Design of 2D-Lattice Plates by Weight Efficiency

Abstract

In this study, a method to design 2D-lattice plates, based on their weight efficiency, is proposed. The 2D-lattice plates considered in this study are made up of Euler-Bernoulli beams and can be modeled as homogeneous orthotropic Kirchhoff plates, derived by the strain-energy-based homogenization method. The weight efficiency of 2D-lattice plates is evaluated using relationships between their effective rigidities and area weight densities. The proposed design method is developed with these relationships. The closed-form effective rigidities of 2D-lattice plates, derived by the strain-energy-based homogenization method, are utilized as convenient design formulas for the proposed design method. A generic symbolic finite element program, written in MATLAB, is used to determine the closed-form solutions of effective properties that include the effective elastic constants, the effective rigidities, and the relationships between the effective rigidities and the area weight densities of 2D-lattice plates. Example design graphs, created by the obtained closed-form solutions, for 2D-lattice plates with different unit cells are presented and discussed. In addition, the usefulness of the obtained weight efficiency is also demonstrated via analysis of 2D-lattice plates with different unit-cell patterns.