A Simple C~0 Continuous Higher Order Hellinger-Reissner Type Element for the Analysis of Magneto-Electro-Elastic Plates featuring Continuous Interlaminar Stresses

摘要

A simple mixed variational formulation for the higher order zig-zag shear deformable coupled magneto-electro-elastic plates with a continuous interlaminar shear-stress is presented in this paper. Starting from a generalized kinematics (i.e., mechanical displacement, electric and magnetic potentials) defined for a generic layer, the simplified laminate kinematics are derived by introducing an average shearing strain like fields along with the usage of continuity condition of transverse shearing stresses. This simplified zig-zag type generalized kinematics involves five mechanical displacement like fields and layerwise higher order electric and magnetic potential fields. A Hellinger-Reissner type functional is constructed using the variationally defined generalized constitutive relation and that is later employed as the foundation of finite element formulation. These developed finite elements are consisting of eight mechanical fields per node including three displacements, two shear-strains and three moment-resultants and the layerwise cubically varying electric and magnetic potential fields. The developed elements pass the inf-sup test and are less sensitive to the mesh distortion. The advantage of the developed model is its applicability to both thin and thick smart sandwich/laminated plates. The accuracy of the present elements are illustrated through numerical examples