基于等几何拓扑优化的柔性机构设计

Design of Compliant Mechanisms by Topology Optimization Based on Isogeometric Analysis

等几何分析能够将几何建模的基函数与结构数值分析的形函数统一,从而得到高精度的结构数值分析结果。面向柔性机构,提出了一种基于等几何拓扑优化的柔性机构设计方法:通过NURBS基函数和Shepard函数构造增强密度分布函数,该函数的高阶连续性可确保优化结构边界的光滑清晰;然后根据密度分布函数建立柔性机构的等几何拓扑优化模型;最后,将该方法应用于柔性机构设计。通过算例结果可知,等几何拓扑优化方法特有的计算原理可提高数值计算的精度和效率,能有效避免由网格依赖、棋盘格现象等产生的边界问题,确保了优化结构均具有较好的光滑性和连续性,验证了提出的方法能有效避免柔性机构的铰链现象。

Isogeometric analysis can unify the basis function of geometric modeling and the shape function of structural analysis to obtain high-precision structural analysis results.The design method for compliant mechanisms based on isogeometric topology optimization is proposed.The NURBS basis function and Shepard function construct the density distribution function,in which high-order continuity can ensure the smooth and clear boundary of the optimized structure.Then,according to the density distribution function,the geometric topology optimization model of the compliant mechanisms is established.Finally,the method is applied to the design of compliant mechanisms.The results of numerical examples show that the unique calculation principle of the isogeometric topology optimization method can improve the accuracy and efficiency of numerical calculation.It can also effectively avoid boundary problems caused by mesh dependency,checkerboard phenomenon,and ensure that the optimized structures have smoothness and continuity.Optimization results verify that the method can effectively avoid the hinge phenomenon of compliant mechanisms.