Higher Order Theory of Electro-Magneto-Elastic Plates and Shells

New higher order models of the electro-magneto-elastic plates and shells have been developed here. The 3-D equations of the linear electro-magneto-elasticity have been presented in an orthogonal system of coordinates. For the creation of 2-D models of plates and shells the curvilinear system of coordinates related to the middle surface of the shell has been used along with special hypothesis based on assumptions that take into account the fact that the considered plates and shells are thin. Higher order theory is based on the expansion of the 3-D equations of the linear theory of the electro-magneto-elasticity into Fourier series in terms of Legendre polynomials. All equations for higher order theory of the electro-magneto-elastic plates in Cartesian and polar coordinates as well as for cylindrical and spherical shells in coordinates related to the shells geometry have been developed and presented here in detail. The obtained equations can be used for calculating the stress-strain and for modelling thin walled structures in macro, micro and nano scale when taking into account coupled electro-magneto-elastic effects.