A Novel Derivative Free Methodology for Topology Optimization Based on Projective Transformations and Boolean Operations

Most existing methods for topology optimization (TO) update the material distribution iteratively based on the derivative information. However, the calculation of gradient is of low accuracy and is even unavailable in some cases. Therefore, it is demanding to develop a derivative methodology for the TO. Two typical types of derivative-free methodologies for the TO, the evolutionary methods and the normalized Gaussian network-based methods (NGnet), still suffer from issues such as checkerboard pattern and heavy dependence on the initial topology. To this end, this article proposes a novel derivative-free methodology for the TO based on projective transformations and Boolean operations (PTBOs). Specifically, the proposed method selects the basic structures to constitute a new topology. PTBOs are employed to represent the evolvement and the way of combinations of the basic structures. According to the comparison of numerical results with other methodologies, the proposed methodology is capable of effectively and efficiently enhancing the parameter performance without a checkerboard pattern.