Coupled consistent third-order theory for hybrid piezoelectric beams under thermal load

A new coupled consistent third-order theory is presented for thermal load on hybrid piezoelectric beams that satisfies exactly the shear traction-free conditions at the top and bottom of the beam for any electrical boundary conditions. The potential and thermal fields are discretized layer-wise as piecewise linear. The axial and transverse electric fields are considered. The deflection is approximated as uniform across the thickness and longitudinal displacement is approximated as a third-order variation. The equilibrium equations and the boundary conditions are derived from a variational principle. Analytical solutions are obtained for simply supported beams. The theory is assessed by comparison with the exact piezothermoelasticity solution and coupled first-order shear deformation theory solution for two thermal loads.