Equilibrium of Kirchhoff’s rods subject to a distribution of magnetic couples

The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The one-dimensional nonlinear equations governing the problem are deduced fro...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:International journal of solids and structures Ročník 238; s. 111393
Hlavní autori: Lembo, Marzio, Tomassetti, Giuseppe
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Elsevier Ltd 01.03.2022
Elsevier BV
Predmet:
Bifurcation and buckling
Control rods
Elastic deformation
Electromagnetic effects
Elliptic functions
Exact solutions
Explicit solutions
Magnetic fields
Magnetism
Nonlinear elasticity
Nonlinear equations
Remote control
Rods
Stability analysis
Three dimensional models
74G05
Explicit solutions
Bifurcation and buckling
74K10
74F15
Electromagnetic effects
Rods
74G60
74B20
Nonlinear elasticity
ISSN:0020-7683, 1879-2146
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The one-dimensional nonlinear equations governing the problem are deduced from a three-dimensional model and are fully consistent with the Kirchhoff’s theory in the sense that they hold at the same order of magnitude. Exact solutions of those equations in terms of Weierstrass elliptic functions are presented with reference to magneto-elastic cantilevers that undergo planar deformations under the action of a terminal force and a magnetic field whose directions are either parallel or orthogonal. The exact solutions are applied to the study of a problem of the remotely controlled deformation of a rod and to a bifurcation problem in which the end force and the component of the magnetic field parallel to the undeformed rod axis can be regarded as imperfection parameters; the stability of the different solutions possible under the same load is assessed by comparing the corresponding energies. •Kirchhoff’s theory is extended to rods subject to distributions of magnetic couples.•Equilibrium equations are obtained from the variation of the magneto-elastic energy.•Exact equilibrium solutions in terms of elliptic functions are deduced.•Remotely controlled deformation of a magneto-elastic rod is examined.•Bifurcation diagrams for magneto-elastic cantilevers are presented.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2021.111393