A differential quadrature analysis of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field

A rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical simulation of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field. Fundamental equations of plane electromagnetic, temperature and elastic fields are formulated. To the best of the authors' knowledge, this is the first attempt to apply the DQM to magneto-thermo-elasticity and the first attempt to analyze a finite two-dimensional magneto-thermo-elastic problem. The fundamental equations and the inhomogeneous time-dependent boundary conditions are discretized in spatial and temporal domain by differential quadrature (DQ) rules. The unknowns satisfying the governing equations, the boundary and initial conditions simultaneously are computed in the entire domain by means of DQM with high efficiency and accuracy using dramatically less grid points in both spatial and time domain. Solutions of magnetic field, eddy current, temperature change and dynamic solutions of stresses and deformations are illustrated graphically.