Static fields in magnetoelectroelastic laminates

The through-thickness elastic, electric, and magnetic fields of laminates composed of elastic, piezoelectric, and magnetostrictive layers are considered under static conditions to determine their fundamental behavior and to investigate the limits of simplified plate theories in which the fields are assumed to possess a specific type of behavior. The weak form of the equations of motion/equilibrium, Gauss's law and Gauss's law for magnetism, are formulated for a rectangular laminate with arbitrary edge boundary conditions under the application of applied surface displacement/traction, electric potential/electric flux, or magnetic potential/magnetic flux. The layers within the laminate are allowed to possess any linear constitutive law consistent with a magnetoelectroelastic solid, and the number of layers is arbitrary. The Ritz method is used in combination with a discrete-layer theory, and approximate solutions for the displacements, electric potential, and magnetic potential are sought to the weak form of the governing equations. The use of linear combinations of through-thickness approximations, along with separate approximations for the in-plane behavior, allows an accurate representation of the break in variable slope across an interface with dissimilar material properties. The model is applied to problems with either known exact solutions or a finite element approximation to the governing equations. Excellent agreement is obtained for all cases.