图  1  典型拓扑优化^{[ 6- 7]}

Figure  1.  Typical topology optimization^{[ 6- 7]}

图  2  基于拓扑优化的3D打印多层级结构骨骼（a）^{[ 5]}和摩托车（b）

Figure  2.  3D printed multi-scale bones (a)^{[ 5]} and motorcycle (b) based on the topology optimization

图  3  航天组件拓扑优化前后对比^{[ 12]}：（a）优化前；（b）优化后

Figure  3.  Aerospace components before and after the topology optimization ^{[ 12]}: (a) before optimization; (b) after optimization

图  4  Altair Inspire软件优化模型^{[ 13]}

Figure  4.  Optimization model of Altair Inspire software^{[ 13]}

图  5  原节点与拓扑节点对比^{[ 14]}：（a）原节点；（b）拓扑优化后节点；（c）优化后内部细节

Figure  5.  Original and topology joint^{[ 14]}: (a) original joint; (b) topology joint after optimization; (c) inner details of topology joint after optiniztion

图  6  3D模型拓扑优化结果打印输出样件^{[ 15]}：（a）吊球；（b）佛像；（c）兔子

Figure  6.  3D printing samples by topology optimization^{[ 15]}: (a) hanging ball; (b) Buddha head; (c) bunny

图  7  微结构构型拓扑形状优化（泊松比为−0.8～0.8）^{[ 17]}：（a）拓扑优化设计的单元格；（b）3D打印的单元格；（c）3×3单远格组成的构造化材料

Figure  7.  Optimized architectures by topology and shape with Poisson ratio of −0.8~0.8^{[ 17]}: (a) designed unit cells by topology optimization; (b) 3D printed unit cells; (c) 3×3 unit cells of the corresponding architectures

图  8  航空器支架拓扑优化过程^{[ 18]}

Figure  8.  Topology optimization process of aerospace bracket^{[ 18]}

图  9  四轴飞行器臂原始设计（a）、优化后的晶格结构（b）与拓扑优化结果（c）^{[ 19]}

Figure  9.  Original design (a) optimized lattice structures (b), and topology optimization result (c) of the quadcopter arm^{[ 19]}

图  10  1％应变下拓扑优化结构（a）与菱形十二面体结构（b）中的应力分布^{[ 22]}

Figure  10.  Stress distribution in topologically optimized structure (a) and rhombic dodecahedron structure (b) at 1% strain^{[ 22]}

图  11  具有拓扑优化结构的多孔CP–Ti透射电子显微形貌^{[ 22]}：（a）透射电镜明场图像；（b）孪晶薄片的明场图像；（c）相应孪晶区域的电子衍射图；（d）孪晶界面的原子尺度图像

Figure  11.  Transmission electron microscopy images of the porous CP–Ti with the topology-optimized structure^{[ 22]}: (a) bright-field image; (b) bright-field image of the twinned flakes; (c) electron diffraction pattern of the corresponding twinned region; (d) atomic-scale image of the twinned interface