Proposal of a modified optimality criteria method for topology optimization analysis in 3-dimensional dynamic oscillation problems

Topology optimization based on the density method commonly employs the optimality criteria (OC) method. However, this method needs certain arbitrary parameters to be set, and the results will depend on those parameters. We propose a modified OC method that does not require those parameters. Our proposed method was developed based on the concept of Newton's method. The optimization problem is to minimize the strain energy. In this article, we perform topology optimization analysis for the 2-dimensional static problem, the 3-dimensional static problem, and the 3-dimensional dynamic oscillation problem. Topology optimization for the 2-dimensional static problem is used to confirm the usefulness and reliability of the proposed method, and finally topology optimization for the 3-dimensional dynamic oscillation problem is performed. In the dynamic oscillation problem, in order to derive the self-adjoint, the strain energy is regarded as the work, and is formulated separately for when it takes positive and negative values. The results of topology optimization for the 2-dimensional static problem demonstrate that our proposed method does not depend on the setting of arbitrary parameters. In conclusion, this article shows that in the three problems, our proposed method can quickly produce clearer results than the conventional OC method.

Automated summary

This article introduces a topology optimization method based on the density approach, and proposes a modified optimality criteria method that does not require arbitrary parameter settings. The method's reliability and utility were verified through topology optimization for 2D static and 3D static problems, and further applied to a 3D dynamic oscillation problem with clear and quick results.