Implicit–explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids

A numerical computer model based on the dual reciprocity boundary element method (DRBEM) is extended to study the generalized theories of magneto-thermoelasticity problems in a rotating anisotropic viscoelastic functionally graded solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a predictor–corrector implicit–explicit time integration algorithm was developed and implemented for use with the DRBEM to obtain the solution for the displacement and temperature fields in the context of the Green and Naghdi theory of type III. A comparison of the results is presented graphically in the absence and presence of magnetic field. Numerical results that demonstrate the validity of the proposed method are also presented graphically.