针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优...针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优化过程不稳定的问题,本文提出一种Multiquadric(MQ)拟插值和BESO结合的参数化水平集方法。首先,借鉴传统BESO计算单元灵敏度;然后,利用MQ拟插值参数化水平集函数,隐式地确定平滑的结构拓扑;最后,采用二分法计算水平函数阈值,驱动体积分数值逐步达到目标值。数值实验结果表明:与传统BESO相比,该方法的优化结果有连续清晰边界;该方法不需要求解大规模线性方程组,计算效率高,稳定性强。所提方法继承了PLSM边界光滑和BESO计算效率高、稳定性强的优点,能够有效解决不同结构拓扑优化问题。展开更多
Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in detai...Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.展开更多
文摘针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优化过程不稳定的问题,本文提出一种Multiquadric(MQ)拟插值和BESO结合的参数化水平集方法。首先,借鉴传统BESO计算单元灵敏度;然后,利用MQ拟插值参数化水平集函数,隐式地确定平滑的结构拓扑;最后,采用二分法计算水平函数阈值,驱动体积分数值逐步达到目标值。数值实验结果表明:与传统BESO相比,该方法的优化结果有连续清晰边界;该方法不需要求解大规模线性方程组,计算效率高,稳定性强。所提方法继承了PLSM边界光滑和BESO计算效率高、稳定性强的优点,能够有效解决不同结构拓扑优化问题。
基金Supported by the National Natural Science Foundation of China( 1 9971 0 1 7,1 0 1 2 5 1 0 2 )
文摘Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.
