论文标题
在拓扑优化中施加最小和最大成员大小,最小腔大小以及固体成员之间的最小分离距离
Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization
论文作者
论文摘要
本文重点介绍了基于密度的拓扑优化,并提出了一种合并的方法,以同时在固相(Minsolid)(Minsolid),空隙相(MinVoid)(MinVoid)和最大长度尺度(MaxSolid)中同时施加最小长度尺度。 Minsolid和MinVoid意味着固体零件和空腔的大小必须大于规定的圆或球的大小。通过基于侵蚀,中间和扩张的设计的强大设计方法来确保这一点。 Maxsolid试图限制大于规定尺寸的固体零件的形成,这是通过局部体积限制施加的。在本文的第一部分中,我们表明,通过按比例限制侵蚀,中间和扩张设计的最大尺寸,可以获得同时,Minsolid,Minvoid和Maxsolid的优化设计。然而,尽管获得了具有清晰边界的设计,但由于存在多个圆形腔,因此很难制造一些结果,这是由最大尺寸限制引入的,其唯一目的是避免结构中厚实的固体成员。为了解决这个问题,在本文的第二部分中,我们提出了一个新的几何约束,该约束旨在控制两个固体成员之间的最小分离距离,也称为最小间隙(mingap)。 Mingap与MinVoid不同,Mingap引入了不一定必须圆形的大空白区域。 2D和3D测试用例表明,同时控制Minsolid,MinVoid,MaxSolid和Mingap对于提高最大尺寸约束设计的制造性很有用。
This paper focuses on density-based topology optimization and proposes a combined method to simultaneously impose Minimum length scale in the Solid phase (MinSolid), Minimum length scale in the Void phase (MinVoid) and Maximum length scale in the Solid phase (MaxSolid). MinSolid and MinVoid mean that the size of solid parts and cavities must be greater than the size of a prescribed circle or sphere. This is ensured through the robust design approach based on eroded, intermediate and dilated designs. MaxSolid seeks to restrict the formation of solid parts larger than a prescribed size, which is imposed through local volume restrictions. In the first part of this article, we show that by proportionally restricting the maximum size of the eroded, intermediate and dilated designs, it is possible to obtain optimized designs satisfying, simultaneously, MinSolid, MinVoid and MaxSolid. However, in spite of obtaining designs with crisp boundaries, some results can be difficult to manufacture due to the presence of multiple rounded cavities, which are introduced by the maximum size restriction with the sole purpose of avoiding thick solid members in the structure. To address this issue, in the second part of this article we propose a new geometric constraint that seeks to control the minimum separation distance between two solid members, also called the Minimum Gap (MinGap). Differently from MinVoid, MinGap introduces large void areas that do not necessarily have to be round. 2D and 3D test cases show that simultaneous control of MinSolid, MinVoid, MaxSolid and MinGap can be useful to improve the manufacturability of maximum size constrained designs.