New shear actuated smart structure beam finite element

We present the formulation and validation of a new adaptive sandwich-beam finite element, capable of dealing with either extension or shear actuation mechanisms, which is reached by coating an elastic core with piezoelectric sheets or sandwiching a piezoelectric core between two elastic faces. The poling direction is taken parallel to the transversely applied electric field for the first mechanism and in the axial direction for the second one. The sandwich construction is made of asymmetric thin faces (Euler-Bernoulli beams) and a relatively thick core (Timoshenko beam). The obtained two-node finite element has only four mechanical degrees of freedom that are the deflection and its derivative and the mean and relative axial displacements of the faces midplanes. Finite element analysis of segmented and continuous cantilever adaptive sandwich beams with active faces (extension actuated) or core (shear actuated) show good comparisons with results found in the literature. Additional parametric studies (actuator's position and thickness, structure's stiffness) with the present element indicate that the shear actuation mechanism presents several promising features over the conventional extension actuation mechanism. In fact, the shear actuation mechanism is better than the extension one for stiff structures and thick piezoelectric actuators.