the results, the peak values of microstreaming-induced shear stress on the vessel wall increases from 0.003 to 26.95kPa and the deformation degree of vessel is raised from 1.01 to 1.49, due to the enhanced acoustic amplitude, or the decreasing vessel size, blood viscosity and microbubble shell visco-elasticity. Moreover, it also suggests that, among above impact parameters, microbubble resonance frequency and UCA shell elasticity might play more dominant roles in dynamic interactions of the bubble–blood–vessel system.

An experimental approach to a simplified model of human birth

This study presents a simplified experimental model of labor for the study of fetal lie and amniotic fluid properties. It mimics a ventouse (vacuum extraction) delivery to study the effect of amniotic fluid properties on force transfer to a passive fetus. The simplified vacuum delivery consists of a solid ovate spheroid being pulled from a passive, flexible spherical elastic shell filled with fluid. We compare the force necessary to remove the ovate fetus in fluids of varying properties. Additionally, the fetal lie—angular deviation from maternal/fetal spinal alignment—is changed by 5° intervals and the pullout force is measured. In both the concentric ovate experiments, the force to remove the fetus changes with the properties of the fluid occupying the space between the fetus and the uterus. Increasing the fluid viscosity by 35% decreases the maximum fetal removal force by up to 52.5%. Furthermore, while the force is dominated by the elastic force of the latex uterus, the properties of the amniotic fluid can significantly decrease the total removal force. This study demonstrates that the fluid components of a birth model can significantly alter the forces associated with fetus removal. This suggests that complete studies of human parturition should be designed to include both the material and fluid systems.

Modeling of offshore pile driving noise using a semi-analytical variational formulation

Underwater noise radiated from offshore pile driving got much attention in recent years due to its threat to the marine environment. This study develops a three-dimensional semi-analytical method, in which the pile is modeled as an elastic thin cylindrical shell, to predict vibration and underwater acoustic radiation caused by hammer impact. The cylindrical shell, subject to the Reissner–Naghdi’s thin shell theory, is decomposed uniformly into shell segments whose motion is governed by a variational equation. The sound pressures in both exterior and interior fluid fields are expanded as analytical functions in frequency domain. The soil is modeled as uncoupled springs and dashpots distributed in three directions. The sound propagation characteristics are investigated based on the dispersion curves. The case study of a model subject to a non-axisymmetric force demonstrates that the radiated sound pressure has dependence on circumferential angle. The case study including an anvil shows that the presence of the anvil tends to lower the frequencies and the amplitudes of the peaks of sound pressure spectrum. A comparison to the measured data shows that the model is capable of predicting the pile driving noise quantitatively. This mechanical model can be used to predict underwater noise of piling and explore potential noise reduction measures to protect marine animals.

Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping.

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes on the atomic scale, using high-resolution (S)TEM images. After quantitative comparison with continuum mechanics shell model, it is verified that the bending behaviour of the studied 2D materials can be well explained by the linear elastic shell model. And the bending rigidities can thus be derived by fitting with our experimental results. Recall almost only theoretical approaches can access the bending properties of these 2D membranes before, now a new experimental method to measure the bending rigidity of such flexible and atomic thick 2D membranes is proposed.

The resultant linear six‐field theory of elastic shells: What it brings to the classical linear shell models?

Basic relations of the resultant linear six‐field theory of shells are established by consistent linearization of the resultant 2D non‐linear theory of shells. As compared with the classical linear shell models of Kirchhoff‐Love and Timoshenko‐Reissner type, the six‐field linear shell model contains the drilling rotation as an independent kinematic variable as well as two surface drilling couples with two work‐conjugate surface drilling bending measures are present in description of the shell stress‐strain state. Among new results obtained here within the six‐field linear theory of elastic shells there are: 1) formulation of the extended static‐geometric analogy; 2) derivation of complex BVP for complex independent variables; 3) description of deformation of the shell boundary element; 4) the Cesáro type formulas and expressions for the vectors of stress functions along the shell boundary contour; 5) discussion on explicit appearance of gradients of 2D stress and strain measures in the resultant stress working.

Simulation of Non-Newtonian Emulsion Flows in Microchannels

Simulation of emulsion flows in differently shaped microchannels to reproduce the choking of such flows as a result of the effect of dynamic blocking has been made. A model of a highly concentrated emulsion as a structure of tightly packed deformed droplets surrounded by elastic shells is considered. The motion of liquid was determined by the method of the lattice Boltzmann equations together with the immersed boundary method. The influence of the non-Newtonian properties and of elastic turbulence of the indicated emulsion, as well as of the elasticity of the shells of its droplets and of the interaction of these shells on the emulsion motion in a microchannel, has been investigated. It is shown that the flow of this emulsion can be slowed down substantially only due to the mutual attraction of the shells of its droplets.

Analysis on mass sensing characteristics of SWCNT-based nano-mechanical resonators using continuum mechanics based finite element analysis

In this study, we used the Finite element method (FEM) based on continuum mechanics, instead of molecular dynamics, to design and analyze an ultra-small mass nanomechanical sensor using Single wall carbon nanotube (SWCNT). We tested the validity of the FEM modeling technique based on continuum mechanics by comparing its analysis results with those of molecular dynamics modeling. After developing an elastic continuum shell model having an effective thickness, Young’s modulus, and Poisson’s ratio, we proved the superiority of the implemented analysis technique by comparing its resonance frequency with that of the molecular dynamics model. Additionally, using the developed model, we established various design parameters for a resonator and observed the parameter-dependent changes in frequency characteristics of the resonator.

Elasticity and glocality: initiation of embryonic inversion in Volvox.

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are glocal, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga Volvox, whose embryos must turn themselves inside out to complete their development. This process has recently been shown to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

DYNAMIC ANALYSIS OF FULLY ANCHORED CIRCULAR CYLINDRICAL LIQUIDS’ STORAGE STEEL TANKS USING FINITE ELEMENT METHOD

A vibration analysis of circular cylindrical steel liquid storage tanks anchored to rigid base is conducted. Empty, partially and completely liquid filled tanks are considered as well as tanks composed of two courses using ANSYS 11.0 finite element package. The tank wall is modeled using linear elastic shell finite element and a new method, based on the added mass approach, is developed to model the effect of the contained liquid. In this method the properties of the shell element is modified to include the effect of the contained liquid. The analysis includes four tank case studies which are empty, fully filled with water, and filled with changeable liquid level in addition to study the effect of the variable thickness of tank on the natural frequencies and mode shapes. The results show that the natural frequency of completely filled tall tank may be less by 70.7% than the natural frequency of empty tank. It is also found that a maximum value of natural frequency can be obtained when the lower thick course consists 0.75 of tank height and its thickness is four times that of the upper one. The natural frequencies decrease with the increasing in liquid level for tall tank. The natural frequency of completely filled tank is less by 70.7% than the natural frequency of empty tank.

Packing of elastic wires in flexible shells

The packing problem of long thin filaments that are injected into confined spaces is of fundamental interest for physicists and biologists alike. How linear threads pack and coil is well known only for the ideal case of rigid containers, though. Here, we force long elastic rods into flexible spatial confinement borne by an elastic shell to examine under which conditions recently acquired knowledge on wire packing in rigid spheres breaks down. We find that unlike in rigid cavities, friction plays a key role by giving rise to the emergence of two distinct packing patterns. At low friction, the wire densely coils into an ordered toroidal bundle with semi-ellipsoidal cross-section, while at high friction, it packs into a highly disordered, hierarchic structure. These two morphologies are shown to be separated by a continuous phase transition. Our findings demonstrate the dramatic impact of friction and confinement elasticity on filamentous packing and might drive future research on such systems in physics, biology and even medical technology toward including these mutually interacting effects.

Estimation of Storage Stability of Aqueous Microbubble Suspensions

Abstract The aqueous suspensions of gaseous microbubbles are currently being used as contrast enhancing agents for ultrasonic imaging and as potential vehicles for targeted drug delivery. The storage stability of microbubble suspensions is very important as for any possible application of microbubbles, a stable microbubble suspension is needed. A stable microbubble suspension is a suspension for which there is no drastic change in concentration (number of microbubbles/mL of storage solution) and microbubble size distribution during the period of storage. To characterize storage stability, half-life of the microbubble suspensions, which is the time required for the microbubble concentration (#/mL) to decrease by 50% during storage, was estimated using a simple model. The proposed model estimates the storage stability of aqueous microbubble suspensions and effect of material properties on their storage stability. It takes into account an inter-bubble mass transfer and combines it with a population balance equation to account for a change in concentration (#/mL) as well as size and size distribution of microbubbles in the aqueous suspensions. The calculations have been performed for microbubbles made of three gases, namely oxygen (O2), sulphur hexafluoride (SF6) and perfluorobutane (PFB). The variation in storage stability of microbubble suspensions was examined by varying microbubble shell properties such as shell elasticity, surface tension and shell resistance as well as the other parameters such as viscosity of the storage medium and the initial size distribution of the microbubbles. The analysis of the results show that, among the shell properties studied, the shell resistance influenced the suspension stability the most and shell elasticity influenced the stability the least. Similarly, a gas with the lower liquid phase diffusivity and lower Ostwald coefficient results in a stable microbubble suspension. Also, higher viscosity of storage solution and microbubbles with larger sizes tend to increase the storage stability. Overall, the increase in the total resistance (combination of shell resistance and resistance in the storage solution) to mass transfer of a gas increases the storage stability of the microbubble suspensions.

Numerical simulation of pressure therapy glove by using Finite Element Method

Pressure therapy garments apply pressure to suppress the growth and flatten hypertrophic scars caused by serious burns. The amount of pressure given by the pressure garments is critical to the treatment adherence and outcomes. In the present study, a biomechanical model for simulating the pressure magnitudes and distribution over hand dorsum given by a pressure glove was developed by using finite element method. In this model, the shape geometry of the hand, the mechanical properties of the glove and human body tissues were incorporated in the numerical stress analyses. The geometry of the hand was obtained by a 3D laser scanner. The material properties of two warp knitted fabrics were considered in the glove fabric model that developed from the glove production pattern with 10% size reduction in circumferential dimensions. The glove was regarded an isotropic elastic shell and the hand was assumed to be a homogeneous, isotropic and linearly elastic body. A glove wearing process was carried in the finite element analysis and the surface-to-surface contact pressure between hand and glove fabric was hence obtained. Through validation, the simulated contact pressure showed a good agreement with the experimental interface pressure measurement. The simulation model can be used to predict and visualise the pressure distribution exerted by a pressure therapy glove onto hand dorsum. It can provide information for optimising the material mechanical properties in pressure garment design and development, give a clue to understand the mechanisms of pressure action on hypertrophic scars and ultimately improve the medical functions of pressure garment.

Shear Effects on Energy Dissipation From an Elastic Beam on a Rigid Foundation

This work describes the energy dissipation arising from microslip for an elastic shell incorporating shear and longitudinal deformation resting on a rough-rigid foundation. This phenomenon is investigated using finite element (FE) analysis and nonlinear geometrically exact shell theory. Both approaches illustrate the effect of shear within the shell and observe a reduction in the energy dissipated from microslip as compared to a similar system neglecting shear deformation. In particular, it is found that the shear deformation allows for load to be transmitted beyond the region of slip so that the entire interface contributes to the load carrying capability of the shell. The energy dissipation resulting from the shell model is shown to agree well with that arising from the FE model, and this representation can be used as a basis for reduced order models that capture the microslip phenomenon.

Driven self-assembly of hard nanoplates on soft elastic shells**Project supported by the National Natural Science Foundation of China (Grant No. 21174131).

The driven self-assembly behaviors of hard nanoplates on soft elastic shells are investigated by using molecular dynamics (MD) simulation method, and the driven self-assembly structures of adsorbed hard nanoplates depend on the shape of hard nanoplates and the bending energy of soft elastic shells. Three main structures for adsorbed hard nanoplates, including the ordered aggregation structures of hard nanoplates for elastic shells with a moderate bending energy, the collapsed structures for elastic shells with a low bending energy, and the disordered aggregation structures for hard shells, are observed. The self-assembly process of adsorbed hard nanoplates is driven by the surface tension of the elastic shell, and the shape of driven self-assembly structures is determined on the basis of the minimization of the second moment of mass distribution. Meanwhile, the deformations of elastic shells can be controlled by the number of adsorbed rods as well as the length of adsorbed rods. This investigation can help us understand the complexity of the driven self-assembly of hard nanoplates on elastic shells.