A Finite Element Framework for Magneto-Actuated Large Deformation and Instability of Slender Magneto-Active Elastomers

2020 ◽  
Vol 12 (01) ◽  
pp. 2050013 ◽  
Author(s):  
Yin Liu ◽  
Shoue Chen ◽  
Xiaobo Tan ◽  
Changyong Cao
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Fields ◽  
Large Deformation ◽  
Rational Design ◽  
Mesh Distortion ◽  
Strongly Coupled ◽  
Background Space ◽  
Spatial Coordinates ◽  
The Magnetic Field

In this paper, we present an efficient finite element framework for modeling the finite deformations of slender magneto-active elastomers (MAE) under applied magnetic fields or currents. For the convenience of numerical modeling, magnetic field is defined at fixed spatial coordinates in the background space rather than in the elastic MAEs using material coordinates. The magnetic field will vary with free or localized currents while the spatial distribution of the magnetic field will evolve with the motion or deformation of the MAE materials, which is actuated by the surface or body forces induced by external magnetic fields or equivalent currents. A staggered strategy and a Riks method are introduced to solve the strongly coupled governing equations of the magnetic field and displacement field using finite element method. The mesh distortion along the interfaces between MAE domain and free-space domain is resolved by considering concurrent deformation of the mesh in these two domains. A few 2D numerical examples demonstrate the validity and efficiency of the developed model for simulating large deformation of MAE with non-uniform spatial magnetic field under different actuation sources such as free currents, magnetization or external magnetic field. This framework offers a new solution strategy for modeling mechano-magneto problems of MAEs and will help rational design and analysis of MAE-based actuators and soft robotics in the future.

Design and Analysis of a Novel 2-D Permanent Magnet Array for Planar Actuator

2013 ◽  
Vol 416-417 ◽  
pp. 253-257
Author(s):  
Liang Guo ◽  
Hao Ding
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Fields ◽  
Permanent Magnet ◽  
3D Finite Element ◽  
3D Finite Element Method ◽  
Magnetic Poles ◽  
The Magnetic Field ◽  
Element Method

A novel 2-D permanent magnet array for a planar actuator was proposed, in which the portion between adjacent magnetic poles was divided to four small rectangular solids. Magnetic fields of the permanent magnet array were analyzed systematically by 3D finite element method. The analysis results show that, compared with the well-known Halbach magnet array, the proposed array has higher permanent magnet utilization. Keeping the whole permanent magnet volume constant, the arrays with several improved structures were put forward. The magnetic field analyze results prove that the utilization is best, when the ratio between the height of the magnetic poles magnetized vertically and the height of the portion magnetized horizontally is about 2.

Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

2000 ◽  
Vol 179 ◽  
pp. 263-264
Author(s):  
K. Sundara Raman ◽  
K. B. Ramesh ◽  
R. Selvendran ◽  
P. S. M. Aleem ◽  
K. M. Hiremath
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Ultra Violet ◽  
Active Regions ◽  
Morphological Properties ◽  
Energy Storage And Conversion ◽  
The Sun ◽  
X Rays ◽  
The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

scholarly journals An 84-μG Magnetic Field in a Galaxy at Z=0.692?

2008 ◽  
Vol 4 (S254) ◽  
pp. 95-96
Author(s):  
Arthur M. Wolfe ◽  
Regina A. Jorgenson ◽  
Timothy Robishaw ◽  
Carl Heiles ◽  
Jason X. Prochaska
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Faraday Rotation ◽  
Large Scale ◽  
Dynamo Model ◽  
Magnetic Field Generation ◽  
Interstellar Gas ◽  
Splitting Technique ◽  
Average Value ◽  
The Magnetic Field

AbstractThe magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars (Beck 2005). The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ≈ 3 μG (Han et al. 2006). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars (Kronberg et al. 2008) suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain.Here we report a measurement of a magnetic field of B ≈ 84 μG in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 μG in the neutral interstellar gas of our Galaxy (Heiles et al. 2004). This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past, rather than stronger (Parker 1970).The full text of this paper was published in Nature (Wolfe et al. 2008).

Magnetic Field Spectroheliograms from the San Fernando Observatory

1971 ◽  
Vol 43 ◽  
pp. 329-339 ◽  
Author(s):  
Dale Vrabec
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Structure ◽  
Longitudinal Component ◽  
Solar Telescope ◽  
Solar Magnetic Fields ◽  
San Fernando ◽  
Field Lines ◽  
The Magnetic Field ◽  
Field Network

Zeeman spectroheliograms of photospheric magnetic fields (longitudinal component) in the CaI 6102.7 Å line are being obtained with the new 61-cm vacuum solar telescope and spectroheliograph, using the Leighton technique. The structure of the magnetic field network appears identical to the bright photospheric network visible in the cores of many Fraunhofer lines and in CN spectroheliograms, with the exception that polarities are distinguished. This supports the evolving concept that solar magnetic fields outside of sunspots exist in small concentrations of essentially vertically oriented field, roughly clumped to form a network imbedded in the otherwise field-free photosphere. A timelapse spectroheliogram movie sequence spanning 6 hr revealed changes in the magnetic fields, including a systematic outward streaming of small magnetic knots of both polarities within annular areas surrounding several sunspots. The photospheric magnetic fields and a series of filtergrams taken at various wavelengths in the Hα profile starting in the far wing are intercompared in an effort to demonstrate that the dark strands of arch filament systems (AFS) and fibrils map magnetic field lines in the chromosphere. An example of an active region in which the magnetic fields assume a distinct spiral structure is presented.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals Finite Element Analysis of Magnetic Field Exciter for Direct Testing of Magnetocaloric Materials’ Properties

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2792
Author(s):  
Wieslaw Lyskawinski ◽  
Wojciech Szelag ◽  
Cezary Jedryczka ◽  
Tomasz Tolinski
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Circuit ◽  
Homogeneous Magnetic Field ◽  
Element Analysis ◽  
Mcm Testing ◽  
Testing Region ◽  
Magnetocaloric Materials ◽  
Field Excitation ◽  
The Magnetic Field

The paper presents research on magnetic field exciters dedicated to testing magnetocaloric materials (MCMs) as well as used in the design process of magnetic refrigeration systems. An important element of the proposed test stand is the system of magnetic field excitation. It should provide a homogeneous magnetic field with a controllable value of its intensity in the MCM testing region. Several concepts of a magnetic circuit when designing the field exciters have been proposed and evaluated. In the MCM testing region of the proposed exciters, the magnetic field is controlled by changing the structure of the magnetic circuit. A precise 3D field model of electromagnetic phenomena has been developed in the professional finite element method (FEM) package and used to design and analyze the exciters. The obtained results of the calculations of the magnetic field distribution in the working area were compared with the results of the measurements carried out on the exciter prototype. The conclusions resulting from the conducted research are presented and discussed.

scholarly journals The Origin and Dynamical Effects of the Magnetic Fields and Cosmic Rays in the Disk of the Galaxy

1970 ◽  
Vol 39 ◽  
pp. 168-183
Author(s):  
E. N. Parker
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Magnetic Fields ◽  
Dynamical Behavior ◽  
Cosmic Ray ◽  
Interested Reader ◽  
Written Text ◽  
The Galaxy ◽  
Basic Ideas ◽  
The Magnetic Field

The topic of this presentation is the origin and dynamical behavior of the magnetic field and cosmic-ray gas in the disk of the Galaxy. In the space available I can do no more than mention the ideas that have been developed, with but little explanation and discussion. To make up for this inadequacy I have tried to give a complete list of references in the written text, so that the interested reader can pursue the points in depth (in particular see the review articles Parker, 1968a, 1969a, 1970). My purpose here is twofold, to outline for you the calculations and ideas that have developed thus far, and to indicate the uncertainties that remain. The basic ideas are sound, I think, but, when we come to the details, there are so many theoretical alternatives that need yet to be explored and so much that is not yet made clear by observations.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

2012 ◽  
Vol 27 (40) ◽  
pp. 1250233 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Topological Charge ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Finite Energy ◽  
Spatial Infinity ◽  
Yang Mills ◽  
The Magnetic Field

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

scholarly journals Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

2014 ◽  
Vol 44 (4) ◽  
pp. 293-312 ◽  
Author(s):  
Tomáš Šoltis ◽  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Inner Core ◽  
Polar Regions ◽  
Number Density ◽  
Magnetic Diffusion ◽  
Spherical Fluid ◽  
The Magnetic Field

Abstract We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion.

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