Physical variational principle and thin plate theory in electro-magneto-elastic analysis

Under the assumption of the quasi-static electric and magnetic fields the electro-magneto-elastic analysis including medium and its environment is studied in this paper. The complete governing equations under the finite deformation can be derived from the physical variational principle. In the physical variational principle the variations of the electric potential and magnetic potential are divided into local variations and migratory variations. From the virtual change of the sum of the electromagnetic energy and the couple energy produced by the migratory variation we can get the electromagnetic force and in this case the virtual variation of the volume should be considered. It is also found that the Maxwell stress is directly related to the strain in a material with piezoelectric or piezomagnetic behavior for the finite deformation case. The thin plate theory in first order is derived from the general theory in this paper and the Maxwell stress is naturally included in the governing equations.