On electromagnetic effects in the theory of shells and plates

Abstract This paper is concerned with the nonlinear and linear thermomechanical theories of deformable shell-like bodies in which account is taken of electromagnetic effects. The development is made by a direct approach with use of the two-dimensional theory of directed media called Cosserat surfaces. The first part of the paper deals with the formulation of appropriate nonlinear equations governing the motion of shell-like bodies in the presence of electromagnetic and thermal effects, as well as a general discussion of appropriate constitutive equations and symmetry restrictions. In the second part of the paper, attention is confined to special or more restrictive nonlinear and linear theories of shells including, for example, the nonlinear membrane theory, a restricted nonlinear bending theory (corresponding to the classical Kirchhoff-Love theory of shells) and a plate theory, all in the presence of electromagnetic effects. Finally, in the third part of the paper, attention is confined to specific topics, e.g. piezoelectricity in elastic plates and electromagnetic effects in a non-conducting plate, and a demonstration of the relevance and the applicability of the present direct formulation of a theory of electromagnetism for shell-like bodies.