A higher order zigzag theory for magnetoelectric composite beams

The third-order approximation is employed to analyze the magnetoelectric composite beams. The axial displacement, the electric and magnetic potentials are assumed as piecewise linear function along the thickness-direction of the beam. With the conditions of zero transverse shear stress at the top and bottom surfaces and the continuity conditions at the interfaces, the expressions of the displacement can be obtained explicitly. The transverse displacement accounts for the piezoelectric and piezomagnetic effect. The governing equations are derived by using the variational principle. The present theory provides an efficient way in analyzing the magnetoelectric beams.