Static and dynamic finite rotation FE-analysis of thin-walled structures with piezoelectric sensor and actuator patches or layers

This paper deals with static and dynamic analysis of thin-walled structures with integrated piezoelectric layers as sensors and actuators in the geometrically nonlinear range of deformations. A variational formulation is derived by using the Reissner-Mindlin first-order shear deformation (FOSD) hypothesis and full geometrically nonlinear strain-displacement relations accounting for finite rotations. The finite rotations are treated by Rodriguez parameterization. In order to enhance the accuracy of a four-node shell element, a combination of an assumed natural strain (ANS) method for the shear strains, an enhanced assumed strain (EAS) method for the membrane strains and an enhanced assumed gradient (EAG) method for the electric field are employed. The present shell element has five mechanical degrees of freedom (DOFs) and three electrical DOFs per node. The Newton-Raphson method for static analysis and the Newmark method for dynamic analysis are used to perform linear and nonlinear simulations. In comparison to the results obtained by simplified nonlinear models reported in the existing literature, the finite-element simulations performed in this paper show the importance of the present model, precisely for structures undergoing finite deformations and rotations.