An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

Abstract

An accurate coupled field piezoelectric beam finite element formulation is presented. The formulation is based on First-order Shear Deformation Theory (FSDT) with layerwise electric potential. An appropriate through-thickness electric potential distribution is derived using electrostatic equilibrium equations, unlike conventional FSDT based formulations which use assumed independent layerwise linear potential distribution. The derived quadratic potential consists of a coupled term which takes care of induced potential and the associated change in stiffness, without bringing in any additional electrical degrees of freedom. It is shown that the effects of induced potential are significant when piezoelectric material dominates the structure configuration. The accurate results as predicted by a refined 2D simulation are achieved with only single layer modeling of piezolayer by present formulation. It is shown that the conventional formulations require sublayers in modeling, to reproduce the results of similar accuracy. Sublayers add additional degrees of freedom in the conventional formulations and hence increase computational cost. The accuracy of the present formulation has been verified by comparing results obtained from numerical simulation of test problems with those obtained by conventional formulations with sublayers and ANSYS 2D simulations.

A beam element for piezoelectric planar frames under small strains but large rotations using the total Lagrangian description

“…where � = +1 − is the voltage (difference of electric potential) in the piezoelectric layer . Marinković et al (2007) and Sulbhewar and Raveendranath (2014) show that an electric potential consistent with a first-order shear deformation theory, as the one based on the Timoshenko assumption, should have an additional quadratic term in related to the curvature. Marinković et al (2007;2009) also show that the use of (13) is sufficiently accurate for typically thin piezoelectric layers.…”

“…The coefficients � 11 , ̃3 1 and ̃3 depend on the type of special assumption made. Following Butz et al (2008), Khdeir et al (2012), Elshafei et al (2014) and Sulbhewar and Raveendranath (2014) Substitution of (9), 14and 19into 17gives…”

A Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations

“…However, assumed higher-order potential distribution in the formulation introduces additional nodal electrical degrees of freedom in the transverse direction and hence increases the computational cost. An alternate efficient way to include the higher-order induced potential in FSDT-based formulation is to use the consistent through-thickness potential distribution derived from the electrostatic equilibrium equation (Sulbhewar and Raveendranath, 2014b).…”

Improved finite element modeling of piezoelectric beam with edge debonded actuator for actuation authority and vibration behaviour

“…In this expression, the quadratic term represents the induced potential, which is dependent on the beam curvature. The modified expression (Sulbhewar and Raveendranath 2014) for through-thickness distribution of potential in the top extension actuator, which is modeled employing Timoshenko's beam theory, is where, u a ð Þ x ð Þ ¼…”