结构拓扑优化变密度法的灰度单元等效转换方法

Equivalent Conversion Method of Gray-Scale Elements for SIMP in Structures Topology Optimization

在连续体结构优化的经典变密度法中,随着优化模型的复杂化,优化结果中容易出现灰度单元过多的问题.为了在优化后得到一个不存在灰度单元、可直接提取的清晰优化构型,提出了一种基于变密度法的灰度单元等效转换方法.该方法通过2个核心算法步骤来彻底消除灰度单元.首先通过转换规则控制算法将拓扑优化计算结果中的单元密度(密度),将单元密度变量从连续的[0,1]分布转换为{0,1}离散分布,得到全局"满状态"单元构型,彻底消除原优化构型中的灰度单元;其次通过转换等效性评估算法,确保在使用该转换方法前后结构的力学性能具有高度的等效性.将等效转换方法与标准SIMP优化算法相结合,便能在结构优化计算结果中得到可直接提取的清晰优化构型.通过二维与三维优化数值算例,将等效转换方法结合到SIMP优化算法中,并与标准的SIMP优化算法对比.结果表明,结合等效转换方法的SIMP优化算法能彻底消除灰度单元,并且不影响标准SIMP优化算法提升结构力学性能,具有降低体积与重量的作用.

Gray-scale elements grow in number in case of topology optimization for complicated continuumstructures.In order to obtain a distinct topological configuration,an equivalent conversion method based onSIMP(solid isotropic microstructures with penalization)is proposed to eliminate all gray-scale elements.The method applies two basic algorithms.Firstly,the conversion-controlling algorithm converts the continuousdistribution([0,1])of material into a discrete one({0,1})without any gray-scale element.Secondly,another algorithm called conversion-equivalence evaluation algorithm can achieve a strong equivalence,therefore the difference between the continuous distribution and the discrete distribution can be ignored.Inthis paper,the equivalent-conversion method is combined with the standard SIMP approach so that a distincttopological configuration can be directly drawn from the calculated result of structural optimization.Themethod is further investigated and realized with numerical examples in both2D and3D models to show itscorrectness and effectiveness.The results show that the mechanics properties of the structures can be kept oreven improved and the gray-scale elements disappear.