基于参数化无梯度方法的形状优化

A GRADIENT-LESS PARAMETER APPROACH FOR SHAPE OPTIMIZATION

采用参数化无梯度方法,针对机械结构在外力作用下,局部出现应力集中现象,进行了形状优化。被优化的边界采用样条曲线代替,通过调整样条曲线控制点的坐标改变边界的形状,进而调整边界上的应力分布。边界上的平均应力被选作参考应力,每一个迭代步中,边界上应力比参考应力大的控制点,其位置往外移动以增加材料;同时,比参考应力小的控制点,其位置减少材料。优化实例定义了两个可行域和三个初始形状,以比较可行域以及初始形状对优化结果的影响。同时还研究了控制数的大小对优化过程和结果的影响。

A gradient-less parametrical approach has been employed to optimize the stress concentration on local part. The design boundary was represented by splines and the shape of boundary can be varied by adjusting the coordinate of control points.By doing so to varying the stress distribution on design boundary. The average stress on design boundary was selected as the reference stress. Control points with higher stress than average stress move outward to add material; meanwhile,control points with lower stress move inward to reduce material to fulfill the shape optimization. Two feasible zones and three start shapes have been employed in optimization instances to compare the influence of the different feasible zones and start shapes,respectively.The influence of the control parameters to the optimization process and result have also been studied.