循环对称结构的多尺度拓扑优化方法

Multi-scale topology optimization method for cyclic symmetric structures

研究了循环对称结构多尺度拓扑优化问题,阐明了均匀化等效性能的基本性质,提出了循环对称单胞的特征参数概念,建立了均匀化映射计算方法,构造了等效性能的三元参数插值模型,有效简化了不同特征参数、微结构构型与体分比下的单胞均匀化等效过程。通过微结构的特征驱动建模与B样条参数化,克服了微结构拓扑优化变量多和变量离散难以保证其光滑连接的问题。给出了典型数值算例,比较了等比例排列单胞与等间距排列单胞对结构优化结果的影响,验证了多尺度优化方法的有效性。

Multiscale topology optimization of cyclic symmetry structures is studied in this paper.Basic characteristics are revealed for the homogenized properties of cyclic-symmetry unit cells.The concept of feature parameters is proposed correspondingly to characterize the unit cells.A three-parameter interpolation model is developed for the homogenized properties so that the homogenization process is greatly simplified.By means of feature-driven microstructure modelling and B-spline parameterization,the number of design variables is reduced and the non-smoothness due to discretization is overcome.Numerical examples are solved to show the effectiveness of the developed method.Results demonstrate the influences of equidistant arrangement and equal proportion arrangement of unit cells on the optimization results.