Equilibrium states of an elastic conducting rod in a magnetic field (Q1118462)

The presented paper studies the properties of the equilibrium configurations of an originally straight flexible nonlinear (hyper)elastic rod loaded by electromagnetic forces due to a current within the rod and a magnetic field in the initial direction of the rod axis. Because the ends of the bar are fixed the problem becomes conservative and can be rendered by a variational formulation. This is embedded in a more general description which is treated by functional analysis methods in a Banach space. The application on the rod problem yields the existence of nontrivial solutions, a certain kind of electromagnetic buckling modes.