关键词：知情构造理论；柔性机构;拓扑优化；材料属性描述

中图分类号：TB472

DOI：10.3969/j.issn.1004-132X.2025.04.025 开放科学（资源服务）标识码（OSID）：

Topology Optimization of Single Material Flexible Mechanisms Based on Informed Tectonics Theory

SU Ke^1∗ WANG Ying1LIANG Tengteng1 WEI Yili² ZHANG Nannan² 1.School of Art and Design，Qilu University of Technology（Shandong Academy of Sciences）， Jinan，250353 2.Weihai Guangtai Airport Equipment Co.，Ltd.，Weihai，Shandong，264200

Abstract： In the topology optimization proceses，the number of subdomains would increase，so that the material distribution would occur at the junctions between the outer diameter and the inner diameter，and the too little optimization spaces in the subdomain of topology design would affect the overall performance of the structures. Therefore，the topological optimization models of single material flexible mechanisms were proposed based on the ITT. Through the description of material properties and attribute parameter calculation，the models made the value of the design subdomain number on the basis of adapting to the material characteristics and distribution of materials，so as to ensure that the structures had enough optimization spaces. Aiming at the maximum geometric gain of the mechanisms，the topological optimization models of single material flexible mechanisms were established based on the element-free Galerkin（EFG）.In the topology optimization processes，the grid-fess Galerkin method was introduced to construct the EFG relative density field，and the EFG nodes in the design domain were used to construct the deformation function. Under the conditions that the material properties were effectively described in advance，the nodes might be flexibly arranged，so as to avoid the phenomenon of numerical instability，which might affect the performance optimization effectiveness. The typical analysis examples demonstrate the effectiveness of the proposed method.

Key words： informed tectonics theory（ITT）； flexible mechanism；; topology optimization; material property description

0 引言

柔性机构是指能够通过自身的可弯曲柔顺性来完成某一特定任务的结构，这种具有自身变形特性的现象在自然界中也能大量发现，如人的心脏、蜜蜂的翅膀、大象的鼻子，都是通过自身柔顺性来实现特定任务的“柔性机构”1]。研究人员的对比研究表明，相较于传统刚体机构，柔性机构具有无摩擦、无间隙、免装配、轻量化、降噪性、易于小型化等特点，已被应用在微电子装配、仿生机器人、生物医疗设备以及超精密定位等领域[2-3]

拓扑优化为柔性机构的主要设计方法之一，研究人员对柔性机构的拓扑优化设计进行了大量研究。LARSEN等[4]提出以几何增益与机械增益的最小误差在规定范围内为目标构建函数，对柔性机构设计的多输出问题进行了研究。朱本亮[5]提出的矫正构造方法和敏度过滤方法提高了水平集法的计算效率。甘为等[针对柔性机构的稳定性要求，研究了屈曲约束下无铰链多输入多输出柔性机构柔度最小化的拓扑优化问题。然而，上述方法均在拓扑优化过程中使用了网格法，这种方法的计算精度依赖网格的类型和质量，利用网格局部近似经常出现误差，在计算过程中易出现数值不稳定的现象，并且在分析结构变形等问题时需要反复地进行网格划分，影响计算效率[7]。

目前，无网格法已广泛应用于拓扑优化等领域，该方法通过用节点离散设计域来摆脱网格的束缚，得以确保相对密度场的高阶连续性，从而使相对密度场的平滑度有所提高，这种方法能够有效抑制如棋盘格、中间密度材料等数值计算不稳定的现象。……