Piezoelectric induced bending and twisting of laminated composite shallow shells

Abstract

The piezoelectric induced bending and twisting deformation of laminated shallow shells has been presented in this report. A simple and efficient method has been developed for the static analysis of shallow shells under mechanical, thermal, and piezoelectric fields. The governing equations are based on the linear theory of piezoelectricity and the classical thin shallow shell assumptions. Approximate solutions have been obtained using the conventional Ritz analysis for different boundary conditions. Comparisons of degenerate cases with published analytical and experimental results show good agreement. Several cases have been reported here, investigating the effects of material stiffness coupling, shell shallowness, and actuator geometric parameters on the bending and twisting deformation of piezoelectric laminated structures. It is shown that the desired shape could be better controlled by a proper selection of the lay-up configuration and geometric characteristics of the structure such as the thickness, size, and location of the piezoelectric actuators.

Numerically Efficient Finite Element Formulation for Modeling Active Composite Laminates

“…This case is also proposed by Kioua and Mirza [28] and solved by already mentioned conventional Ritz analysis based on the shallow-shell theory, whereby variable radius of the shell was considered. The results obtained with the Shell9 and the Semi-Loof element for the cylindrical shell with R = 10 × b are compared in Table 3, which has the same structure as Table 2.…”

“…All the below given examples consider composite structures with two types of layers-the graphite/epoxy layer and the PZT layer. The properties of the layers are given in Table 1, which is in full (except for thermo-elastic properties) taken from the reference [28]. Not specified piezoelectric constants are considered to be equal to zero.…”

“…The voltage giving the shape that corresponds mostly to the initial undeformed shape is found. This example is originally proposed by Kioua and Mirza [28] whose approximate solution is obtained using the conventional Ritz analysis based on the shallow-shell theory.…”

“…The refinement of the mesh does not affect the mechanical stiffness matrix only, but also the piezoelectric stiffness matrix, and, in further instance, the mechanical loads originating from the piezoelectric coupling. Furthermore, the description of the piezoelectric coupling obtained by the shallow shell assumptions [28]. The indicator of bending deformation is taken similarly to the previous case, i.e., the ratio (w 2 /b) is observed, while the ratio (w 3 − w 1 )/b is taken as an indicator of twisting.…”

Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics

“…The structure analyzed in this numerical section is similar to those analyzed in the works of Kioua & Mirza [58], and Kpeky et al [59]. The present single-and multi-model solutions are compared with a calculated three-dimensional FEM ABAQUS solution.…”