Nonlinear static analysis of composite beams with piezoelectric actuator patches using the Refined Zigzag Theory

Piezoelectric actuators have been highly successful in a wide range of structural control applications. As such, there is an ongoing need for rapid and accurate structural analysis techniques, particularly for highly heterogeneous composite materials and accounting for the actuator as a patch. Here, a new model based on the Refined Zigzag Theory (RZT) formulation that includes geometric nonlinearities is proposed for buckling, postbuckling and nonlinear static response analyses of geometrically imperfect composite beams with piezoelectric actuators. Both the analytical and the finite element (FE) formulation are presented for symmetrically and non-symmetrically laminated beams. The FE approximation is further generalised to the case of beams with geometric discontinuities to model composite beams with piezoelectric actuator patches. The new RZT model is numerically verified through comparisons to Abaqus solutions for buckling and postbuckling analyses and for the geometrically nonlinear response to an applied voltage of geometrically imperfect composite beams with piezoelectric actuator patches. This work presents a new model for composite beams with piezoelectric actuators and confirms the remarkable advantages of RZT in terms of accuracy and computational efficiency also for challenging nonlinear analyses, where the RZT computational time is generally less than half the time required by the FE commercial code.