Size-dependent bending behavior of three-layered doubly curved shells: Modified couple stress formulation

In this paper, modified couple stress formulation of a small scale doubly curved piezoelectric shell resting on Pasternak's foundation is presented based on first-order shear deformation theory. Size-dependent electro-elastic results of doubly curved shell are presented based on an analytical approach. The doubly curved piezoelectric shell is subjected to uniform transverse loads and applied voltage. To account the size dependency, modified couple stress theory is employed in conjunction with principle of virtual work. The numerical results are presented in both tabular and graphical forms to show the influence of small scale parameter, applied voltage, geometries and two parameters of Pasternak's foundation on the electro-elastic results of size-dependent doubly curved piezoelectric shell.

Voltage-Induced Snap-Through of an Asymmetrically Laminated, Piezoelectric, Thin-Film Diaphragm Micro-Actuator—Part 2: Numerical and Analytical Results

In Part 2 of the two-paper series, the asymmetrically laminated piezoelectric shell subjected to distributed bias voltage as modeled in Part 1 is analytically and numerically investigated. Three out-of-plane degrees-of-freedom (DOFs) and a number of in-plane DOFs are retained to study the shell's snap-through phenomenon. A convergence study first confirms that the number of the in-plane DOFs retained affects not only the number of predicted equilibrium states when the bias voltage is absent but also the prediction of the critical bias voltage for snap-through to occur and the types of snap-through mechanisms. Equilibrium states can be symmetric or asymmetric, involving only a symmetric out-of-plane DOF, and additional asymmetric out-of-plane DOFs, respectively. For symmetric equilibrium states, the snap-through mechanism can evolve from the classical bidirectional snap-through and latching to a new type of snap-through that only allows snap-through in one direction (i.e., unidirectional snap-through), depending on the distribution of the bias voltage. For asymmetric equilibrium states, degeneration can occur to the asymmetric bifurcation points when the radii of curvature are equal. Finally, the unidirectional snap-through renders an explanation to the experimental findings in Part 1.

Energy Release Rate of Delaminated Piezoelectric Shell Subjected to Electro-Thermo-Mechanical Loadings

The delamination growth may occur in delaminated piezoelectric shell subjected to external load and it will further cause structural failure. Based on the variational principle of moving boundary and considering the contact effect between delamination regions, in this paper, the nonlinear governing equations for the delaminated piezoelectric shell under electro-thermo-mechanical loadings are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the energy release rate and delamination growth of axisymmetrical piezoelectric cylindrical shell are analyzed, and the effects of voltage, temperature and humidity, mechanical load, delamination length and depth on delamination growth are discussed.