Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 1: foundation of the theory

Abstract

A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed. In this context, the first-order transversely shearable plate theory in conjunction with von-Kármán geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Amp e ` re, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2-D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.