Reissner-Mindlin Based Isogeometric Finite Element Formulation for Piezoelectric Active Laminated Shells

The paper deals with the isogeometric analysis (IGA) of active composite laminates with piezoelectric layers. IGA is a special formulation of the finite element method (FEM) that aims at seamless integration of geometric and finite element modelling. NURBS basis functions are employed to develop isogeometric shell formulation based on the Reissner-Mindlin kinematics. Piezolayers characterized by electro-mechanical coupled field effects enable active behavior of the considered structures. The electric field acts across the thickness of the piezolayers and is coupled to the in-plane strains. In addition to a number of advantages that NURBS modelling provides, defining the surface normal vector at the points of the control polygon, which are generally not located on the surface, creates certain difficulties. A method of determining the surface normal vectors at the points of the control polygon based on the Greville's points is discussed. In order to demonstrate the applicability of the developed formulation, a benchmark case is computed and the results are compared with those obtained by means of classical FEM formulation, which are available in the literature.