Finite element modeling of warping in smart piezoelectric noncircular shaft

Abstract

Torsion often occurs in real engineering structures such as beams, shafts, and framed structures in conjunction with bending actions. This work mainly focuses on torsion of shafts with noncircular sections. Generally, torsion of beam with noncircular cross-section produces warping or nonuniform out-of-plane displacements in the cross-section. Warping introduces longitudinal strains as the section twists and significantly affects the torsional stiffness. The principal objective of this work is the development of a smart structure technique, which involves piezoelectric materials that necessarily involve coupled mechanical and electrical field, for the control of warping displacement of twisted noncircular shafts. In this work, expressions for warping displacement and shear stress at a section have been derived for the coupled load case. This work focuses on two interrelated cases in relation to the warping of the noncircular bar. Firstly, the warping of cross-section of host structure is analyzed. Secondly, the warping control of a smart shaft with selected noncircular cross-section is analyzed. The paper also describes a Finite Element procedure for the 2D and 3D analysis. In this paper, numerical results have been generated and plotted using MATLAB® for different cases like pure mechanical loading, pure electrical loading, and the coupled field loading with a view to quantify the stiffness characteristics of smart shaft. The finite element calculations are made with ANSYS® for the present analysis work.