Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures

Fiber-reinforced composite laminates involving piezoelectric layers represent a very attractive material system. It combines the advantages of using rather lightweight and stiff material with the possibility of sensing structural changes and actively influencing its state by means of sensors and actuators. A three-node shell element is proposed as an efficient tool for modeling structures made of such a material system. Thoroughly tested solutions are implemented to resolve locking problems intrinsic for shell elements. The embedded piezoelectric layers are considered to be polarized in the thickness direction. Furthermore, the extension of the formulation to geometrically nonlinear finite element analysis is based on a co-rotational formulation. Numerical examples are given to demonstrate the applicability of developed element in linear and geometrically nonlinear finite element analyses covering both actuator and sensor cases.