An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner-Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.Keywords Piezoelectric smart plate, Shear and peel stresses, Debonding detection
IntroductionOur recent research (Luo and Tong 2002a, b) has indicated that peel stress plays an important role in a smart beam with the surface bonded piezoelectric (PZT) patches. It is particularly true for the flexible host beam, debonding analysis of PZT patches and dynamic responses. This work is to present the finite element analysis (FEA) formulation for PZT smart plates including peel stress.Analytical solutions to smart structures are either limited or too complicated for practical applications, and hence FEA formulation is presented in this paper. Tzou and Tseng (1990) proposed a PZT solid element with internal degrees of freedom (DOF). It is well known that a 3D FEA for smart plates can be computational expensive and may even introduce an ill-conditioned problem, and thus a classical laminate theory (Chandrashekhara and Agarwal 1993; Hwang and Park 1993), layer-wise theory (Saravanos et al. 1997), higher order theory (Seeley and Chattopadhyay 1999;Gu et al. 2000) and mixed model (Mitchell and Reddy 1995;Chee et al. 1999) are widely used in FEA for PZT smart plates. Reddy (1999) presented the theoretical and FEA formulations of laminated plates with PZT layers using classical and shear deformation laminated plate theory, which included the first-order shear deformation theory (FSDT) and the third order theory. 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 e...