Optimal Design of Wire-and-Arc Additively Manufactured I-Beams for Prescribed Deflection
DOI:
https://doi.org/10.24423/cames.469Keywords:
structural optimization, topology optimization, wire-and-arc additive manufacturing, I-beams, orthotropic material, additive manufacturing, 3D printingAbstract
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.
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.
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
2022-07-01
Issue
pp. 357–378
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Bruggi, M., Laghi, V., & Trombetti, T. (2022). Optimal Design of Wire-and-Arc Additively Manufactured I-Beams for Prescribed Deflection. Computer Assisted Methods in Engineering and Science, 29(4), 357–378. https://doi.org/10.24423/cames.469
