MITC FINITE ELEMENTS FOR MAGNETO-ELECTRO-ELASTIC PLATES BASED ON EQUIVALENT SINGLE-LAYER THEORY

Abstract

Finite elements for magneto-electro-elastic laminated plates are formulated. They are 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. To infer the plate model, the electro-magnetic state is firstly determined and condensed to the the mechanical primary variables, namely the generalized displacements. In turn, this result is used into the layers constitutive law to obtain the equivalent single-layer laminate constitutive relationship that expresses 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 formulate the finite element matrices. Numerical results obtained by implementing an isoparametric four-node MITC finite element are presented to show the features and potentiality of the approach.