Bandgap Analysis of Periodic Composite Microplates with Curvature-Based Flexoelectricity: A Finite Element Approach

Abstract

A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect. In this model, we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis. The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions. It is based on a non-conforming interpolation scheme which provides nodal C1 continuity and ensures compatibility with curvature-based flexoelectricity. The approach accounts for microstructure effects and, owing to the triangular element topology, can be used to assist the design of microplates with complex microstructures. Validation of the approach is performed through comparison with both analytical and numerical models, in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.