Energy-based homogenization method for lattice structures with generalized periodicity
Shijie Xu, Weihong Zhang
Abstract
This paper presents an energy-based homogenization method (EBHM) to calculate the equivalent elastic properties of lattice structures with generalized periodicity. Unlike the traditional implementation of the homogenization method, expressions of closed-form are derived for the equivalent elastic matrix, equivalent coefficients of thermal stress and thermal expansion in terms of the elastic strain energy of the unit cell so that the tedious numerical solution and programming are avoided. It is shown that the elastic strain energy can easily be calculated by mapping the unit cell with the imposition of specific periodic boundary conditions. The implementation can resort to any available finite element tools. Numerical examples are used to compare the EBHM with the homogenization mapping method, classical homogenization method and direct finite element analysis (FEA). The computational accuracy is investigated to show the effectiveness of the EBHM.