Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements

Abstract

In the recent development of active structural systems and microelectromechanical systems, piezoelectrics are widely used as sensors and actuators. Because of the limitations of theoretical and experimental models in design applications, finite element development and analysis are proposed and presented in this paper. A new laminated quadratic C° piezoelastic triangular shell finite element is developed using the layerwise constant shear angle theory. Element and system equations are also derived. The developed piezoelastic triangular shell element is used to model 1) a piezoelectric bimorph pointer and 2) a semicircular ring shell. Finite element (triangular shell finite element) solutions are compared closely with the theoretical, experimental, and finite element (thin solid finite element) results in the bimorph pointer case. Natural frequencies and distributed control effects of the ring shell with piezoelectric actuators of various length are also studied. Finite element analyses suggested that the inherent piezoelectric effect has little effect on natural frequencies of the ring shell. Vibration control effect increases as the actuator length increases, and it starts leveling off at the seven-patch (70%) actuator. Coupling and control spillover of lower natural modes are also observed.

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

“…The semicircular ring shell is a popular example for the dynamic analysis of piezoelectric curved structures and may be found in [19,17,15]. In the geometrically linear case the presented element verifies well known results form the literature.…”

“…However, it seems to have only a minor influence to this example. In contrast to [19,17,15] the present element is not restricted to geometrically linear examples. To produce large deflections the actuator (the outer PZT layer) is loaded by an electric potential ϕ(t) = 450 cos(2 πf 1 t) at the outside, where f 1 is the lowest eigenfrequency.…”

“…The sensor sense a strain and provides an electric output signal, which may be used as an input signal for the actuator to control the structural behavior. Here, a negative velocity proportional feedback is used in the analysis, see also [19], [17], [15]. The global Eq.…”

Numerically Efficient Finite Element Formulation for Modeling Active Composite Laminates

“…The 4-node element is based on the Mindlin-Reissner kinematics, has a plane form and takes the full piezoelectric coupling into account. Tzou and Ye [6] have developed a triangular solid-shell element with biquadratic shape functions for the in-plane mechanical degrees of freedom and linear shape functions for both mechanical and electrical degrees of freedom in the thickness direction. Gabbert et al [7] have extended a Semi-Loof shell element to an electromechanical coupled element for modeling active composite laminates.…”

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

“…Tzou and Tseng (1991) proposed a non-conforming hexahedron piezoelectric finite element by adding internal degrees of freedom to the original eight node hexahedron solid element (Tzou and Tseng, 1988), to give improved performance in thin structural analysis. Tzou and Ye (1996) developed a new laminated quadratic C 0 piezoelastic triangular shell finite element using layerwise constant shear angle theory. 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.…”