FEM formulation for size-dependent theory with application to micro coated piezoelectric and piezomagnetic fiber-composites

The finite element method (FEM) is developed to analyze general two-dimensional boundary value problems in size-dependent magnetoelectroelastic solids. The size-effect phenomena in micro/nano electronic structures are described by the strain gradient effect. The electric and magnetic field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions by virtue of the variational principle. The FEM formulation is subsequently developed and implemented for strain-gradient magnetoelectroelasticity and a couple of numerical examples are presented to illustrate the strain gradient effect on the fields.