On Anisothermal Electromagnetic Elastic Deformations in Flight in Fair Weather and Lightning Storms

The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and spatial dependence only on the coordinate orthogonal to the slab; (ii) the displacement vector orthogonal to the slab; (iii) the magnetic field orthogonal to the electric field, with both in the plane parallel to the sides of the slab. The exact analytical solution is obtained in the linear approximation for the displacement vector, electric and magnetic fields and temperature as function of the coordinate normal to the slab, taking into account heating by the Joule effect of Ohmic electric currents and Fourier thermal conduction. These specify the strain and stress tensors, the electric current and the heat flux. The material properties involved include the mass density, dielectric permittivity, magnetic permeability, elastic stiffness tensor, electromagnetic coupling and thermal stress tensors, pyroelectric and pyromagnetic vectors and piezoelectric and piezomagnetic tensors. The analytic results of the theory are simplified assuming (i) isotropic material properties; (ii) a steady state independent of time. The profiles as a function of the coordinate normal to the slab of the electric and magnetic fields, temperature and heat flux and displacement, strain and stress are obtained in these conditions.