Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Abstract

Mechanical properties of hierarchical lattice structures depend not only on their overall shapes and topologies, but also on their microstructural configurations. This paper proposes a new method for concurrent topology optimization of structures composed of layer-wise graded lattice microstructures. Both macroscale design variables representing the distribution of different lattice materials and microscale design variables defining the topologies of the microstructural unit cells are to be simultaneously optimized. This formulation thus integrates the microstructure design into the structural design, instead of pursuing a grey macroscale design and then interpreting the intermediate densities into certain microstructures. The proposed method also enlarges the design space by allowing for graded microstructures. Two new design constraints, namely the structural coverage constraint and the average porosity constraint, are introduced into the proposed optimization formulation to reduce the complexity of the constraints in the layer-wise graded design. The macroscale and microscale designs are linked by using the Asymptotic homogenization method to compute the effective elastic properties of the microstructured materials. Numerical examples show validity of the proposed method. It is also found that layer-wise graded lattice structures outperform those with uniform lattice microstructures in terms of structural stiffness. Finite element simulations of constructed models of the optimized designs suggest that graded lattice structures exhibit higher buckling resistance and ultimate load bearing capacity than single-scale solid material structures or uniform lattice structures under the same material usage.