Exact solution for the cylindrical bending of laminated plates with embedded piezoelectric shear actuators

An exact three-dimensional state space solution is obtained for the static cylindrical bending of simply supported laminated plates with embedded shear mode piezoelectric actuators, and subjected to mechanical and electric loading on the upper and lower surfaces. Each layer of the laminate is made of either an orthotropic elastic material or a piezoelectric material whose poling direction lies in the plane of the plate, with perfect bonding between the adjoining layers. The displacements and stresses for a homogeneous piezoelectric plate for various length-to-thickness ratios are compared with those obtained by the first-order shear deformation theory. Results are also presented for a hybrid laminate with a shear mode piezoelectric core sandwiched between two elastic layers. A comparison of stresses with those in the corresponding surface-mounted extension actuation configuration shows that the longitudinal and shear stresses within the actuator are significantly smaller for the shear actuation mechanism. The analytical results can be used to assess the accuracy of different plate theories and/or validating finite element codes.