Multi‐objective topology optimisation for microstructure of periodic composite material

Abstract

By using the homogenisation method and finite element method (FEM) jointly, a multi‐objective optimisation model for the microstructure of a periodic composite material was developed in which the objective was to maximise the weighted sum of the main diagonal elements of the equivalent elasticity modular matrix and to restrain the amount of material in the microstructure. An optimisation of material distribution in the microstructure was carried out. In the optimisation, the design objective and material distribution were controlled by the optimisation criteria method and the chequerboard influence was eliminated using the sensitivity filter method. Influences of volume fraction and finite element (FE) mesh sizes on the optimal microstructures are discussed. Numerical examples indicate that the present optimisation model and method are effective.

Keywords:

• Homogenisation method
• Topology optimisation
• Microstructure design
• Multiple objective function
• Composite material

The paper is supported by the Science and Technology Development Foundation of China Academy of Engineering Physics (No. 2008A0302011).