Topological shape optimization of 3D micro-structured materials using energy-based homogenization method. (February 2018) - Gao, Jie; Li, Hao; Gao, Liang; Xiao, Mi
Highlights: A reasonable classification of nodes in 3D material microstructures is developed to formulate boundary constraint equations. A new 3D periodic boundary formulation is developed to formulate an effective 3D energy-based homogenization method. An effective design method is proposed for 3D micro-structured materials to attain extreme mechanical properties. The optimized 3D micro-structured materials are featured with smooth boundaries and clear interfaces without the post-processing mechanism. Abstract: This paper proposes an effective method for the design of 3D micro-structured materials to attain extreme mechanical properties, which integrates the firstly developed 3D energy-based homogenization method (EBHM) with the parametric level set method (PLSM). In the 3D EBHM, a reasonable classification of nodes in periodic material microstructures is introduced to develop the 3D periodic boundary formulation consisting of 3D periodic boundary conditions, 3D boundary constraint equations and the reduced linearly elastic equilibrium equation. Then, the effective elasticity properties of material microstructures are evaluated by the average stress and strain theorems rather than the asymptotic theory. Meanwhile, the PLSM is applied to optimize microstructural shape and topology because of its positive characteristics, like the perfect demonstration of geometrical features and high optimization efficiency. Numerical examples are provided to demonstrate the advantages of the proposed design method. Results indicate that the optimized 3D material microstructures with expected effective properties are featured with smooth structural boundaries and clear interfaces.