Topology optimization of 3D shell structures with porous infill 
期刊名称Acta Mechanica Sinica
作者Anders Clausen; Erik Andreassen; Ole Sigmund
摘要This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same conditions. The study indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology optimization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells significantly improves the performance of porous structures due to the sandwich effect. Furthermore, the paper introduces improved filter boundary conditions to ensure a completely uniform coating thickness at the design domain boundary.
关键词Topology optimization; Coating; Shell structure; Two-step filtering
参考文献1. Clausen, A., Aage, N., Sigmund, O.:Topology optimization of coated structures and material interface problems. Comput. Methods Appl. Mech. Eng. 290, 524-541 (2015)  
2. Schaedler, T. A., Jacobsen, A. J., Torrents, A., et al.:Ultralight metallic microlattices. Science 334(6058), 962-965 (2011)  
3. Møller, P., Nielsen, L. P:Advanced Surface Technology, vols. 1-2. Møller and Nielsen (2013). ISBN 9788792765239
4. Clausen, A., Aage, N., Sigmund, O.:Exploiting additive manufacturing infill in topology optimization for improved buckling load. Engineering 2(2), 250-257 (2016)  
5. Vermaak, N., Michailidis, G., Parry, G., et al.:Material interface effects on the topology optimization of multi-phase structures using a level set method. Struct. Multidiscip. Optim., 1-22 (2014) (online)
6. Donoso, A., Sigmund, O.:Topology optimization of piezo modal transducers with null-polarity phases. Struct. Multidiscip. Optim. 53(2), 193-203 (2016)  
7. Aage, N., Andreassen, E., Lazarov, B. S.:Topology optimization using PETSc:an easy-to-use, fully parallel, open source topology optimization framework. Struct. Multidiscip. Optim. 51(3), 565-572 (2015)  
8. Hashin, Z., Shtrikman, S.:A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127-140 (1963)  
9. Torquato, S., Gibiansky, L. V., Silva, M. J., et al.:Effective mechanical and transport properties of cellular solids. Int. J. Mech. Sci. 40(1), 71-82 (1998)  
10. Andreassen, E., Lazarov, B. S., Sigmund, O.:Design of manufacturable 3D extremal elastic microstructure. Mech. Mater. 69(1), 1-10 (2014)  
11. Clausen, A., Andreassen, E.:On filter boundary conditions in topology optimization. Struct. Multidiscip. Optim. (2017). doi:10. 1007/s00158-017-1709-1
12. Sigmund, O.:Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33(4-5), 401-424 (2007)
13. Lazarov, B. S., Sigmund, O.:Filters in topology optimization based on Helmholtz-type differential equations. Int. J. Numer. Methods Eng. 86(6), 765-781 (2011)  
14. Guest, J. K., Prevost, J. H., Belytschko, T.:Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 61(2), 238-254 (2004)  
15. Xu, S., Cai, Y., Cheng, G.:Volume preserving nonlinear density filter based on heaviside functions. Struct. Multidiscip. Optim. 41(4), 495-505 (2010)  
16. Wang, F., Lazarov, B. S., Sigmund, O.:On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 43(6), 767-784 (2011)  
17. Zhou, M., Lazarov, B. S., Wang, F., et al.:Minimum length scale in topology optimization by geometric constraints. Comput. Methods Appl. Mech. Eng. 293, 266-282 (2015)  
18. Svanberg, K.:Method of moving asymptotes-a new method for structural optimization. Int. J. Numer. Methods Eng. 24(2), 359-373 (1987)  
19. Sigmund, O., Aage, N., Andreassen, E.:On the (non-)optimality of Michell structures. Struct. Multidiscip. Optim. 54(2), 361-373 (2016)  
基金项目The authors acknowledge financial support from the Villum Foundation (the NextTop Project) and DTU Mechanical Engineering.
作者地址Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, 2800 Lyngby, Denmark

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