Showing papers on "Spherical shell published in 2018"
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07 Aug 2018
TL;DR: In this paper, the plate equations were derived from 3D elasticity by formal expansion from three-dimensional elasticity, and a calculus of variations was used to describe the geometrical rigidity of surfaces.
Abstract: 1. Introduction 2. Three-dimensional elasticity I: RODS 3. Equations for elastic rods 4. Mechanics of the human hair 5. Rippled leaves, uncoiled springs II: PLATES 6. The equations for elastic plates 7. End effects in plate buckling 8. Finite amplitude buckling of a strip 9. Crumpled paper 10. Fractal buckling near edges III: SHELLS 11. Geometric rigidity of surfaces 12. Shells of revolution 13. The elastic torus 14. Spherical shell pushed by a wall Appendix A: Calculus of variations: a worked example Appendix B: Boundary and interior layers Appendix C: The geometry of helices Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity
286 citations
TL;DR: It is found that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold, however, for thinner shells, indentation leads to asymmetrical buckling beforesnap-through, while also making these shells more ‘robust’ to snap-through.
Abstract: Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two 'self-equilibrated' states, one natural and the other inside out (or 'everted'). Though this is familiar from everyday life-an umbrella is remarkably stable, yet a contact lens can be easily turned inside out-the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more 'robust' to snap-through. Our work sheds new light on the robustness of the 'mirror buckling' symmetry of spherical shell caps.
54 citations
TL;DR: In this article, a semi-analytical approach is employed to analyze the free vibration characteristics of uniform and stepped combined paraboloidal, cylindrical and spherical shells subject to arbitrary boundary conditions.
54 citations
TL;DR: In this paper, a three-dimensional sono-elastic method in the frequency domain is proposed to conduct the comprehensive analysis of fluid-structure interactions, acoustic radiation and acoustic propagation.
38 citations
TL;DR: In this article, a new model of gravastar in higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ was presented, where the pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell.
34 citations
TL;DR: The development of the PRSS unmanned aerial vehicle (UAV) with a passive rotating spherical shell that can easily maneuver while protecting itself is explained and satisfies the mandatory requirements of the Next Generation Robots for Social Infrastructure (NGRSI) program.
33 citations
TL;DR: In this article, the authors investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero and identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number becomes very small.
Abstract: We investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero. We identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number becomes very small. First are modes associated with attractors of characteristics that are made of thin shear layers closely following the periodic orbit traced by the characteristic attractor. Second are modes made of shear layers that connect the critical latitude singularities of the two hemispheres of the inner boundary of the spherical shell. Third are quasi-regular modes associated with the frequency of neutral periodic orbits of characteristics. We thoroughly analyse a subset of attractor modes for which numerical solutions point to an asymptotic law governing the eigenvalues. We show that three length scales proportional to , and control the shape of the shear layers that are associated with these modes. These scales point out the key role of the small parameter in these oscillatory flows. With a simplified model of the viscous Poincare equation, we can give an approximate analytical formula that reproduces the velocity field in such shear layers. Finally, we also present an analysis of the quasi-regular modes whose frequencies are close to and explain why a fluid inside a spherical shell cannot respond to any periodic forcing at this frequency when viscosity vanishes.
30 citations
TL;DR: In this paper, the authors used finite element simulations to determine the threshold between bistability and monostability for shells of different solid angles, and compared these results with the prediction from shallow shell theory.
Abstract: Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two `self-equilibrated' states, one natural and the other inside out (or `everted'). Though this is familiar from everyday life -- an umbrella is remarkably stable, yet a contact lens can be easily turned inside out -- the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more `robust' to snap-through. Our work sheds new light on the robustness of the `mirror buckling' symmetry of spherical shell caps.
23 citations
TL;DR: In this article, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered, and a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time.
Abstract: For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders. While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.
22 citations
TL;DR: In this paper, the authors present the dynamic buckling behavior of spherical shell structures colliding with an obstacle block under the sea, where the effect of deep water has been considered as a uniform external pressure.
Abstract: This paper is the first to present the dynamic buckling behavior of spherical shell structures colliding with an obstacle block under the sea. The effect of deep water has been considered as a uniform external pressure by simplifying the effect of fluid–structure interaction. The calibrated numerical simulations were carried out via the explicit finite element package LS-DYNA using different parameters, including thickness, elastic modulus, external pressure, added mass, and velocity. The closed-form analytical formula of the static buckling criteria, including point load and external pressure, has been firstly established and verified. In addition, unprecedented parametric analyses of collision show that the dynamic buckling force (peak force), mean force, and dynamic force redistribution (skewness) during collisions are proportional to the velocity, thickness, elastic modulus, and added mass of the spherical shell structure. These linear relationships are independent of other parameters. Furthermore, it can be found that the max force during the collision is about 2.1 times that of the static buckling force calculated from the analytical formula. These novel insights can help structural engineers and designers determine whether buckling will happen in the application of submarines, subsea exploration, underwater domes, etc.
21 citations
TL;DR: In this article, the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume are modeled as curvilinear meshes that can adapt to realistic structural settings.
Abstract: Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume. These solutions form the basis of curvilinear meshes that can adapt to realistic structural settings, such as a mantle wedge corner, a spherical shell around a magma chamber, or an aquifer. I provide computer programs to evaluate them in the cases of anti-plane strain, in-plane strain, and three-dimensional deformation. These tools may prove useful in the modeling of deformation data in tectonics, volcanology, and hydrology.
TL;DR: In this article, two opening reinforcement methods of spherical shells under uniform external pressure were investigated to reduce the local weakening and buckling effects of openings in spherical shells, designs comprising the wall reinforcement and the combination of a wall and thick plate reinforcement were employed to minimize buckling instability.
TL;DR: In this paper, the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume are modeled as curvilinear meshes that can adapt to realistic structural settings.
Abstract: Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume. These solutions form the basis of curvilinear meshes that can adapt to realistic structural settings, such as a mantle wedge corner, a spherical shell around a magma chamber, or an aquifer. I provide computer programs to evaluate them in the cases of anti-plane strain, in-plane strain, and three-dimensional deformation. These tools may prove useful in the modeling of deformation data in tectonics, volcanology, and hydrology.
TL;DR: Guerrero et al. as mentioned in this paper proposed a method for the 2D and 3D modeling of the universe using the viscosity fluid, and showed that it is possible to construct a 3D model of the world from 2D images.
Abstract: VISCOSITY FLUID: IMPLICATIONS FOR THE 2D AND 3D MODELING OF MOONS. J. M. Guerrero, J. P. Lowman, F. Deschamps & P. J. Tackley, Department of Physics, University of Toronto, Toronto M5S 1A7, Canada (joshua.guerrero@mail.utoronto.ca), Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada., Institute of Earth Sciences, Academia Sinica, 128 Academia Road Sec. 2, Nangang, Taipei 11529, Taiwan., Department of Earth Sciences, ETH-Zurich, Sonneggstrasse 5, 8092 Zurich, Switzerland.
TL;DR: In this article, a new, refined analytical solution for mechanochemical corrosion of a thin-walled spherical shell is presented that is valid for any combination of pressures and conditions for cessation of the corrosion process before any limiting stress is reached.
TL;DR: In this article, optical properties of particles consisting of light-absorbing carbon (or soot) and a weakly absorbing coating material are computed at a wavelength of 355 and 532 nm.
Abstract: Optical properties of particles consisting of light-absorbing carbon (or soot) and a weakly absorbing coating material are computed at a wavelength of 355 nm and 532 nm. A morphological particle model is used, in which small amounts of coating are applied as a thin film to the surface of the aggregate, while heavily coated aggregates are enclosed in a spherical shell. As the amount of coating material is increased, a gradual transition from film-coating to spherical-shell coating is accounted for. The speed of this transition can be varied by specifying a single parameter. Two different choices of this parameter, corresponding to a slow and a rapid transition from film-coating to spherical-shell coating, respectively, are investigated. For low soot volume fractions the impact of this transition on the linear depolarisation ratio δl is most pronounced. The model that describes a rapid transition to a spherical coating yields results for δl that are more consistent with existing lidar field measurements than the slow-transition model. At 532 nm the relative uncertainty in modelled δl for a rapid transition values due to uncertainties in the aggregate’s geometry and chemical composition are estimated to range from 109 to 243%, depending on the soot volume fraction. At 355 nm the relative uncertainties were estimated to range from 90.9 to 200%.
TL;DR: In this article, the spherical Couette system, consisting of a viscous fluid between two differentially rotating concentric spheres, is studied using numerical simulations and compared with experiments performed at BTU Cottbus-Senftenberg, Germany.
Abstract: The spherical Couette system, consisting of a viscous fluid between two differentially rotating concentric spheres, is studied using numerical simulations and compared with experiments performed at BTU Cottbus-Senftenberg, Germany. We concentrate on the case where the outer boundary rotates fast enough for the Coriolis force to play an important role in the force balance, and the inner boundary rotates slower or in the opposite direction as compared to the outer boundary. As the magnitude of differential rotation is increased, the system is found to transition through three distinct hydrodynamic regimes. The first regime consists of the emergence of the first non-axisymmetric instability. Thereafter one finds the onset of ‘fast’ equatorially antisymmetric inertial modes, with pairs of inertial modes forming triadic resonances with the first instability. A further increase in the magnitude of differential rotation leads to the flow transitioning to turbulence. Using an artificial excitation, we study how the background flow modifies the inertial mode frequency and structure, thereby causing departures from the eigenmodes of a full sphere and a spherical shell. We investigate triadic resonances of pairs of inertial modes with the fundamental instability. We explore possible onset mechanisms through numerical experiments.
TL;DR: In this paper, the impact of non-integer dimensional (NID) space on cloaking and magnification introduced through polarly radially anisotropic (PRA) cylindrical shell/spherically radially aisotropic spherical shell was studied.
TL;DR: In this article, the authors deal with certain aspects related to the dynamic behaviour of isotropic shell-like structures analyzed by the use of a higher order transversely deformable shell-type spectral finite element newly formulated and the approach known as the Time-domain Spectral Finite Element Method (TD-SFEM).
14 May 2018
TL;DR: In this article, the scaling laws for nonlinear buckling of stiffened orthotropic shallow spherical shells are presented by applying similitude transformation to the total energy of the structural system.
Abstract: General similitude requirements and the scaling laws for nonlinear buckling of stiffened orthotropic shallow spherical shells are presented by applying similitude transformation to the total energy of the structural system. In the absence of the experimental data, structural similitude is completed by numerical experiments. The predicted values of the prototype, obtained by substituting the model results into the scaling laws, are compared with those values of the prototype. In practical engineering, it may be hard to fulfill the complete similarity requirements. Thus, several cases of partial similitude are mainly investigated, including models distorted in material properties of ribs, in material properties and in material properties and geometry. By using specific formulas of stiffness parameters and the displacement scale factor, distorted models can predict geometric nonlinear buckling behavior of the prototypes of the stiffened orthotropic shallow spherical shell under external pressure with good accuracy.
TL;DR: In this paper, the authors demonstrate a significant delay of failure on an amorphous carbon hollow nanosphere due to the buckling and post-buckling deformation of the spherical shell.
TL;DR: In this paper, a differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially varying transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions.
Abstract: Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (\(d=2,3\)). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.
TL;DR: This paper proposes a benchmark problem for the two- and three-dimensional Cahn–Hilliard equations, which describe the process of phase separation and shows numerical results by using the explicit Euler’s scheme with a very fine time step size and presents a comparison test with Eyre's convex splitting schemes.
TL;DR: In this article, an eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials.
Abstract: The present article deals with the viscoelastic modeling and dynamic responses of the carbon nanotubes (CNTs)-based carbon fiber-reinforced polymer (CNTs-CFRP) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of CNTs-based polymer matrix phase. Further, the strength of material method has been employed to formulate the viscoelastic material behavior of the homogenized hybrid CNTs-CFRP composite materials. An eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials. Frequency- and temperature-dependent material properties of such hybrid composite materials have been obtained and analyzed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters on the material properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-based proposed composite materials.
TL;DR: In this article, an analytical formulation that calculates pressure was developed by integrating both the small-density method and the Bessel function method, and the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid.
Abstract: This paper is the first to highlight the vibrations of a hemispherical shell structure interacting with both compressible and incompressible fluids. To precisely calculate the pressure of the shell vibrating in the air, a novel analytical approach has been established that has existed in very few publications to date. An analytical formulation that calculates pressure was developed by integrating both the ‘small-density method’ and the ‘Bessel function method’. It was considered that the hemispherical shell vibrates as a simple harmonic function, and the fluid is non-viscous. For comparison, the incompressible fluid model has been analyzed. Surprisingly, it is the first to report that the pressure of the shell surface is proportional to the vibration acceleration, and the velocity amplitude decreased at the rate of 1 r 2 when the fluid was incompressible. Otherwise, the surface pressure of the hemispherical shell was proportional to the vibration velocity, and the velocity amplitude decreased with the rate of 1 r when the fluid was compressible. The compressibility of fluid played an important role in the dynamic pressure of the shell structure. Furthermore, the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid ( ρ o c ) exactly. In this study, the analytical solutions were verified by the calibrated numerical simulations, and the analytical formulation were rigorously tested by extensive parametric studies. These new findings can be used to guide the optimal design of the spherical shell structure subjected to wind load, seismic load, etc.
TL;DR: A dense imploding spherical shell, where perturbations on the inner surface grow due to hydrodynamic instabilities, geometric convergence and compression, is considered, and the presented perturbation amplitudes can inform future non-linear modeling.
TL;DR: Through coarse-grained molecular dynamics simulations, this work explores the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses.
Abstract: Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.
TL;DR: This QDs spherical shell structure demonstrates superior performance of QDs films for WLEDs applications, and is mainly attributed to larger heat dissipation area and separated heat source.
Abstract: White light-emitting diodes (WLEDs) based on quantum dots (QDs) are gaining increasing attention due to their excellent color quality. QDs films with planar structure are universally applied in WLEDs for color conversion, while they still face great challenges in high light extraction and thermal stability. In this study, a QDs film with a spherical shell structure was proposed to improve the optical and thermal performance for WLEDs. Compared with the conventional planar structure, the luminous efficacy of the QDs spherical shell structure is improved by 12.9% due to the reduced total reflection effect, and the angular-dependent correlated color temperature deviation is decreased from 2642 to 283 K. Moreover, the highest temperature of the WLED using a QDs spherical shell is 4.8 °C lower than that of the conventional WLED with a planar structure, which is mainly attributed to larger heat dissipation area and separated heat source. Consequently, this QDs spherical shell structure demonstrates superior performance of QDs films for WLEDs applications.
TL;DR: In this article, the buckling behavior of a complete spherical shell under external pressure and of a half-sphere under torsion is investigated, and several parametric studies are performed to identify the different key parameters of the corresponding buckling capacity curves and lead up to both a qualitative and quantitative discussion about the imperfection sensitivity of such structures under each fundamental load.
Abstract: In this paper, the buckling behavior of a complete spherical shell under external pressure and of a half-sphere under torsion are first investigated. Several parametric studies are performed, which rely on the European Recommendations framework (ECCS text), so as to identify the different key parameters of the corresponding buckling capacity curves and lead up to both a qualitative and quantitative discussion about the imperfection sensitivity of such structures under each fundamental load. The related results allow us to completely describe the buckling behavior of a spherical shell under combined external pressure and circumferential shear by means of interactive buckling curves, without the need of many supplementary computations for any arbitrary combined loading case.
TL;DR: In this paper, an exact expression for the stored electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave, is derived.
Abstract: An exact expression is derived for the time-averaged electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contribution to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: the dielectric shell and dispersive metamaterial core, and vice-versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.