A new boundary element model for magneto-thermo-elastic stress sensitivities in anisotropic functionally graded materials

Abstract A computational model using the dual reciprocity boundary element method (DRBEM) is developed to analyze magneto-thermo-elastic stress sensitivity in nonlinear time-dependent anisotropic functionally graded materials (FGMs) via conduction and radiation mechanisms. The concept is demonstrated on a nonlinear time-dependent anisotropic functionally graded material which has been submerged in a uniform principal magnetic field emanating in the $$z$$ z -direction. A numerical strategy for method implementation for plane deformation is described, along with numerical computations for temperature, displacement, and thermal stress. First, the Kirchhoff transformation partially linearizes the heat conduction equation. The resultant equation was then discretized with the DRBEM. The heat radiation integral equation has been discretized using the DRBEM. The consequent two equation systems have been connected by removing the radiative heat fluxes from each set. The temperature field was determined by solving the final system of ordinary differential equations using a self-adaptive technique based on the Runge–Kutta method. The displacement field can then be determined with the equation of motion. The validity of DRBEM is checked by evaluating a nonlinear time-dependent anisotropic functionally graded material occupying a rectangular region, and the results agree well with previous ones. The data clearly reveal the impact of magnetic fields on the thermal stress sensitivity of isotropic, transversely isotropic, and orthotropic materials. The results also reveal the influence of graded parameters on the magneto-thermo-elastic stress sensitivity in conduction when compared to radiation.