Layerwise mechanics and finite element model for laminated piezoelectric shells

A discrete-layer shell theory and associated finite element model is constructed for general laminated piezoelectric composite shells. The discrete-layer shell theory is based on linear piezoelectricity and accounts for general through-thickness variations of displacement and electrostatic potential by implementing one-dimensional piece-wise continuous Lagrange interpolation approximations over a specified number of sublayers. The formulation applies to shells of general shape and lamination. Initially, the static and dynamic behavior of a simply supported flat plate is studied to compare with available exact solutions, with excellent agreement being obtained. Static loading and free vibration of a cylindrical ring are then considered to evaluate the element and to study the fundamental behavior of active/sensory piezoelectric shells.