A locking-free coupled polynomial Timoshenko piezoelectric beam finite element

Abstract

Purpose – Piezoelectric extension mode smart beams are vital part of modern control technology and their numerical analysis is an important step in the design process. Finite elements based on First-order Shear Deformation Theory (FSDT) are widely used for their structural analysis. The performance of the conventional FSDT-based two-noded piezoelectric beam formulations with assumed independent linear field interpolations is not impressive due to shear and material locking phenomena. The purpose of this paper is to develop an efficient locking-free FSDT piezoelectric beam element, while maintaining the same number of nodal degrees of freedom. Design/methodology/approach – The governing equations are derived using a variational formulation to establish coupled polynomial field representation for the field variables. Shape functions based on these coupled polynomials are employed here. The proposed formulation eliminates all locking effects by accommodating strain and material couplings into the field interpolation, in a variationally consistent manner. Findings – The present formulation shows improved convergence characteristics over the conventional formulations and proves to be the most efficient way to model extension mode piezoelectric smart beams, as demonstrated by the results obtained for numerical test problems. Originality/value – To the best of the authors’ knowledge, no such FSDT-based finite element with coupled polynomial shape function exists in the literature, which incorporates electromechanical coupling along with bending-extension and bending-shear couplings at the field interpolation level itself. The proposed formulation proves to be the fastest converging FSDT-based extension mode smart beam formulation.