Topology Optimization with Explicit Components Considering Stress Constraints

Abstract

Topology optimization focuses on the conceptual design of structures, characterized by a large optimization space and a significant impact on structural performance, and has been widely applied in industrial fields such as aviation and aerospace. However, most topology optimization methods prioritize structural stiffness and often overlook stress levels, which are critical factors in engineering design. In recent years, explicit topology optimization methods have been extensively developed due to their ability to produce clear boundaries and their compatibility with CAD/CAE systems. Nevertheless, research on incorporating stress constraints within the explicit topology optimization framework remains scarce. This paper is dedicated to investigating stress constraints within the explicit topology optimization framework. Due to the clear boundaries and absence of intermediate density elements in the explicit topology optimization framework, this approach avoids the challenge of stress calculation for intermediate density elements encountered in the traditional density method. This provides a natural advantage in solving topology optimization problems considering stress constraints, resulting in more accurate stress calculations. Compared with existing approaches, this paper proposes a novel component topology description function that enhances the deformability of components, improving the representation of geometric boundaries. The lower-bound Kreisselmeier–Steinhauser aggregation function is employed to manage the stress constraint, reducing the solution scale and computational burden. The effectiveness of the proposed method is demonstrated through two classic examples of topology optimization.

Keywords

• topology optimization
• stress concentration
• explicit components
• stress aggregation function
• method of moving asymptotes