Large-deflection and stress analysis of multilayered plates with induced-strain actuators

Due to the growing interest in adaptive structures, recently a number of specific plate theories with various degrees of accuracy and complexity, depending on the object under investigation, have been developed. In fact, the modelling of the thicknesswise stress, strain and displacement distributions induced by the actuator activation is of increasing interest, together with the prediction of the effect of control on static and dynamic deflections. Hence, plate models including the layerwise kinematics are well suited to the purpose. In spite of the need for layerwise plate models for stress analyses of adaptive laminated beams, plates and shells, work to date has left layerwise kinematics out of consideration. Another topic that has received rather scant attention is the active control of large deflections of these structural elements. To fill the gaps, the present paper deals with a detailed investigation of the 3-D stress field of multilayered intelligent plates based on the von Kàrmàn strain - displacement relations. A third-order zigzag layerwise plate theory is developed for multilayered, intelligent, anisotropic plates with a surface-bonded piezoelectric actuator layer. The theory accounts for a piecewise cubic through-the-thickness variation of the in-plane displacements with discontinuous derivatives at the interfaces, in order to satisfy the transverse stress continuity conditions, and for a piecewise linear variation of the static electric scalar potential. Numerical results are presented for simply supported cross-ply plates with top and bottom actuators in cylindrical bending under distributed transverse loading. Comparisons with available elasticity solutions and other approximate analyses are made. For all of the cases examined it is found that the active control of deflections is effective, the effectiveness increasing for decreasing length-to-thickness ratios. The pre-existing stress field is considerably modified by the activation: cases are found where a tensile exists that can lead to delamination. The large deflections reduce and increase at the midplane, whereas they reduce both and close to the upper surface.