A refined layerwise finite element modeling of delaminated composite laminates with piezoelectric layers

A finite element model for static response and free vibration analysis of delaminated composite laminates with active layers is developed based on a coupled layerwise laminate theory. The proposed model assumes full layerwise variations for both mechanical displacements and the electric field, and more importantly, both strong and weak discontinuous functions are introduced into the displacement fields to model the displacement discontinuity induced by the delamination and strain discontinuity induced by the interface between the layers, respectively. This refined layerwise mechanics can give a more accurate description of displacement discontinuity. The formulation naturally includes the coupling and interactions between the composite laminates and piezoelectric layers. Various examples are investigated by the developed model and the results are compared with previously obtained alternative solutions or experimental results to verify the justification and accuracy of the present formulation. Finally, the effect of delamination on static response and vibration mode are studied in detail to provide beneficial information for the promising damage identification techniques.