基于小波三次样条插值的柔顺机构拓扑图提取

针对拓扑优化结果中普遍存在的棋盘格现象,采用小波变换与三次样条插值相结合的方法,对柔顺机构的拓扑图提取进行了研究.首先将拓扑优化解非线性变换到中间变量,以保证算法处理结果满足拓扑变量的约束条件;然后通过小波变换,将中间变量分解为近似系数和细节系数,并利用三次样条插值对近似系数进行处理;接着,将处理后的近似系数进行小波重构,再对重构结果进行非线性逆变换,得到相应的拓扑图;最后,基于拓扑优化的体积约束,评价算法处理结果及确定小波分解尺度.实验结果表明,该算法能有效消除拓扑优化结果中的棋盘格,提取出所希望的柔顺机构拓扑图.

Topology Extraction of Compliant Mechanism Based on Wavelet and Cubic Spline Interpolation

In order to remove the checkerboard patterns in an optimized topology solution,wavelet transform and cubic spline interpolation are combined to perform the topology extraction of a compliant mechanism.In the extraction,first,the optimized topology solution is mapped into intermediate variables via nonlinear transformation to ensure the side constraints imposed on the direct topology variables. Then,the intermediate variables are decomposed into approximated and detail coefficients via wavelet transform,and the approximated coefficients are further treated via cubic spline interpolation.After that,the approximated coefficients are reconstructed by wavelet and the corresponding topology result is obtained by the anti-nonlinear transformation of the reconstructed coefficients.Finally,based on the volume restriction of topology optimization,the obtained result is evaluated and the wavelet decomposition scale is determined.Experimental results show that the proposed algorithm can effectively remove the checkerboard patterns in an optimized topology solution and extract the expected topology of a compliant mechanism.