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Meccanica

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11-01-2022

Topology optimization of light structures using the natural neighbour radial point interpolation method

Authors: D. C. Gonçalves, J. D. F. Lopes, R. D. S. G. Campilho, J. Belinha

Published in: Meccanica | Issue 3/2022

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Abstract

In this work, a bi-directional evolutionary topology optimization algorithm capable of reinforcing the structure at critical high stress regions is combined with the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM uses the Voronoï diagram and natural neighbour concept to establish the background integration points, enforce the nodal connectivity, and construct the RPI shape functions. State-of-the-art of meshless methods in topology optimization is limited when compared with the classic Finite Element Method. Hence, this work originally introduces an accurate truly meshless method, the NNRPIM, to the topology optimization field. The proposed algorithm is validated by solving several benchmark topology optimization problems. A parametric study on algorithm parameters and mesh influence is performed, and the computational processing time is also evaluated Finally, the proposed calibrated method is extended to design lightweight aircraft industry components.

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Gu YT (2005) Meshfree methods and their comparisons. Int J Comput Methods 02(04):477–515. https://doi.org/10.1142/s0219876205000673CrossRefMATH

Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763–813. https://doi.org/10.1016/j.matcom.2008.01.003MathSciNetCrossRefMATH

Chen JS, Hillman M, Chi SW (2017) Meshfree methods: progress made after 20 years. J Eng Mech, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001176

Liu GR (2016) An overview on meshfree methods: for computational solid mechanics. Int J Comput Methods 13(5):1630001. https://doi.org/10.1142/S0219876216300014MathSciNetCrossRefMATH

Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389CrossRef

Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10(5):307–318. https://doi.org/10.1007/BF00364252MathSciNetCrossRefMATH

Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37(2):229–256. https://doi.org/10.1002/nme.1620370205MathSciNetCrossRefMATH

Wing Kam L, Jun S, Yi Fei Z (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20(8–9):1081–1106MathSciNetMATH

Atluri SN, Zhu T (1998) A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22(2):117–127. https://doi.org/10.1007/s004660050346MathSciNetCrossRefMATH

10.

De S, Bathe KJ (2000) The method of finite spheres. Comput Mech 25(4):329–345. https://doi.org/10.1007/s004660050481MathSciNetCrossRefMATH

11.

Braun J, Sambridge M (1995) A numerical method for solving partial differential equations on highly irregular evolving grids. Nature 376:655–660. https://doi.org/10.1038/376655a0CrossRef

12.

Sukumar N, Moran B, Belytschko T (1998) The natural element method in solid mechanics. Int J Numer Methods Eng 43:839–887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5%3c839::AID-NME423%3e3.0.CO;2-RMathSciNetCrossRefMATH

13.

Liu GR, Gu YT (2001) A point interpolation method for two-dimensional solids. Int J Numer Methods Eng 50(4):937–951. https://doi.org/10.1002/1097-0207(20010210)50:4%3c937::AID-NME62%3e3.0.CO;2-XCrossRefMATH

14.

Wang JG, Liu GR (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54(11):1623–1648. https://doi.org/10.1002/nme.489CrossRefMATH

15.

Dinis LMJS, Natal Jorge RM, Belinha J (2007) Analysis of 3D solids using the natural neighbour radial point interpolation method. Comput Methods Appl Mech Eng, 196, 2009–2028. https://doi.org/10.1016/j.cma.2006.11.002.

16.

Belinha J, Dinis LMJS, Jorge RMN (2012) The natural radial element method. Int J Numer Methods Eng, 1885–1891. https://doi.org/10.1002/nme

17.

Belinha J, Dinis LMJS, Jorge RMN (2013) Composite laminated plate analysis using the natural radial element method. Compos Struct 103:50–67. https://doi.org/10.1016/j.compstruct.2013.03.018CrossRef

18.

Belinha J, Dinis LMJS, Natal Jorge RM (2013) Analysis of thick plates by the natural radial element method. Int J Mech Sci, 76, 33–48. https://doi.org/10.1016/j.ijmecsci.2013.08.011.

19.

Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T (2019) Artificial neural network methods for the solution of second order boundary value problems. Comput Mater Contin 59(1):345–359. https://doi.org/10.32604/cmc.2019.06641CrossRef

20.

Samaniego E et al (2020) An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Comput Methods Appl Mech Eng 362:112790. https://doi.org/10.1016/j.cma.2019.112790MathSciNetCrossRefMATH

21.

Querin OM, Victoria M, Alonso C, Ansola R, Martí P (2017) Topology design methods for structural optimization, 1st ed. Elsevier

22.

Bendsøe MP, Sigmund O (2004) Topology optimization, 2nd ed. Springer, Berlin

23.

Zhou M, Rozvany GIN (1993) DCOC: an optimality criteria method for large systems part II: Algorithm. Struct Optim 6(4):250–262. https://doi.org/10.1007/BF01743384CrossRef

24.

Zhou M, Rozvany GIN (1992) DCOC: an optimality criteria method for large systems part I: theory. Struct Optim 5(1–2):12–25. https://doi.org/10.1007/BF01744690CrossRef

25.

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202. https://doi.org/10.1007/BF01650949CrossRef

26.

Zhou M, Rozvany GIN (1991) The COC algorithm, part II: Topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336. https://doi.org/10.1016/0045-7825(91)90046-9CrossRef

27.

Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252. https://doi.org/10.1007/bf01742754CrossRef

28.

Jia H, Beom HG, Wang Y, Lin S, Liu B (2011) Evolutionary level set method for structural topology optimization. Comput Struct 89(5–6):445–454. https://doi.org/10.1016/j.compstruc.2010.11.003CrossRef

29.

Wang MY, Chen S, Wang X, Mei Y (2005) Design of multimaterial compliant mechanisms using level-set methods. J Mech Des Trans ASME 127(5):941–956. https://doi.org/10.1115/1.1909206CrossRef

30.

Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393. https://doi.org/10.1016/j.jcp.2003.09.032MathSciNetCrossRefMATH

31.

Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528. https://doi.org/10.1006/jcph.2000.6581MathSciNetCrossRefMATH

32.

Allaire G, Jouve F, Toader AM (2002) A level-set method for shape optimization. Comptes Rendus Math 334:1125–1130. https://doi.org/10.1016/S1631-073X(02)02412-3MathSciNetCrossRefMATH

33.

Wallin M, Ristinmaa M (2014) Boundary effects in a phase-field approach to topology optimization. Comput Methods Appl Mech Eng 278:145–159. https://doi.org/10.1016/j.cma.2014.05.012MathSciNetCrossRefMATH

34.

Bourdin B, Chambolle A (2003) Design-dependent loads in topology optimization. ESAIM Control Optim Calc Var 9:19–48. https://doi.org/10.1051/cocv:2002070MathSciNetCrossRefMATH

35.

Ghasemi H, Park HS, Rabczuk T (2017) A level-set based IGA formulation for topology optimization of flexoelectric materials. Comput Methods Appl Mech Eng 313:239–258. https://doi.org/10.1016/j.cma.2016.09.029MathSciNetCrossRefMATH

36.

Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896CrossRef

37.

Querin OM, Steven GP, Xie YM (1998) Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Eng Comput 15(8):1031–1048. https://doi.org/10.1108/02644409810244129CrossRefMATH

38.

Yang XY, Xie YM, Steven GP, Querin OM (1999) Bi-directional evolutionary method for stiffness optimisation. AIAA J 37(11):1493–1488. https://doi.org/10.2514/3.14346CrossRef

39.

Querin OM, Steven GP, Xie YM (2000) Evolutionary structural optimisation using an additive algorithm. Finite Elem Anal Des 34(3–4):291–308. https://doi.org/10.1016/S0168-874X(99)00044-XCrossRefMATH

40.

Querin OM, Young V, Steven GP, Xie YM (2000) Computational efficiency and validation of bi-directional evolutionary structural optimization. Comput Methods Appl Mech Eng 189(2):559–573. https://doi.org/10.1016/S0045-7825(99)00309-6CrossRefMATH

41.

Voronoi G (1908) Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxiäme Memoire. Reeherches sur les parallelloedres primitifs., J. für die Reine und Angew. Math., 134, 198–287

42.

Delauney B (1934) SUR LA SPHÈRE VIDE. A LA MÉMOIRE DE GEORGES VORONOÏ,” Izv. Akad. Nauk SSSR, Otd. Mat. i Estestv. Nauk, pp 793–800

43.

Sibson R (1981) A brief description of natural neighbor interpolation. Barnett V Interpret. Multivar. data. Wiley, Chichester, pp 21–36

44.

Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tessellations: concepts and applications of Voronoï diagrams, 2nd edn. Wiley, ChichesterCrossRef

45.

Belinha J (2014) Meshless methods in biomechanics - bone tissue remodelling analysis, 1st edn. Springer, ChamCrossRef

46.

Preparata FP, Shamos MI (1985) Computational geometry: an introduction. Springer, New YorkCrossRef

47.

Boots BN (1986) Voronoï (Thiessen) polygons. Geo Books, Norwich

48.

Wang JG, Liu GR (2002) On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput Methods Appl Mech Eng 191(23–24):2611–2630. https://doi.org/10.1016/S0045-7825(01)00419-4MathSciNetCrossRefMATH

49.

Hardy RL (1990) Theory and applications of the multiquadric-biharmonic method. Comput Math with Appl 19(8–9):163–208. https://doi.org/10.1016/0898-1221(90)90272-LMathSciNetCrossRefMATH

50.

Golberg MA, Chen CS, Bowman H (1999) Some recent results and proposals for the use of radial basis functions in the BEM. Eng Anal Bound Elem 23(4):285–296. https://doi.org/10.1016/s0955-7997(98)00087-3CrossRefMATH

51.

Belinha J (2014) Meshless methods in biomechanics - bone tissue remodelling analysis, 1st edn. Springer, Porto, p 2014CrossRef

52.

Rinku A, Ananthasuresh, GK (2015) Topology and size optimization of modular ribs in aircraft wings. In: 11th World Congr. Struct. Multidiscip. Optim., pp. 1–6

Title: Topology optimization of light structures using the natural neighbour radial point interpolation method
Authors: D. C. Gonçalves
J. D. F. Lopes
R. D. S. G. Campilho
J. Belinha
Publication date: 11-01-2022
Publisher: Springer Netherlands
Published in: Meccanica / Issue 3/2022
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-021-01459-4

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