A four-node MITC finite element for magneto-electro-elastic multilayered plates

• A four-node MITC finite element for layered magneto-electro-elastic plates is developed.
• It is based on a magneto-electro-elastic equivalent single-layer model.
• The element is validated.
• The element is reliable, accurate and effective for thin to moderately thick plates.
• The element is well-suited for use in general purpose finite element computer programs.

An isoparametric four-node finite element for multilayered magneto-electro-elastic plates analysis is presented. It is based on an equivalent single-layer model, which assumes the first order shear deformation theory and quasi-static behavior for the electric and magnetic fields. First, the electro-magnetic state of the plate is determined in terms of the mechanical primary variables, namely the generalized displacements, by solving the strong form of the magneto-electric governing equations coupled with the electro-magnetic interface continuity conditions and the external boundary conditions. In turn, this result is used into the layers constitutive law to infer the equivalent single-layer laminate constitutive relationships that express the plate mechanical stress resultants in terms of the generalized displacements taking the magneto-electro-elastic couplings into account. The weak form of the mechanical equilibrium equations is then written and used to determine the mechanical primary variables. Once these are determined the magneto-electric state can be recovered by simple post-processing. The finite element is formulated by using the mixed interpolation of tensorial components approach where the kinematical variables are usually written in terms of nodal values through shape functions, whereas the transverse shear strains are differently interpolated. These approximations are used in the weak form of the equilibrium equations to obtain the discrete stiffness and mass matrices together with the expression of the equivalent forces. The finite element is validated for static and free vibrations problems by comparison with available 3-D solutions. Its characteristics are ascertained in terms of convergence, accuracy and sensitivity with respect to plate thickness and element distortion. Performances of the method for the computation of through-the-thickness variables distributions are also investigated.