Study Of Magneto-thermo-elastic Stresses In A Plane

Magneto-thermo-elasticity is a special subject, in which we investigate the interaction among the strain, electromagnetic fields and temperature fields. The influence of the electromagnetic field on the strain occurs by means of Lorentz forces appearing in the equations of motion. The Ohm law contains a term describing the increment of density of the electric field developing on the velocity of the material particles moving in the magnetic field. The arbitrary variation of magnetic field can generate eddy current in the media. The eddy current heats the body, which generates thermo stress. The influence of the strain on the temperature field occurs by means of a term containing strain rate appearing in the heat conduction function.The article aims at the analysis of the coupling problem in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field. The model is assumed as a circular plate, and the coupling problem will be discussed in two ways, with and without the coupling term which shows the interact between strain and electromagnetic field, but the influence strain rate to thermal field is not considered. The fundamental equation of electromagnetic field, temperature field and elastic field are formulated. An accurate and efficient differential quadrature method is employed for numerical simulation of magneto-thermo-elastic stresses in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field. The fundamental equations and both boundary conditions and initial conditions are discretized in spatial and temporal domain by differential quadrature rules. The unknown variables satisfy the governing equations, the boundary conditions and the initial conditions simultaneously, and they are computed in entire domain by means of DQM. Accurate solutions can be obtained by using less grid points in both spatial and time domain. Solutions of magnetic field, temperature field and stresses and deformation are illustrated graphically. The comparison between two kinds of calculated results is also illustrated graphically and analyzed theoretically.