Layerwise Analysis of Thermal Shape Control in Graded Piezoelectric Beams

A layerwise finite element formulation developed for piezoelectric materials is used to investigate the displacement and stress response of a functionally graded piezoelectric bimorph actuator. The formulation is based on the principles of linear thermopiezoelectricity and accounts for the coupled mechanical, electrical, and thermal response of piezoelectric materials. The layerwise laminate theory is implemented into a linear beam element in order to provide a more accurate representation of the transverse and shear effects that are induced by increased inhomogeneities introduced through-the-thickness by using functionally graded materials. The accuracy of the formulation is verified with previously published experimental results for a piezoelectric bimorph actuator. Additional studies are conducted to analyze the impact of electric and thermal loads on the deflections and stresses in a bimorph actuator. Results of the study help demonstrate the capability of the layerwise theory to provide a more complete representation of shear effects that are no longer negligible even in thin piezoelectric beams. In addition, the effects of varying piezoelectric properties through-the-thickness of the beam are shown to provide additional benefits in minimizing the induced deformations and stresses.