Concurrent topological design of composite structures and the underlying multi-phase materials. (15th January 2017) - Da, D.C.; Cui, X.Y.; Long, K.; Li, G.Y.
Highlights: A new topology optimization algorithm of multiscale structure is proposed based on BESO. Optimization is carried out for composite structures and the underlying multi-phase materials simultaneously. Homogenization is used to evaluate the effective constitutive behavior of three or more phase materials. The develop algorithm shows high stability and requires a small number of iterations for convergence. The generated interfaces between different base materials are clear and distinctive. Abstract: This paper presents a concurrent topology optimization approach for simultaneous design of composite structures and their periodic material microstructures with three or more phases. The effective properties of multi-phase materials are obtained via homogenization technique which serves as a bridge of the finite element models of the macrostructure and the material microstructure. The base materials of periodic microstructures used in each phase of the macrostructure are divided into several groups and sensitivity analysis are carried out on them one by one. Meanwhile, the sensitivity number at the macrostructure is derived which is coupled with the designed material properties. Then, the composite configurations of material microstructures and macrostructures are inversely optimized concurrently based on the bi-directional evolutionary structural optimization (BESO) algorithm. Several 2D and 3D numerical examples are presented to demonstrate the effectiveness of proposed design approach.