Static and Dynamic Analysis of Thick Functionally Graded Plates with Piezoelectric Layers Using Layerwise Finite Element Model

In this paper, static and dynamic analysis of a functionally graded material (FGM) plate with surface-bonded piezoelectric layers is studied. A general finite element formulation based on the layerwise theory is developed for modelling an FG plate with piezoelectric layers or patches. The intermediate FG layer is assumed to be made of many sublayers. Each sublayer is considered as an isotropic layer with constant material properties calculated by the rule of mixtures at the bottom of sublayer. The developed FE model is used for analyzing the quasi-static, free vibration and response of plate to impulse loads. The effects of span-to-thickness ratio and the volume fractions of constituents on the natural frequencies, transverse and in-plane deflections, stress distribution and induced electric potential in piezoelectric layers are scrutinized and the results are compared with the previously reported analytical and numerical works in the literature, where available. It is shown that by using the proposed three-dimensional based finite element model, static and dynamic analysis of thin to thick FG plates with bonded piezoelectric layers can be performed with sufficient accuracy. Also, the non-linear distribution of electric potential in thick piezoelectric layers, which is ignored by most previous works, can be captured using the proposed model.