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.
Highlights
Piezoelectric smart structures have a unique capability to control their behaviour, by virtue of electromechanical coupling present in them (Crawley and de Luis, 1987)
First-order Shear Deformation Theory (FSDT) based analytical closed form solutions given by Abramovich (1998), Sun and Huang (2000) and finite elements proposed by Shen (1995), Narayanan and Balamurugan (2003), Neto et al (2009), Rathi and Khan (2012) can be used for static and dynamic analyses of surface mounted extension mode smart beams
An extension mode piezoelectric beam structure is studied for different proportions of piezoelectric material in the total thickness of the beam, to capture the effect of geometry on the induced potential
Summary
Piezoelectric smart structures have a unique capability to control their behaviour, by virtue of electromechanical coupling present in them (Crawley and de Luis, 1987). Robbins and Reddy (1991) proposed two Equivalent Single Layer (ESL, Euler-Bernoulli and Timoshenko) and two Layerwise (one with constant while other with layerwise linear transverse deflection through the thickness) models for integrated smart beams, which considered strain induced by piezoelectric material as applied strain These models are without electrical degrees of freedom. First-order Shear Deformation Theory (FSDT) based analytical closed form solutions given by Abramovich (1998), Sun and Huang (2000) and finite elements proposed by Shen (1995), Narayanan and Balamurugan (2003), Neto et al (2009), Rathi and Khan (2012) can be used for static and dynamic analyses of surface mounted extension mode smart beams. An ESL-FSDT based piezoelectric extension mode beam finite element with layerwise coupled higher order through-thickness distribution of electric potential is presented. The efficiency and accuracy of the present formulation over the conventional formulations have been proved by the comparison of numerical results of test problems
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