Fig. 1. Continuum structure topology optimization about cantilever beam. (a) Variable density method using HyperWorks; (b) evolutionary structural optimization method^[19]; (c) level set method^[20]; (d) moving morphable component method^[21]; (e) feature-driven method^[22]

Fig. 2. Numerical instability and improvement of topology optimization method based on elements

Fig. 3. Initial dependence and inability to open holes of level set method^[44]. (a) 2 initial holes; (b) 9 initial holes; (c) 40 initial holes

Fig. 4. MBB beam level set topology optimization.(a) Topological gradient^[45]; (b) PS-Kriging interpolation^[55]

Fig. 5. Metal additive manufacturing technologies. (a)-(e) Schematics^[75]; (f)-(j) products^[73,76-78]

Fig. 6. Additive manufacturing printing failure^[102]. (a) Assembly hole material collapse; (b) fracture of support structure; (c) internal support cannot be removed

Fig. 7. Topology optimization design for metal additive manufacturing

Fig. 8. Topology optimization considering minimum size constraint. (a) Nodal design variable and projection functions^[105]; (b) robust formulation^[106]; (c) spatial gradient operators^[108]; (d) skeleton extraction and minimum feature optimization^[12]

Fig. 9. MBB beam self-supporting optimization. (a) Overhang projection constraint^[127]; (b) optimizing overhang angle and printing direction^[21]; (c) polygon-featured holes^[22]; (d) nonlinear virtual temperature method^[128]

Fig. 10. Topology optimization considering connectivity constraints. (a) Virtual temperature method^[102]; (b) shortest connection tunnels^[131]; (c) side constraint^[132]; (d) stress minimization^[133]

Fig. 11. Topology optimization considering material anisotropy. (a) Strength anisotropy^[14]; (b) quantified additive manufacturing process parameters^[138]