Keywords: simple piezoelectric materials, smart structures, piezoelectric sensors and actuators, nonlinear shell theory, finite element method, electromechanical coupling.

In this paper smart structures, in which piezoelectric sensors and actuators are attached onto the surface of a thin shell are considered. The tasks of structural health monitoring, damping of vibrations, etc. can be solved with an appropriate strategy for the optimal placement of electroded piezoelectric patches, processing of the signals and application of the actuation voltage by a controller. Developing such a strategy raises the need for a reliable simulation tool for the coupled electromechanical behavior of a thin shell.

Geometrically nonlinear effects, which are usually displayed in the form of a local buckling, are known to be important for curved thin shells even at relatively low overall deformations. Practically used piezoelectric materials, such as ceramics, can significantly affect the structural behavior due to their own high rigidity. Modeling of finite deformations of layered shell structures with additional electrical effects is the main goal of the present research.

In the framework of the direct approach to shells as material surfaces pure mechanical properties of the shell cross-section together with the piezoelectric coupling are described in terms of the enthalpy per unit area of the shell, which is a function of the voltage between the pair of electrodes in the cross-section and the in-plane and bending strain measures. The expression of the enthalpy can be deduced from the results of the asymptotic analysis of the corresponding linear three-dimensional problem.

Finite element modeling is based on a variational principle, which is formulated in terms of the total enthalpy of the shell. Four-node finite elements with nine mechanical degrees of freedom per node, which were used in the present study, provide the necessary smoothness of the approximation of the surface of the shell. The total enthalpy of the structure is a function of the mechanical degrees of freedom in the nodes and of the voltages at each pair of electrodes existing in the structure. In the case of an actuator, the voltage is prescribed, and the electromechanical coupling is reduced to the equivalent mechanical loading in the structure. In the case of a sensor, when the electric circuit between the electrodes remains open, the voltage values appear as an additional non-mechanical variable.

According to the variational principle, finding a static equilibrium at given mechanical and electrical loadings requires an iterative search of a stationary point of the functional. For a sample problem, results of successful comparison with a reference three-dimensional solution, as well as with an analytical solution are presented in the paper.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)