Optimal Design of Wire-and-Arc Additively Manufactured I-Beams for Prescribed Deflection

  • Matteo Bruggi Politecnico di Milano
  • Vittoria Laghi University of Bologna
  • Tomaso Trombetti University of Bologna

Abstract

Alloys fabricated by wire-and-arc additive manufacturing (WAAM) exhibit a peculiar anisotropy in their elastic response. As shown by recent numerical investigations concerning the optimal design of WAAM-produced structural components, the printing direction remarkably affects the stiffness of the optimal layouts, as well as their shape. So far, single-plate specimens have been investigated. In this contribution, the optimal design of WAAM-produced I-beams is addressed assuming that a web plate and two flat flanges are printed and subsequently welded to assemble the structural component. A formulation of displacement-constrained topology optimization is implemented to design minimum weight specimens resorting to a simplified two-dimensional model of the I-beam. Comparisons are provided addressing solutions achieved by performing topology optimization with (i) conventional isotropic stainless steel and with (ii) WAAM-produced orthotropic stainless steel at prescribed printing orientations. Lightweight solutions arise whose specific shape depends on the selected material and the adopted printing direction.

Keywords

structural optimization, topology optimization, wire-and-arc additive manufacturing, I-beams, orthotropic material, additive manufacturing, 3D printing,

References

1. M. Carpo, The digital turn in architecture 1992–2012, John Wiley and Sons, 2013, doi: 10.1002/9781118795811.
2. S. Adriaenssens, P. Block, D. Veenendaal, C. Williams, Shell structures for architecture: form finding and optimization, Routledge, 2014, doi: 10.4324/9781315849270.
3. T. Lewinski, T. Sokół, C. Graczykowski, Michell Structures, Springer 2018, doi: 10.1007/978-3-319-95180-5.
4. M. Bruggi, A constrained force density method for the funicular analysis and design of arches, domes and vaults, International Journal of Solids and Structures, 193–194: 251–269, 2020, doi: 10.1016/j.ijsolstr.2020.02.030.
5. C. Boje, A. Guerriero, S. Kubicki, Y. Rezgui, Towards a semantic Construction Digital Twin: Directions for future research, Automation in Construction, 114: 103179, 2020, doi: 10.1016/j.autcon.2020.103179.
6. W.E. Frazier, Metal additive manufacturing: A review, Journal of Materials Engineering and Performance, 23: 1917–1928, 2014, doi: 10.1007/s11665-014-0958-z.
7. B. Wu et al., A review of the wire arc additive manufacturing of metals: properties, defects and quality improvement, Journal of Manufacturing Processes, 35: 127–139, 2018, doi: 10.1016/j.jmapro.2018.08.001.
8. C. Buchanan, L. Gardner, Metal 3D printing in construction: A review of methods, research, applications, opportunities and challenges, Engineering Structures, 180: 332–348, 2019, doi: 10.1016/j.engstruct.2018.11.045.
9. M. Dinovitzer, X. Chen, J. Laliberte, X. Huang, H. Frei, Effect of wire and arc additive manufacturing (WAAM) process parameters on bead geometry and microstructure, Additive Manufacturing, 26: 138–146, 2019, doi: 10.1016/j.addma.2018.12.013.
10. L. Ji, J. Lu, C. Liu, C. Jing, H. Fan, S. Ma, Microstructure and mechanical properties of 304L steel fabricated by arc additive manufacturing, MATEC Web of Conferences, 2017, doi: 10.1051/matecconf/201712803006.
11. V. Laghi, M. Palermo, G. Gasparini, V.A. Girelli, T. Trombetti, Experimental results for structural design of Wire-and-Arc Additive Manufactured stainless steel members, Journal of Constructional Steel Research, 167: 105858, 2020, doi: 10.1016/j.jcsr.2019.105858.
12. V. Laghi, M. Palermo, L. Tonelli, G. Gasparini, L. Ceschini, T. Trombetti, Tensile properties and microstructural features of 304L austenitic stainless steel produced by wire-and-arc additive manufacturing, International Journal of Advanced Manufacturing Technology, 106(9–10): 3693–3705, 2020, doi: 10.1007/s00170-019-04868-8.
13. V. Laghi, M. Palermo, G. Gasparini, V.A. Girelli, T. Trombetti, On the influence of the geometrical irregularities in the mechanical response of wire-and-arc additively manufactured planar elements, Journal of Constructional Steel Research, 178: 106490, 2021, doi: 10.1016/j.jcsr.2020.106490.
14. P. Kyvelou et al., Mechanical and microstructural testing of wire and arc additively manufactured sheet material, Materials and Design, 192: 108675, 2020, doi: 10.1016/j.matdes.2020.108675.
15. V. Laghi et al., Experimentally-validated orthotropic elastic model for wire-and-arc additively manufactured stainless steel, Additive Manufacturing, 42: 101999, 2021, doi: 10.1016/j.addma.2021.101999.
16. N. Hadjipantelis, B. Weber, C. Buchanan, L. Gardner, Description of anisotropic material response of wire and arc additively manufactured thin-walled stainless steel elements, Thin-Walled Structures, 171: 108634, 2022, doi: 10.1016/j.tws.2021.108634.
17. W. Zhang, J. Zhu, T. Gao, Topology Optimization in Engineering Structure Design, Elsevier, 2016.
18. M.P. Bendsoe, O. Sigmund, Topology Optimization: Theory, Methods and Applications, Springer, 2003.
19. O. Sigmund, K. Maute, Topology optimization approaches: A comparative review, Structural and Multidisciplinary Optimization, 48(6): 1031–1055, 2013, doi: 10.1007/s00158-013-0978-6.
20. J. Liu et al., Current and future trends in topology optimization for additive manufacturing, Structural and Multidisciplinary Optimization, 57(6): 2457–2483, 2018, doi: 10.1007/s00158-018-1994-3.
21. L. Meng et al., From topology optimization design to additive manufacturing: Today’s success and tomorrow’s roadmap, Archives of Computational Methods in Engineering, 27(2020): 805–830, 2019, doi: 10.1007/s11831-019-09331-1.
22. G. Allaire, B. Bogosel, Optimizing supports for additive manufacturing, Structural and Multidisciplinary Optimization, 58(6): 2493–2515, 2018, doi: 10.1007/s00158-018-2125-x.
23. M. Bruggi, N. Parolini, F. Regazzoni, M. Verani, Topology optimization with a timeintegral cost functional, Finite Elements in Analysis and Design, 140: 11–22, 2018, doi: 10.1016/j.finel.2017.10.011.
24. G. Allaire, C. Dapogny, R. Estevez, A. Faure, G. Michailidis, Structural optimization under overhang constraints imposed by additive manufacturing technologies, Journal of Computational Physics, 351: 295–328, 2017, doi: 10.1016/j.jcp.2017.09.041.
25. O. Amir, Y. Mass, Topology optimization for staged construction, Structural and Multidisciplinary Optimization, 57(4): 1679–1694, 2018, doi: 10.1007/s00158-017-1837-7.
26. X. Guo, J. Zhou, W. Zhang, Z. Du, C. Liu, Y. Liu, Self-supporting structure design in additive manufacturing through explicit topology optimization, Computer Methods in Applied Mechanics and Engineering, 323: 27–63, 2017, doi: /10.1016/j.cma.2017.05.003.
27. M. Langelaar, Combined optimization of part topology, support structure layout and build orientation for additive manufacturing, Structural and Multidisciplinary Optimization, 57(5): 1985–2004, 2018, doi: 10.1007/s00158-017-1877-z.
28. W. Wang, D. Munro, C.C.L. Wang, F. van Keulen, J. Wu, Space-time topology optimization for additive manufacturing: Concurrent optimization of structural layout and fabrication sequence, Structural and Multidisciplinary Optimization, 61: 1–18, 2020, doi: 10.1007/s00158-019-02420-6.
29. M. Bruggi, V. Laghi, T. Trombetti, Simultaneous design of the topology and the build orientation of Wire-and-Arc Additively Manufactured structural elements, Computers and Structures, 242: 106370, 2021, doi: 10.1016/j.compstruc.2020.106370.
30. L.L. Stromberg, A. Beghini, W.F. Baker, G.H. Paulino, Topology optimization for braced frames: Combining continuum and beam/column elements, Engineering Structures, 37: 106–124, 2012, doi: 10.1016/j.engstruct.2011.12.034.
31. K. Svanberg, Method of moving asymptotes – A new method for structural optimization, International Journal for Numerical Methods in Engineering, 24(2): 359–373, 1987, doi: 10.1002/nme.1620240207.
32. S.W. Williams, F. Martina, A.C. Addison, J. Ding, G. Pardal, P. Colegrove, Wire + Arc additive manufacturing, Materials Science and Technology, 32(7): 641–647, 2016, doi: 10.1179/1743284715Y.0000000073.
33. V. Laghi et al., Mechanical response of dot-by-dot wire-and-arc additively manufactured 304L stainless steel bars under tensile loading, Construction and Building Materials, 318: 125925, 2022, doi: 10.1016/j.conbuildmat.2021.125925.
34. M.M. Mehrabadi, S.C. Cowin, Eigentensors of linear anisotropic elastic materials, Quarterly Journal of Mechanics and Applied Mathematics, 43: 15–41, 1990, doi: 10.1093/qjmam/43.1.15.
35. P. Vannucci, Anisotropic elasticity, [in:] Lecture Notes in Applied and Computational Mechanics book series, Vol. 85, Springer International Publishing, 2018, doi: 10.1007/978-981-10-5439-6.
36. European Committee for Standardization CEN (2015) EN 1993-1-4:2006+a1:2015 Eurocode 3 Design of Steel Structures, Part 1–4: General Rules Supplementary Rules for Stainless Steel.
37. M. Bruggi, A. Taliercio, Optimal strengthening of concrete plates with unidirectional fiber-reinforcing layers, International Journal of Solids and Structures, 67–68: 311–325, 2015, doi: 10.1016/j.ijsolstr.2015.04.033.
38. D. Briccola, M. Bruggi, Analysis of 3D linear elastic masonry-like structures through the API of a finite element software, Advances in Engineering Software, 2019, 133: 60–75, doi: 10.1016/j.advengsoft.2019.04.009.
39. M. Bruggi, A. Taliercio, Hierarchical infills for additive manufacturing through a multiscale approach, Journal of Optimization Theory and Applications, 187(3): 654–682, 2020, doi: 10.1007/s10957-020-01685-y.
40. F. Ferrari, O. Sigmund, A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D, Structural and Multidisciplinary Optimization, 62(4): 2211–2228, 2020, doi: 10.1007/s00158-020-02629-w.
41. T. Borrvall, J. Petersson, Topology optimization using regularized intermediate density control, Computer Methods in Applied Mechanics and Engineering, 190(37–38): 4911–4928, 2001, doi: 10.1016/S0045-7825(00)00356-X.
42. B. Bourdin, Filters in topology optimization, International Journal for Numerical Methods in Engineering, 50(9): 2143–2158, 2001, doi: 10.1002/nme.116.
43. F. Wang, B. Lazarov, O. Sigmund, On projection methods, convergence and robust formulations in topology optimization, Structural and Multidisciplinary Optimization, 43(6): 767–784, 2011, doi: 10.1007/s00158-010-0602-y.
44. B. Blachowski, P. Tauzowski, J. Logo, Yield limited optimal topology design of elastoplastic structures, Structural and Multidisciplinary Optimization, 61(5): 1953–1976, 2020, doi: 10.1007/s00158-019-02447-9.
Published
Jul 1, 2022
How to Cite
BRUGGI, Matteo; LAGHI, Vittoria; TROMBETTI, Tomaso. Optimal Design of Wire-and-Arc Additively Manufactured I-Beams for Prescribed Deflection. Computer Assisted Methods in Engineering and Science, [S.l.], v. 29, n. 4, p. 357–378, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/469>. Date accessed: 28 mar. 2024. doi: http://dx.doi.org/10.24423/cames.469.