Coupled high-order shear layerwise analysis of adaptive sandwich piezoelectric composite beams

A high-order discrete layer theoretical framework and a finite element are presented for predicting the electrostatic response of multifunctional beams with piezoelectric layers. A new layerwise coupled piezoelectric laminate theory is developed, in which quadratic and cubic fields are added to the in-plane displacement and electric potential approximation in each discrete layer. Interlaminar shear stress continuity is imposed through the thickness. Stiffness, piezoelectric, and permittivity matrices are formulated from ply to structural level. A finite element method and a beam element are further developed and used to predict the electrostatic response of piezocomposite beams. Numerical results and comparisons with linear layerwise beam finite element predictions illustrate the accuracy and capability of the developed mechanics to capture the local electric and shear stress response of smart piezoelectric composite beams efficiently and accurately, including beams of high thickness, beams with sandwiched foam cores, and/or beams with compliant shear layers.