A finite element formulation for smart piezoelectric composite shells: Mathematical formulation, computational analysis and experimental evaluation

A formulation of a smart shell finite element for laminated curved structures with piezoelectric layers working under either the d31 or d33 effects has been developed in order to simulate dynamic tests. The electrical domain was modeled using a first order theory for the electrical field and a layer-wise approach. The mechanical domain is modeled using a degenerated shell theory with implicit curvature, considering a first order shear deformation theory and an equivalent single layer approach. The final formulation was implemented within Abaqus™ commercial finite element analysis package using its User Element (UEL) subroutine. First, some results provided by the proposed formulation were compared to numerical analyses shown by the literature. Second, the implemented finite element was evaluated using modal and frequency domain experiments for a cantilever aluminum beam with two piezoelectric transducers working under the d31 effects, and a free-free curved composite plate with four piezoelectric transducers working under the d33 effects. Comparisons between the natural frequencies and the frequency response functions amplitudes obtained from the experiments and the computational analyses were performed in order to discuss the limitations and potentialities of the proposed formulation.