Topology Optimization using Lattice Materials with Isotropy Condition

Abstract

Lattice materials have a lot of advantages such as lightness, stiffness, vibration damping, and heat insulation. Nowadays the use of lattice materials has begun to become widespread in many different areas since the designs which are generated by lattice materials can be manufactured with additive manufacturing technologies. When the design is performed by lattice materials proper densities of lattice cells in a part are determined by doing density mapping with homogenization-based topology optimization. However, the mechanical behaviors of most of the lattice materials which change by direction as with composite materials are not isotropic. For the Solid Isotropic Material with Penalization (SIMP) method, which is used commonly in topology optimization for density mapping in commercial software due to its simplicity, some problems appear in the use of lattice materials, since homogenized properties, which are not isotropic, generate different stress and displacement in different direction. The method of isotropy conditioned density mapping (ICDM) is proposed to solve the problem within the scope of this thesis. Lattice cells, which are modeled by strut elements that ensure isotropy condition of homogenized elastic properties at whole density values, are determined with this proposed model. Since these lattice cells ensure isotropy conditions, the SIMP method can be used in topology optimization. The density range, which can be used in topology optimization, is determined to be produced with additive manufacturing. To show the effectiveness of the proposed method, three-dimensional examples used in the literature have been designed. The results of the optimized design which is generated by the proposed ICDM model are compared with the results in the literature to demonstrate its effectiveness. It was shown that macroscopic distributions of lattice cells can be obtainable with topology optimization with the SIMP method available in commercial software when the lattice configurations, which ensure isotropy condition, are determined with this proposed method.