Finite Element Modeling of Thermopiezomagnetic Smart Structures

thermal elds are presented with the aid of a thermodynamic potential. A thermopiezomagnetic medium can be formed by bonding together a piezoelectric and magnetostrictive composite. Two energy functionals are de ned. It is shown via Hamilton’s principle that these functionals yield the equations of motion for the mechanical eld, Maxwell’s equilibrium equations for the electrical and magnetic elds, and the generalized heat equation for the thermal eld. Finite element equations for the thermopiezomagnetic media are obtained by using the linear constitutive equations in Hamilton’s principle together with the nite element approximations.The nite element equations are utilized on an example two-layer smart structure, which consists of a piezoceramic (barium titanate) layer at the bottom and a magnetoceramic (cobalt ferrite) layer at the top. An electrostatic eld applied to the piezoceramic layer causes strain in the structure. This strain then produces magnetic eld in the magnetoceramic layer. Nomenclature A = vector of magnetic potential B = vector of magnetic ux density b = matrix of electromagnetic coef cients c = matrix of elastic stiffness coef cients