Multi-layered plate finite element models with node-dependent kinematics for smart structures with piezoelectric components

Abstract This article presents a type of plate Finite Element (FE) models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches. The p-version shape functions are used in combination with the higher-order Layer-Wise (LW) kinematics adopting hierarchical Legendre polynomials. Node-Dependent Kinematics (NDK) is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer (ESL) approach. Through the proposed NDK FE models, the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency, and various patch configurations can be conveniently modeled through one set of mesh grids. Moreover, the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated.