A derivative-free level-set method for topology optimization

• A non-gradient topology optimization NGTO method is proposed.
• Limitations of NGTO, e.g., coarse FE mesh, poor topological details, are eliminated.
• Drawbacks of checkboard pattern and problem of connectivity constraint are avoided.
• The computational cost is significantly reduced.
• Less than 10% of FEA evaluations in [26], [27] and [32] can achieve better results.

Topology optimization of continuum structures is a promising field that plays an important role in the design process. Although the gradient optimization methods are highly developed and succeeded in solving different problems, they are limited to problems with convex, continuous objective functions where the gradient information is known. In this paper, we propose a derivative-free level-set method using pattern search and topology description function, i.e., level-set function. The proposed approach starts with a single uniform material distribution pattern and ends by the optimized layout, without a need for prior knowledge about the objective function. In order to demonstrate the effectiveness of our approach, we tested it by solving eight benchmark problems of compliance minimization with variations in load cases, boundary conditions and topological details. The results indicate the ability of the proposed method to overcome the drawbacks of non-gradient topology optimization methods that appeared in the literature. These drawbacks include coarse finite elements (FE) meshing, checkboard pattern, inferior solutions and poor attainable topological details. In addition, the computational cost is significantly reduced.