Simulation of Thin Piezoelectric Structures Using Anisotropic Hierarchic Finite Elements

Thin piezoelectric structures are important parts of active-noise cancellation devices and smart structures. For these kind of applications it is crucial to get an accurate prediction of the frequency characteristics using the Finite Element Method (FEM). Instead of using plate elements, we concentrate on a pure three dimensional approach using hierarchic ansatz spaces for hexahedral elements with the option of anisotropic choice of approximation order. The use of higher order Legendre polynomials reduces the susceptibility to locking, while the anisotropic choice of approximation order allows to minimize the number of degrees of freedom for the mechanical displacement and electric potential. The applicability of the method is proven by a pure mechanical example of a plate under uniform pressure, as well as for a piezoelectric bimorph beam.