基于水平集带方法的柔顺机构拓扑优化研究

Research on Topology Optimization of Compliant Mechanisms Based on Level Set Band Method

水平集方法在拓扑优化问题中采用隐式函数的零水平集描述结构边界,由于可以方便的表达结构拓扑变化并使结构边界保持清晰和光滑的特性,水平集方法很快成为拓扑优化领域的重要方法之一。但是由于水平集方法在优化过程中存在拓扑变化的不连续性,容易出现数值不稳定、初始设计依赖性等问题。近年来水平集带方法的提出可以有效改善这一现象,成为提升水平集方法拓扑表达能力的重要手段。本文将水平集带引入到参数化水平集拓扑优化方法中,并对其在柔顺机构优化设计问题中的应用开展研究。水平集带方法在水平集函数的零水平集附近引入水平集带区域,采用水平集函数插值可以得到带宽范围内[0,1]区间连续分布的材料密度,并在优化过程中通过逐渐减小水平集带的宽度使带宽范围内的材料密度逐渐收敛至0-1分布。该方法结合了变密度法的优势,使优化过程中材料密度变化保持连续,可以提升参数化水平集方法的稳定性,得到更优的目标函数值,并有效改善水平集方法的初始设计依赖性问题。本文通过多个柔顺机构的拓扑优化算例从不同初始设计、不规则设计域及几何非线性等多方面分析和验证了该方法的有效性,计算结果表明该方法对面向实际工程的复杂设计问题具有较好的适用性。

The level set method uses a zero level set of the implicit level set function to describe the structure boundary in topology optimization problems.Since it can conveniently express structural topological changes and keep the structure boundary clear and smooth,the level set method has quickly become one of the important methods in the field of topology optimization.However,due to the discontinuity of topological changes during the optimization process,the level set method is prone to facing problems such as numerical instability and initial design dependence.In recent years,the level set band method has been proposed to effectively improve this phenomenon and has become an important means to improve the topological expression ability of the level set methods.This paper introduced the level set band into the parameterized level set-based topology optimization methods,and studied its application in compliant mechanism optimization design problems.The level set band method introduces a level set band area near the zero level set of the level set function.The level set function interpolation can be used to obtain the material density continuously distributed in the[0,1]interval within the bandwidth range.During the optimization process,the material density within the bandwidth range can gradually converge to a 0-1 distribution by gradually reducing the of the level set bandwidth.This method combines the advantages of the variable density method to maintain continuous material density changes during the optimization process,which can improve the stability of the parameterized level set method,obtain better objective function values,and effectively evaluate the initial design dependence of the level set method.This paper verified the effectiveness of the proposed method by studying various compliant mechanism optimization examples from the aspects of different initial designs,irregular design domain,geometric nonlinearity,etc.The optimization results show that the proposed method has good applicability for complex design problems in practical engineering.