基于改进离散-连续参数化的结构和连续材料方向协同拓扑优化方法

Improved discrete-continuous parameterization method for concurrent topology optimization of structures and continuous material orientations

结构和材料方向的并行拓扑优化是过去几十年来的一个热门话题.然而,如何避免此类问题掉入局部最优相当具有挑战性。为了解决这个问题,我们在以前的工作中提出了一种将离散材料优化方法和连续纤维取向优化方法相结合的方法,称之为离散-连续参数化(DCP),该方法同时继承了离散方法的全局搜索能力和连续方法的全设计空间然而,DCP方法需要太多设计变量,导致了巨大的计算负担.因此,我们在本工作中提出了一种改进的DCP方法,以减少设计变量的数量,同时又不牺牲优化问题的凸性。在该方法中,我们提出了一种扩展的多材料插值方法,该方法能够大大减少设计变量的数量。然后,我们将所提出的插值方法集成到DCP方法中,最终建立了结构拓扑和纤维取向协同优化的改进DCP方法.几个基准优化实例表明,该方法可以在能大大降低陷入局部最优的风险的同时,使用更少的设计变量.

Concurrent topology optimization of structures and material orientations is a hot topic over the past decades.However,how to avoid the local optima of such problems is quite challenging.To handle this issue,a method combining the discrete material optimization method and continuous fiber orientation optimization method is proposed in our previous work,referred to as discrete-continuous parameterization(DCP),which takes advantage of the global search capability of discrete methods and the full design space of continuous methods.However,the DCP method requires too many design variables,resulting in a huge computational burden.Hence,we provide an improved DCP method to reduce the number of design variables and at the same time without sacrificing the convexity of the optimization problem in this work.In the proposed method,an extended multimaterial interpolation is firstly developed,which is capable of reducing the number of design variables greatly.Then,we integrate the proposed interpolation into the DCP method,generating an improved DCP method for the concurrent optimization of structural topology and fiber orientation.Several benchmark optimization examples show that the proposed method can greatly reduce the risk of falling into local optima with much fewer design variables.