Finite Element Modelling with Abaqus and Tosca for Topology Optimization of Steel
Tiago Ribeiro （ Department of Civil Engineering and Architecture, University of Beira Interior, 6201-001 Covilhã, Portuga. ）
Luís Bernardo （ Department of Civil Engineering and Architecture, University of Beira Interior, 6201-001 Covilhã, Portuga. ）
Ricardo Carrazedo （ Department of Structural Engineering, University of São Paulo, Av. Trabalhador Saocarlense, 400 Parque Arnold Schimidt, São Carlos, SP 13566-590, Brazil. ）
https://doi.org/10.37155/2811-0730-0201-3Abstract
Finite Element Method (FEM) is widely employed for solids and multiphysics problems analysis in practically all engineering and science fields. Yet, when it comes to Topology Optimization (TO), significant issues arise concerning the geometry, hence the mesh, and non-stationary condition. Contrarily to broader Finite Element Modelling, FEM for TO has much less bibliographic support and research. Herein we depict, apply and discuss the major challenges and options concerning modelling with finite elements within TO problems. It is shown that, for the optimization of a steel connection part, mesh refinement is critical for effective yet computationally efficient analysis. Moreover, a case-based and user-friendly approach, in the form of tutorial, is proposed to address the practical FE meshing for TO.
Keywords
Finite Element Method; Topology Optimisation; Steel; Mesh Convergence Studies; Connections; Joints; Mesh Refinement; Design for Additive ManufacturingFull Text
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51. Baandrup, M.; Sigmund, O.; Polk, H.; Aage, N. Closing the gap towards super-long suspension bridges using computational morphogenesis. Nat. Commun. 2020, 11, 1–7, doi:10.1038/s41467-020-16599-6.
52. Aage, N.; Andreassen, E.; Lazarov, B.S.; Sigmund, O. Giga-voxel computational morphogenesis for structural design. Nature 2017, 550, 84–86, doi:10.1038/nature23911.
53. Sousa, A.M.; Andrade, T.A.; Errico, M.; Coelho, P.; Filipe, R.M.; Matos, H.A. Fatty Acid Content in Biomasses: State-of-the-Art and Novel Physical Property Estimation Methods. Int. J. Chem. Eng. 2019.
2. Šimůnek, J.; Genuchten, M.T.; Šejna, M. Development and Applications of the HYDRUS and STANMOD Software Packages and Related Codes. Vadose Zo. J. 2008, doi:10.2136/vzj2007.0077.
3. Böl, M.; Ehret, A.E.; Bolea Albero, A.; Hellriegel, J.; Krull, R. Recent advances in mechanical characterisation of biofilm and their significance for material modelling. Crit. Rev. Biotechnol. 2013.
4. Vinogradov, A.; Estrin, Y. Analytical and numerical approaches to modelling severe plastic deformation. Prog. Mater. Sci. 2018.
5. Sigmund, O. Design of multiphysics actuators using topology optimization - Part I: One-material structures. Comput. Methods Appl. Mech. Eng. 2001, doi:10.1016/S0045-7825(01)00251-1.
6. Sigmund, O. Design of multiphysics actuators using topology optimization - Part II: Two-material structures. Comput. Methods Appl. Mech. Eng. 2001, doi:10.1016/S0045-7825(01)00252-3.
7. Deaton, J.D.; Grandhi, R. V. A survey of structural and multidisciplinary continuum topology optimization: Post 2000. Struct. Multidiscip. Optim. 2014, 49, 1–38, doi:10.1007/s00158-013-0956-z.
8. Crisfield, M.A.; Tassoulas, J.L. Non‐Linear Finite Element Analysis of Solids and Structures, Volume 1 . J. Eng. Mech. 1993, doi:10.1061/(asce)0733-9399(1993)119:7(1504).
9. de Borst, R.; Crisfield, M.A.; Remmers, J.J.C.; Verhoosel, C. V. Non-Linear Finite Element Analysis of Solids and Structures: Second Edition; 2012; ISBN 9780470666449.
10. Voyiadjis, G.Z.; Woelke, P. General non-linear finite element analysis of thick plates and shells. Int. J. Solids Struct. 2006, doi:10.1016/j.ijsolstr.2005.07.012.
11. Sousa, A.M.; Azevedo, L.; Pereira, M.J.; Matos, H.A. The influence of solar heating upon ground temperature. In Proceedings of the Journal of Physics: Conference Series; 2021; Vol. 2116, p. 012120.
12. Gaur, H. A new approach of material nonlinear finite element analysis. Def. Technol. 2020, doi:10.1016/j.dt.2020.02.018.
13. Michell, A.G.M. The limits of economy of material in frame-structures. London, Edinburgh, Dublin Philos. Mag. J. Sci. 1904, 8, 589–597, doi:10.1080/14786440409463229.
14. Hegemier, G.A.; Prager, W. On Michell trusses. Int. J. Mech. Sci. 1969, 11, 209–215, doi:10.1016/0020-7403(69)90006-X.
15. Prager, W. A note on discretized michell structures. Comput. Methods Appl. Mech. Eng. 1974, doi:10.1016/0045-7825(74)90019-X.
16. Prager, W.; Rozvany, G.I.N. Optimization of Structural Geometry; ACADEMIC PRESS, INC., 1977;
17. Rozvany, G.I.N. Grillages of maximum strength and maximum stiffness. Int. J. Mech. Sci. 1972, 14, 651–666, doi:10.1016/0020-7403(72)90023-9.
18. Rozvany, G.I.N. Optimal load transmission by flexure. Comput. Methods Appl. Mech. Eng. 1972, 1, 253–263, doi:10.1016/0045-7825(72)90007-2.
19. Rozvany, G.I.N.; Zhou, M.; Rotthaus, M.; Gollub, W.; Spengemann, F. Continuum-type optimality criteria methods for large finite element systems with a displacement constraint. Part I. Struct. Optim. 1989, doi:10.1007/BF01743809.
20. Rozvany, G.I.N.; Zhou, M.; Gollub, W. Continuum-type optimality criteria methods for large finite element systems with a displacement constraint. Part II. Struct. Optim. 1990, doi:10.1007/BF01745456.
21. Bendsoe, M.P.; Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 1988, 71, 197–224.
22. Bendsøe, M.P. Optimal shape design as a material distribution problem. Struct. Optim. 1989, 1, 193–202, doi:10.1007/BF01650949.
23. Suzuki, K.; Kikuchi, N. Shape and topology optimization by a homogenization method. Am. Soc. Mech. Eng. Appl. Mech. Div. AMD 1990, 115, 15–30.
24. Pedersen, P. On the optimal layout of multi-purpose trusses. Comput. Struct. 1972, 2, 695–712, doi:10.1016/0045-7949(72)90032-6.
25. Kirsch, U. Optimal topologies of truss structures. Comput. Methods Appl. Mech. Eng. 1989, 72, 15–28, doi:10.1016/0045-7825(89)90119-9.
26. Tyflopoulos, E.; Steinert, M. Messing with boundaries - quantifying the potential loss by pre-set parameters in topology optimization. In Proceedings of the Procedia CIRP; 2019.
27. Angelucci, G.; Spence, S.M.J.; Mollaioli, F. An integrated topology optimization framework for three‐dimensional domains using shell elements. Struct. Des. Tall Spec. Build. 2020, 1–17, doi:10.1002/tal.1817.
28. Tsavdaridis, K.D.; Kingman, J.J.; Toropov, V. V. Application of structural topology optimisation to perforated steel beams. Comput. Struct. 2015, doi:10.1016/j.compstruc.2015.05.004.
29. Bagherinejad, M.H.; Haghollahi, A. Study on Topology Optimization of Perforated Steel Plate Shear Walls in Moment Frame Based on Strain Energy. Int. J. Steel Struct. 2020, 20, 1420–1438, doi:10.1007/s13296-020-00373-x.
30. Weldeyesus, A.G.; Stolpe, M. Free material optimization for laminated plates and shells. Struct. Multidiscip. Optim. 2016, 53, 1335–1347, doi:10.1007/s00158-016-1416-3.
31. Kanyilmaz, A.; Berto, F. Robustness‐oriented topology optimization for steel tubular joints mimicking bamboo structures. Mater. Des. Process. Commun. 2019, 1, e43, doi:10.1002/mdp2.43.
32. Kanyilmaz, A.; Berto, F.; Paoletti, I.; Caringal, R.J.; Mora, S. Nature-inspired optimization of tubular joints for metal 3D printing. Struct. Multidiscip. Optim. 2020, doi:10.1007/s00158-020-02729-7.
33. Hassani, V.; Khabazi, Z.; Mehrabi, H.A.; Gregg, C.; O’Brien, R.W. Rationalization algorithm for a topologically-optimized multi-branch node for manufacturing by metal printing. J. Build. Eng. 2020, 29, 101146, doi:10.1016/j.jobe.2019.101146.
34. Ribeiro, T.; Bernardo, L.; Andrade, J. Topology Optimisation in Structural Steel Design for Additive Manufacturing. Appl. Sci. 2021, doi:10.3390/app11052112.
35. Lange, J.; Feucht, T.; Erven, M. 3D printing with steel: Additive Manufacturing for connections and structures. Steel Constr. 2020, 13, 144–153, doi:10.1002/stco.202000031.
36. Ribeiro, T.; Bernardo, L.; Carrazedo, R.; Domenico, D. De Eurocode-compliant Topology Optimisation and Analysis of a Steel Cover-plate in a Splice Moment Connection. In Proceedings of the Materials Today: Proceedings - Recent Advancements in Construction Materials & Structures, ICCMS-2021; Elsevier, 2022.
37. Dassault Systèmes Tosca Structure.
38. Wang, Y.; Pasiliao, C.L. Modeling ablation of laminated composites: A novel manual mesh moving finite element analysis procedure with ABAQUS. Int. J. Heat Mass Transf. 2018, 116, 306–313, doi:10.1016/j.ijheatmasstransfer.2017.09.038.
39. Lee, S.H.; Abolmaali, A.; Shin, K.J.; Lee, H. Du ABAQUS modeling for post-tensioned reinforced concrete beams. J. Build. Eng. 2020, 30, 101273, doi:10.1016/j.jobe.2020.101273.
40. Yussof, M.M.; Silalahi, J.H.; Kamarudin, M.K.; Chen, P.S.; Parke, G.A.R. Numerical evaluation of dynamic responses of steel frame structures with different types of haunch connection under blast load. Appl. Sci. 2020, 10, doi:10.3390/app10051815.
41. Matos, M. Sizing Optimization for Industrial Applications. In Proceedings of the 11th World congress on structural and multidisciplinary optimization (WCSMO-11); 2015; Vol. 51, pp. 799–800.
42. Pedersen, C.B.W.; Allinger, P. Industrial implementation and applications of topology optimization and future needs. Solid Mech. its Appl. 2006, 137, 229–238, doi:10.1007/1-4020-4752-5_23.
43. Rozvany, G.I.N. A critical review of established methods of structural topology optimization. Struct. Multidiscip. Optim. 2009, 37, 217–237, doi:10.1007/s00158-007-0217-0.
44. Gerzen, N.; Clausen, P.M.; Suresh, S.; Pedersen, C.B.W. Fatigue Sensitivities for Sizing Optimization of Shell Structures. Proc. 12th World Congr. Struct. Multidiscip. Optim. 2017, 1–13.
45. Saadlaoui, Y.; Milan, J.L.; Rossi, J.M.; Chabrand, P. Topology optimization and additive manufacturing: Comparison of conception methods using industrial codes. J. Manuf. Syst. 2017, 43, 178–186, doi:10.1016/j.jmsy.2017.03.006.
46. Garcia-Granada, A.A.; Catafal-Pedragosa, J.; Lemu, H.G. Topology optimization through stiffness/weight ratio analysis for a three-point bending test of additive manufactured parts. In Proceedings of the IOP Conference Series: Materials Science and Engineering; 2019; Vol. 700.
47. Lagaros, N.D.; Vasileiou, N.; Kazakis, G. A C# code for solving 3D topology optimization problems using SAP2000. Optim. Eng. 2019, 20, doi:10.1007/s11081-018-9384-7.
48. Cai, L.; Nauman, E.A.; Pedersen, C.B.W.; Neu, C.P. Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization. Sci. Rep. 2020, 10, 1–13, doi:10.1038/s41598-020-64723-9.
49. Benoist, V.; Arnaud, L.; Baili, M. A new method of design for additive manufacturing including machining constraints. Int. J. Adv. Manuf. Technol. 2020, 111, 25–36, doi:10.1007/s00170-020-06059-2.
50. Fedulov, B.; Fedorenko, A.; Khaziev, A.; Antonov, F. Optimization of parts manufactured using continuous fiber three-dimensional printing technology. Compos. Part B Eng. 2021, 227, 109406, doi:10.1016/j.compositesb.2021.109406.
51. Baandrup, M.; Sigmund, O.; Polk, H.; Aage, N. Closing the gap towards super-long suspension bridges using computational morphogenesis. Nat. Commun. 2020, 11, 1–7, doi:10.1038/s41467-020-16599-6.
52. Aage, N.; Andreassen, E.; Lazarov, B.S.; Sigmund, O. Giga-voxel computational morphogenesis for structural design. Nature 2017, 550, 84–86, doi:10.1038/nature23911.
53. Sousa, A.M.; Andrade, T.A.; Errico, M.; Coelho, P.; Filipe, R.M.; Matos, H.A. Fatty Acid Content in Biomasses: State-of-the-Art and Novel Physical Property Estimation Methods. Int. J. Chem. Eng. 2019.
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