基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)的多材料柔性机构拓扑优化是将原问题分解成若干子问题进行分层优化,成倍地增加了设计变量数量,且该方法利用传统的有限元离散,为了得到清晰的拓扑结构...基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)的多材料柔性机构拓扑优化是将原问题分解成若干子问题进行分层优化,成倍地增加了设计变量数量,且该方法利用传统的有限元离散,为了得到清晰的拓扑结构网格数量必然巨大,这两方面的因素造成了该方法计算效率低下。因此,基于幂函数多项式提出序列插值模型,用该模型进行多材料布局迭代,使不同材料在设计域内序列向预定义的多个材料点聚集,无须分解成子问题即可在单一优化框架下完成多材料的拓扑优化,且没有增加设计变量数量。以机构的几何增益最大为目标,建立多材料柔性机构拓扑优化模型。在利用有限元求解控制方程过程中引入多重网格方法,网格划分粒度层次递进,将粗网格水平下位移场作为细网格上的初始场量,避免直接用细密网格将设计域整体离散带来的高计算成本问题,提升计算效率。通过改进的优化准则法求解模型,得到序列最优布局型式的多材料柔性机构。通过典型算例及与基于SIMP的方法相应结果对比,验证了提出方法的有效性。展开更多
Univariate Gonarov polynomials arose from the Goncarov interpolation problem in numerical analysis.They provide a natural basis of polynomials for working with u-parking functions,which are integer sequences whose ord...Univariate Gonarov polynomials arose from the Goncarov interpolation problem in numerical analysis.They provide a natural basis of polynomials for working with u-parking functions,which are integer sequences whose order statistics are bounded by a given sequence u.In this paper,we study multivariate Goncarov polynomials,which form a basis of solutions for multivariate Goncarov interpolation problem.We present algebraic and analytic properties of multivariate Gonarov polynomials and establish a combinatorial relation with integer sequences.Explicitly,we prove that multivariate Goncarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in Nk.It leads to a higher-dimensional generalization of parking functions,for which many enumerative results can be derived from the theory of multivariate Goncarov polynomials.展开更多
文摘基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)的多材料柔性机构拓扑优化是将原问题分解成若干子问题进行分层优化,成倍地增加了设计变量数量,且该方法利用传统的有限元离散,为了得到清晰的拓扑结构网格数量必然巨大,这两方面的因素造成了该方法计算效率低下。因此,基于幂函数多项式提出序列插值模型,用该模型进行多材料布局迭代,使不同材料在设计域内序列向预定义的多个材料点聚集,无须分解成子问题即可在单一优化框架下完成多材料的拓扑优化,且没有增加设计变量数量。以机构的几何增益最大为目标,建立多材料柔性机构拓扑优化模型。在利用有限元求解控制方程过程中引入多重网格方法,网格划分粒度层次递进,将粗网格水平下位移场作为细网格上的初始场量,避免直接用细密网格将设计域整体离散带来的高计算成本问题,提升计算效率。通过改进的优化准则法求解模型,得到序列最优布局型式的多材料柔性机构。通过典型算例及与基于SIMP的方法相应结果对比,验证了提出方法的有效性。
基金supported by the National Priority Research Program (Grant No. #[5101-1-025]) from the Qatar National Research Fund (a member of Qatar Foundation)
文摘Univariate Gonarov polynomials arose from the Goncarov interpolation problem in numerical analysis.They provide a natural basis of polynomials for working with u-parking functions,which are integer sequences whose order statistics are bounded by a given sequence u.In this paper,we study multivariate Goncarov polynomials,which form a basis of solutions for multivariate Goncarov interpolation problem.We present algebraic and analytic properties of multivariate Gonarov polynomials and establish a combinatorial relation with integer sequences.Explicitly,we prove that multivariate Goncarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in Nk.It leads to a higher-dimensional generalization of parking functions,for which many enumerative results can be derived from the theory of multivariate Goncarov polynomials.
