Effective out-of-plane rigidities of 2D lattices with different unit cell topologies

Abstract

In this study, the effective out-of-plane rigidities of several 2D lattices, consisting of Euler beams, with different common unit cell topologies are investigated. The effective out-of-plane rigidities per weight density of these lattices, normalized by those of the full solid plates with the same material and thickness, are determined. The effective out-of-plane rigidities are computed by the homogenization method based on equivalent strain energy and the Kirchhoff plate theory. Particularly, the homogenization-related equations, including the equivalent strain energy equation itself, are not taken from their corresponding equations for 3D solids, but are derived directly using the Kirchhoff plate equations. Moreover, the exact forms, having some dimensionless factors, of the effective material constants for 2D-lattice plates are analytically derived. By using exact curve fitting, these exact forms, in most cases, yield the closed forms of the effective material constants. Finally, the efficiency of the considered unit cell topologies, in terms of the normalized effective rigidities per weight density of their resulting lattices, is discussed.