A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates

Abstract

Composite micro plates with periodic microstructure at very small length scale have been a focus of intensive research. When length scale of the microstructure descends below millimetre level, size effects may emerge. To account for microstructure effect on the elastic wave band gap of microscopic composite plates, we propose a numerical framework based on the modified couple stress theory of elasto-dynamics associated with a non-classical 3-node triangular (T3) Mindlin plate finite element. Since couple stress elasto-dynamics incorporates dependence on the material scale length, the proposed approach is sensitive to size effects with microscopic problems while remaining compatible with macroscopic problems. In terms of the finite element implementation, we implemented a T3 plate finite element with 9 nodal degrees of freedom under the Mindlin kinematics assumptions. The approach presents enhanced flexibility to discretize complex microstructures owing to the triangular element topology, and offers sensitivity to account for size effects of microscopic problems. Therefore, it represents a good option for the design of band gap periodic composite micro plates. Validation of the framework is performed through comparison with both analytical and numerical models.