Topology optimization method by continuous approximation of material distribution

We propose a new method for topology optimization, which is free from numerical instabilities such as checkerboard patterns and mesh-dependency, without introducing any additional constraint parameters. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, continuous distribution like checkerboard patterns disappears without any filtering schemes. We call this technique the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the "material field". Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against the numerical instabilities.