An accurate higher-order modelling of extension mode smart beams with consistent through-thickness electric potential distribution

The present work is devoted to accurate higher-order shear deformation theory (HSDT)-based coupled field finite-element modelling of piezoelectric extension mode beam. Unlike conventional formulations available in the literature, an accurate through-thickness electric potential distribution consistent with HSDT has been derived from electrostatic equilibrium equations. The derived coupled quartic polynomial field accounts for the induced potential and hence the associated change in stiffness, without introducing any additional electrical degrees of freedom. The parametric studies carried out show the importance of considering induced potential. Conventional independent linear potential formulations available in the literature require a number of sublayers in mathematical modelling of the physical piezoelectric layer to achieve the accurate results, while the present formulation which uses coupled consistent potential efficiently reproduces accurate results, with single-layer modelling of the physical piezoelectric layer. The numerical accuracy and efficiency of the present formulation has been demonstrated by comparing the results obtained for test problems with those obtained by conventional formulations and ANSYS 2D finite-element simulation.