An accurate laminated element for piezoelectric smart beams including peel stress

Abstract

This paper presents a laminated element for piezoelectric (PZT) smart beams in taking into account peel stresses. In the finite element analysis (FEA) formulation, a coupled electrical and mechanical beam element is used to model PZT patches, and a conventional structural element is used to model a host beam. A continuous adhesive element with shear and peel stiffness is derived to form a PZT laminated element. For a smart beam with a partially bonded PZT patch or distributed PZTs, the laminated element is applied to an area of the host beam with PZTs and the conventional element is used in the host beam where no PZT is bonded. A novel PZT laminated element is firstly derived based on the Timoshenko beam theory, in which the FEA formulation based on the Euler-Bernoulli beam theory can be considered as its special case. FEA numerical results of static and dynamic analyses based on the Euler-Bernoulli beam theory are compared with the exact static and dynamic solutions to validate the present FEA formulation. The present FEA framework based on the Timoshenko beam theory is then used to investigate the effects of PZT debondings on static behaviors and dynamic responses, and an original and effective procedure for detecting debondings in PZT actuators or sensors is proposed. IntroductionIn the model developed by Crawley and de Luis (1987), the finite thickness adhesive was assumed to transfer shear stresses only. In our recent studies (Luo and Tong, 2002a, b), it has been shown that peel stresses in adhesive can significantly affect mechanical behaviors and dynamic responses of smart structures. This is especially true for flexible smart structures and in the presence of debondings. Analytical solutions to smart structures are either limited or too complicated for practical applications, and FEA has been widely used in smart structures as it can effectively deal with complex geometric shapes, loadings and boundary conditions. Allik and Hughes (1970) presented a finite element method for piezoelectric or electroelastic structures. They developed FEA formulations by applying the principle of virtual displacements to a continuum under the influence of electrical and mechanical forces. In smart structures, PZT patches are normally bonded to or embedded in a host structure to achieve active control function, and therefore, FEA implementation for smart structures should take into consideration both PZT patch elements and conventional structural elements.A full 3D FEA is an effective tool for solving smart structures. Tzou and Tseng (1990) proposed a thin PZT solid element with internal degrees of freedom (DOF). Kim et al. (1997) presented a finite element model for structures including piezoelectric active devices, in which, full 3D elements were used to model piezoelectric devices and conventional plate elements to model a host plate. Seshu and Naganathan (1997) used a full 2D nine-noded Lagrangian element to model PZT patches, adhesive layers and a host beam.However, it is well known that a full 3D FEA for smart plates ...

An adhesively laminated plate element for PZT smart plates

“…By following the same procedure as that of the FEA formulation for a smart beam (Luo and Tong 2004), dynamic equations of a smart plate in a global coordinate system can be obtained:…”

“…(19), fu i g e is the nodal displacement vector of an adhesively laminated PZT element, which is given by:…”

“…In this paper, an adhesively PZT laminated element will be formulated, which is an extension of the previous FEA for smart beams (Luo and Tong 2004). In this FEA formulation, the adhesive with the shear and peel stiffness is modeled so that the PZT debonding can be easily investigated.…”

“…Gopinathan et al (2000) presented a review of the different laminated FEA theories for PZT smart structures. It was shown that the many publications on PZT laminates were a natural extension of the FSDT.In this paper, an adhesively PZT laminated element will be formulated, which is an extension of the previous FEA for smart beams (Luo and Tong 2004). In this FEA formulation, the adhesive with the shear and peel stiffness is modeled so that the PZT debonding can be easily investigated.…”

Finite Beam Element With Piezoelectric Layers and Functionally Graded Material of Core

“…Electric field intensity in piezoelectric layer is constant and for top layer can by expressed as [4,5] …”