基于节点密度法的连续体结构拓扑优化结果提取

Topology Extraction in the Topological Optimization of Continuum Structure Based on Nodal Density

研究影响拓扑优化结果提取的各类因素及解决方法.基于节点变密度法建立连续体结构拓扑优化模型,连续密度场在结构拓扑数学描述上抑制了棋盘格现象.采用密度过滤技术进一步提高密度场的连续性和光滑性,从而消除了网格依赖性现象.密度-弹性模量惩罚措施及两步过滤策略减少了中间密度节点数目并消除图像扩散现象.拓扑优化密度云图输出方式得到光滑的轮廓边界.通过二维经典拓扑优化数值算例验证了方法的正确性.

To investigate the factors and methods to extract clear configuration in the topological optimization of continuum structure, a topological optimization model using nodal density as the design variable is established. Checkerboard patterns are naturally avoided based on the continuous density field. Combined with density filtering technique to improve the smoothness of density field, the mesh-dependence phenomenon is overcome. Solid isotropic microstructures with penalization （SIMP） density-stiffness interpolation and a modified two-step filtering scheme suggested not only to eliminate the image diffuse phenomena, but also to decrease the number of nodes composed of gray level images. Density contours are adopted to interpret the topological optimization result and continuous contour thus obtained. The validity of the proposed methods are substantiated by some typical two-dimensional examples.