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Compliant mechanisms, which achieve input-output functions through continuous elastic deformation, offer inherent advantages such as frictionless motion, absence of backlash, and suitability for microscale fabrication. These features render them highly promising for advanced engineering applications. However, traditional topology optimization approaches, typically relying on fixed solid material distributions, often produce localized geometric hinges at theoretically optimal configurations, thereby limiting manufacturability and compromising operational reliability. To overcome these challenges, this paper presents a novel particle-flow topology optimization (PFTO) framework grounded in a Lagrangian-Eulerian hybrid formulation. By explicitly incorporating particle mobility and interactions, the proposed method enhances the adaptability of compliant mechanisms to complex loading and deformation scenarios encountered in practical engineering. The approach introduces two key innovations: (1) the application of a smoothed particle hydrodynamics (SPH) kernel function for weighted smoothing of particle properties, effectively suppressing numerical instabilities arising from irregular particle distributions and insufficient local interactions; (2) the facilitation of free particle migration and self-organization during iterative optimization, which eliminates conventional fixed-geometry hinges and enables the structure to naturally accommodate large deformations and dynamic loading conditions. Numerical examples involving both two- and three-dimensional compliant mechanisms demonstrate the superior performance and robustness of the PFTO method, underscoring the critical role of particle motion in avoiding undesirable hinge formation and improving structural functionality.
Zhu et al. (Thu,) studied this question.