基于水平集方法的均布式柔性机构的拓扑优化设计  

Topology optimization of distributed compliant mechanisms base on level set method

作　　者：罗俊召[1] 王书亭[1] 陈立平[1] 

机构地区：[1]华中科技大学国家CAD支撑软件工程技术研究中心,武汉430074

出　　处：《计算力学学报》2009年第6期804-810,共7页Chinese Journal of Computational Mechanics

基　　金：国家'高档数控机床与基础制造装备'科技重大专项(2009ZX040001-015);国家'863'高技术研究发展计划(2006AA04Z162);国家自然科学基金(50975107)资助项目

摘　　要：提出一种利用水平集方法进行均布式柔性机构设计的新方法。根据水平集边界表达方法中具有几何信息的特点,将图像分析中的二次能量函数引入到水平集模型中,以控制柔性机构拓扑优化设计结果的几何尺寸,得到等宽带状均布的柔性机构,较好地解决了传统柔性机构拓扑优化中容易出现单点铰链问题。应用半隐式的加性分裂算子(AOS)算法求解水平集方程,松弛了逆风格式中CFL(Courant-Frie drichs-Lewy)条件对时间步长的限制,提高了求解效率。通过一个典型的二维算例来验证方法的有效性。A new method for designing the distributed compliant mechanisms is presented based on level set method. The quadratic energy function used in image analysis is introduced into the level set model to control the minimal geometrical dimension of the compliant mechansim optimized results and gain a strip-like even-distributed compliant mechanisms, which solves well the problems of one-node-connected hinges that exit in the conventional topology optimization of compliant mechanism. A semi-implicit additive operator splitting （AOS） scheme is adopted to solve the level set equation. In this method the time step decided by the CFL condition in the Up-wind scheme is clearly relaxed and it improves the efficiency of the optimization arithmetic. A typical two dimensional example is applied to demonstrate the validity of the presented method.

关 键 词：水平集方法 柔性机构 拓扑优化 二次能量函数 加性算子分裂算法 逆风格式 

分 类 号：O342[理学—固体力学]