Steel and Composite Structures

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Multi-material topology optimization for crack problems based on eXtended isogeometric analysis

  • Banh, Thanh T. (Department of Architectural Engineering, Sejong University) ;
  • Lee, Jaehong (Department of Architectural Engineering, Sejong University) ;
  • Kang, Joowon (Department of Architecture, Yeungnam University) ;
  • Lee, Dongkyu (Department of Architectural Engineering, Sejong University)
  • Received : 2020.03.27
  • Accepted : 2020.11.27
  • Published : 2020.12.25
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Abstract

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

Keywords

Acknowledgement

This research was supported by a grant (NRF-2020R1A4A2002855) from NRF (National Research Foundation of Korea) funded by MEST (Ministry of Education and Science Technology) of Korean government.

References

  1. Alonso, C., Ansola, R. and Querin, O.M. (2014), "Topology synthesis of multi-material compliant mechanisms with a Sequential Element Rejection and Admission method", Finite Elem. Anal. Des., 85, 11-19. https://doi.org/10.1016/j.finel.2013.11.006.
  2. Banh, T.T. and Lee, D. (2018b), "Multi-material topology optimization of Reissner-Mindlin plates using MITC4", Steel Compos. Struct., 27(1), 27-33. https://doi.org/10.12989/scs.2018.27.1.027.
  3. Banh, T.T. and Lee, D. (2019), "Topology optimization of multidirectional variable thickness thin plate with multiple materials", Struct. Multidiscip. O., 59, 1503-1520. 10.1007/s00158-018-2143-8.
  4. Banh, T.T. and Lee, DK (2018a), "Multi-material topology optimization design for continuum structures with crack patterns", Compos. Struct., 186, 193-209. 10.1016/j.compstruct.2017.11.088.
  5. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Method. Appl. M., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2.
  6. Benson, D.J., Bazilevs, Y., Luycker, E.D. and Belytschko, T. (2010), "A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM", Int. J. Numer. Method. Eng., 83, 765-785. https://doi.org/10.1002/nme.2864.
  7. Buffa, A., Sangalli, G. and Vazquez, R. (2010), "Isogeometric analysis in electromagnetics: B-splines approximation", Comput. Method. Appl. M., 199, 17-20. https://doi.org/10.1016/j.cma.2009.12.002.
  8. Cottrell, J.A., Hughes, T.J.R. and Bazilevs, Y. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley and Sons, United Kingdom.
  9. Doan, Q.H. and Lee, D. (2019), "Optimal formation assessment of multi-layered ground retrofit with arch-grid units considering buckling load factor", Int. J. Steel Struct., 19, 269-282. https://doi.org/10.1007/s13296-018-0115-x.
  10. Ghorashi, S.S., Valizadeh, N. and Mohammadi, S. (2012), "Extended isogeometric analysis for simulation of stationary and propagating cracks", Int. J. Numer. Method. Eng., 89, 1069-1101. 10.1002/nme.3277.
  11. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Method. Appl. M., 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008.
  12. Khatir, S. and Abdek Wahab, M. (2018), "Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm", Eng. Fract. Mech., doi:10.1016/j.engfracmech.2018.09.032.
  13. Khatir, S. and Abdek Wahab, M. (2019), "A computational approach for crack identification in plate structures using XFEM, XIGA, PSO and Jaya algorithm", Theor. Appl. Fract. Mech., 103, 102240. https://doi.org/10.1016/j.tafmec.2019.102240.
  14. Khatir, S., Benaissa, B., Roberto, C. and Abdek Wahab, M. (2017), "Damage detection in CFRP composite beams based on vibration analysis using proper orthogonal decomposition method with radial basis function and Cuckoo Search algorithm", Compos. Struct., 187 344-353. https://doi.org/10.1016/j.compstruct.2017.12.058.
  15. Khatir, S., Boutchicha, D., Le, C.T., Tran, H.N., Nguyen, T.N. and Abdek Wahab, M. (2020), "Improved ANN technique combined with Jaya algorithm for crack identification in plates using XIGA and experimental analysis", Theor. Appl. Fract. Mech., 107 102554. https://doi.org/10.1016/j.tafmec.2020.102554.
  16. Khatir, S., Tiachacht, S., Cuong-LeThanh, Quoc Bui T. and Abdel Wahab, M. (2019a), "Damage assessment in composite laminates using ANN-PSO-IGA and Corn- well indicator", Compos. Struct., 230 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  17. Khatir, S., Wahab, M.A., Djilali, B. and Khatir, T. (2019b), "Structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis", J. Sound Vib., 448, 230-246. https://doi.org/10.1016/j.jsv.2019.02.017.
  18. Lee, D., Starossek, U. and Shin, S. (2010), "Topological optimized design considering dynamic problem with non-stochastic structural uncertainty", Struct. Eng. Mech., 36(1), 79-94. https://doi.org/10.12989/sem.2010.36.1.079.
  19. Lieu, Q.X. and Lee, J. (2017), "Multiresolution topology optimization using isogeometric analysis", Int. J. Numer. Method. Eng., 114, 2025-2047. 10.1002/nme.5593.
  20. Liu, Q., Chan, R. and Huang, X. (2016), "Concurrent topology optimization of macrostructures and material microstructures for natural frequency", Mater. Design, 106, 380-390. https://doi.org/10.1016/j.matdes.2016.05.115.
  21. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A Finite Element Method for Crack Growth without Remeshing", Int. J. Numer. Method. Eng.., 46, 131-150. https://doi.org/10.1002/(SICI)10970207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.
  22. Mohammadi, S. (2008), Extended Finite Element Method: for Fracture Analysis of Structures, Blackwell Publishing Ltd, United Kingdom.
  23. Nazargah, M.L. (2014), "An isogeometric approach for the analysis of composite steel-concrete beams", Eng. Fract. Mech., 84, 406-415. https://doi.org/10.1016/j.tws.2014.07.014.
  24. Nguyen, A.P., Banh, T.T., Lee, DK, Lee, J., Kang, J., Shin, S. (2018), "Design of multiphase carbon fiber reinforcement of crack existing concrete structures using topology optimization" Steel Compos. Struct., 29(5), 635-645. https://doi.org/10.12989/scs.2018.29.5.635.
  25. Nguyen, V.P. and Bordas, S. (2005), "Extended Isogeometric Analysis for Strong and Weak Discontinuities", Isogeometric Method. Numer. Simul., 21-120. https://doi.org/10.1007/978-3-7091-1843-6_2.
  26. Qian, X. (2010), "Full analytical sensitivities in NURBS based isogeometric shape optimization", Comput. Method. Appl. M., 199, 29-32. https://doi.org/10.1016/j.cma.2010.03.005.
  27. Qian, X. (2013), "Topology optimization in B-spline space", Comput. Method. Appl. M., 265 15-35. 10.1016/j.cma.2013.06.001.
  28. Qiao, S., Han, X., Zhou, K. and Ji, J. (2016), "Seismic analysis of steel structure with brace configuration using topology optimization", Steel Compos. Struct., 21(3), 501-515. https://doi.org/10.12989/scs.2016.21.3.501.
  29. Shobeiri, V. (2015), "The topology optimization design for cracked structures", Eng. Anal. Bound. Elem., 58, 26-38. 10.1016/j.enganabound.2015.03.002.
  30. Shojaee, S. and Daneshmand, A. (2015), "Crack analysis in media with orthotropic Functionally Graded Materials using eXtended Isogeometric Analysis", Eng. Fract. Mech., 147, 203-227. 10.1016/j.engfracmech.2015.08.025.
  31. Tavakoli, R. and Mohsenind, S.M. (2014), "Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation", Struct. Multidiscip. O., 49, 621-642. 10.1007/s00158-013-0999-1.
  32. Wall, W.A., Frenzel, M.A. and Cyron, C. (2008), "Isogeometric structural shape optimization", Comput. Method. Appl. M., 197, 2976-2988. https://doi.org/10.1016/j.cma.2008.01.025.
  33. Yang, Z., Zhou, K. and Qiao, S. (2018), "Topology optimization of reinforced concrete structure using composite truss-like model", Struct. Eng. Mech., 67(1), 79-85. https://doi.org/10.12989/sem.2018.67.1.079.
  34. Yi, L.V. and Liu, S. (2018), "Topology optimization and heat dissipation performance analysis of a micro-channel heat sink", Meccanica, 53, 3693-3708. 10.1007/s11012-018-0918-z.
  35. Yun, K.S. and Youn, S.K. (2017), "Multi-material topology optimization of viscoelastically damped structures under time-dependent loading", Finite Elem. Anal. Des., 123, 9-18. 10.1016/j.finel.2016.09.006.
  36. Zhou, S. and Wang, M.Y. (2007), "Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition", Struct. Multidiscip. O., 33, 89-111. 10.1007/s00158-006-0035-9.
  37. Zhou, S.W. and Wang, M.Y. (2006a), "Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition", Struct. Multidiscip. O., 33, 89-111. 10.1007/s00158-006-0035-9.
  38. Zhou, S.W. and Wang, M.Y. (2006b), "3D Multi-material structural topology optimization with the generalized Cahn-Hilliard equations", Comput. Model. Eng. Sci., 16, 83-101. http://hdl.handle.net/1783.1/74250.
  39. Zuo, K.T., Chen, L.P., Zhang, Y.Q. and Yang, J. (2007), "Study of key algorithms in topology optimization", Int. J. Adv. Manufact. Technol., 32, 787-796. 10.1007/s00170-005-0387-0.