Equilibrium states of an elastic conducting rod in a magnetic field

DOI10.1007/BF00251533zbMath0668.73071MaRDI QIDQ1118462

Peter Wolfe, Thomas I. Seidman

Publication date: 1988

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

conservativeexistence of nontrivial solutionselectromagnetic buckling modesstraight flexible nonlinear (hyper)elastic rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Electromagnetic effects in solid mechanics (74F15) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items

Hanging cables with small bending stiffness, Buckling of a nonlinearly elastic column: Variational principles, bifurcation and asymptotics, Nonlinear stability analysis of a clamped rod carrying electric current, Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories, Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum, The parabolic-hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods, Geodesic finite elements for Cosserat rods

Cites Work

• Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
• Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
• Ordinary differential equations of non-linear elasticity. II: Existence and regularity theory for conservative boundary value problems
• Equilibrium States of an Elastic Conductor in a Magnetic Field: A Paradigm of Bifurcation Theory
• The ambiguous twist of Love