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
A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity numb...A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.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This research work is supported by the National Natural Science Foundation of China(Grant No.51975227).
文摘A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.
