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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.

In light of recent advancements in synchrotron radiation technology and nano-technology, there has been a marked increase in the need for ultra-precision nano-positioning mechanisms. This paper presents a method that integrates physical models with multi-objective optimization for developing an optical angle nano-positioning mechanism. We begin by examining the actual motion law of the mechanism, based on kinematic principles. The outcomes from this kinematic analysis facilitate a static analysis of the flexible hinge, identified as a critical component of the mechanism. Subsequently, we establish a dynamic model for the entire mechanism. By employing the physical model as a base and combining it with the optimization algorithm, we identify the optimal design parameters for the mechanism. The design achieves a resolution of 50 nrad and meets the specified requirements. The first-order inherent frequency of the mechanism is approximately 43.75 Hz. There is a discrepancy of 2.63% from the finite element modal analysis results and a 3.33% difference from the theoretical analysis results, validating the reliability of the design method proposed in this study.