Closed-form effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates

Abstract

This study derives closed-form expressions for the effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates. The derivation utilizes the homogenization method based on equivalent strain energy and the Kirchhoff plate theory. Rigorous accuracy assessments of the closed forms are conducted through comparisons with the existing literature and direct finite element analysis. A detailed parametric study is also conducted using the obtained closed forms to provide insights into the relationships between the effective elastic properties and the unit-cell shape. Lastly, general forms for some effective properties applicable to out-of-plane and in-plane situations are presented for hexagonal lattices.

Keywords:

• Lattice plate
• hexagonal unit cell
• homogenization
• effective elastic property
• closed form
• metamaterial

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors would like to extend their gratitude and acknowledge Chiang Mai University, which has partially financially supported this study through the Research Center Scheme (RG20/2566).