Coupled fields in layered thermomagnetoelectroelastic spheres

A discrete-layer model is presented and applied to layered anisotropic spheres with coupling among the elastic, electric, magnetic, and temperature fields under static conditions. The governing differential equations that represent these interactions are solved using a combination of one-dimensional finite element approximations in the radial direction with analytic functions over the polar and azimuthal coordinates of the sphere. This allows for an excellent representation of the type of variability in behavior across an interface between two dissimilar materials while keeping computational cost relatively low. Results from this model are in excellent agreement with existing analytic solutions, and the methodology is applied to several new problems with practical applications.