Composite material design of two-dimensional structures using the homogenization design method (Q2712700)

The paper deals with a design of composite materials of two-dimensional structures using the homogenization method. The composite material is made of two or three different material phases. Designing the composite material consists of finding a distribution of material phases that minimizes the mean compliance of the microstructure subject to volume fraction constraints on the constituent phases within a unit cell of periodic microstructures. At the start of the computational solution, the material distribution of the microstructure is represented as a pure mixture of the constituent phases. As the iteration procedure unfolds, the component phases separate themselves out to form distinctive interfaces. The effective material properties of the artificially mixed materials are defined by the interpolation of constituents, and the corresponding optimization problem is solved using sequential linear programming method. Both the macrostructure and microstructures are analyzed using finite element method at each iteration step. The authors present several examples of optimal topology design of composite material to demonstrate the validity of the algorithm.