DOI QR코드

DOI QR Code

Frequency-constrained polygonal topology optimization of functionally graded systems subject to dependent-pressure loads

  • Thanh T. Banh (Department of Architectural Engineering, Sejong University) ;
  • Joowon Kang (Department of Architecture, Yeungnam University) ;
  • Soomi Shin (Research Institute of Industrial Technology, Pusan National University) ;
  • Lee Dongkyu (Department of Architectural Engineering, Sejong University)
  • 투고 : 2023.10.03
  • 심사 : 2024.04.30
  • 발행 : 2024.05.25

초록

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

키워드

과제정보

This research was supported by and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003776).

참고문헌

  1. Banh, T.T. and Lee, D. (2024), "Comprehensive polygonal topology optimization for triplet thermo-mechanical-pressure multi-material systems", Eng. Comput., https://doi.org/10.1007/s00366-024-01982-4.
  2. Banh, T.T., Lieu, Q.X., Kang, J., Ju, Y., Shin, S. and Lee D. (2023c), "A novel robust stress-based multimaterial topology optimization model for structural stability framework using refined adaptive continuation method", Eng. Comput., 1-37.
  3. Banh, T.T., Lieu, X.Q., Lee, J., Kang, J. and Lee, D. (2023b), "A robust dynamic unified multi-material topology optimization method for functionally graded structures", Struct. Multidiscipl. Optimiz., 66. https://doi.org/10.1007/s00158-023-03501-3.
  4. Banh, T.T., Luu, G.N. and Lee D. (2023a), "A smooth boundary scheme-based topology optimization for functionally graded structures with discontinuities", Steel Compos. Struct., 48, 73-88. https://doi.org/10.12989/scs.2023.48.1.073.
  5. Banh, T.T., Luu, G.N., Lieu, X.Q., Lee, J., Kang, J. and Lee, D. (2021b), "Multiple bi-directional FGMs topology optimization approach with a preconditioned conjugate gradient multigrid", Steel Compos. Struct., 41(3), 385-402. https://doi.org/10.12989/scs.2021.41.3.385.
  6. Banh, T.T., Luu, N.G. and Lee, D. (2021a), "A non-homogeneous multi-material topology optimization approach for functionally graded structures with cracks", Compos. Struct., 273, 114230. https://doi.org/10.1016/j.compstruct.2021.114230.
  7. Banh, T.T., Shin, S., Kang, J. and Lee D. (2024a), "Frequency-constrained topology optimization in incompressible multi-material systems under design-dependent loads", Thin-Wall. Struct., 196, 111467. https://doi.org/10.1016/j.tws.2023.111467.
  8. Banh, T.T., Shin, S., Kang, J. and Lee D. (2024b), "Comprehensive multi-material topology optimization for stress-driven design with refined volume constraint subjected to harmonic force excitation", Eng. Comput., https://doi.org/10.1007/s00366-023-01939-z.
  9. Batchelor, G. (2000), "An introduction to fluid dynamics", Cambridge Univ. Press.
  10. Bendsoe M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using homogenization", Comput. Meth. Appl. Mech. Eng., 71, 197-224. https://doi.org/10.1016/0045-7825(88)90086-2.
  11. Bendsoe, M.P. (2011), "Optimal shape design as a material distribution problem", Struct Optim., 10, 193-202. https://doi.org/10.1007/BF01650949.
  12. Bendsoe, M.P. and Sigmund,, O. (1999), "Material interpolation in topology optimization", Arch. Appl. Mech., 69, 635-654. https://doi.org/10.1007/s004190050248.
  13. Cai, K., Cao, J., Shi, J., Liu, L. and Qin, Q.H. (2016), "Optimal layout of multiple bi-modulus materials", Struct. Multidiscipl. Optimiz., 53, 801-811. https://doi.org/10.1007/s00158-015-1365-2
  14. Chen, B.C. and Kikuchi, N. (2001), "Topology optimization with design-dependent loads", Finite Elem Anal Des., 39, 57-70. https://doi.org/10.1016/S0168-874X(00)00021-4.
  15. Floater, M., Gillette, A. and Sukumar, N. (2014), "Gradient bounds for Wachspress coordinates on polytopes", SIAM J. Numer. Anal., 52(1), 515-532. https://doi.org/10.1137/130925712.
  16. Hammer, V. and Olhoff, N. (2000), "Topology optimization of continuum structures subjected to pressure loading", Struct Multidisc Optim, 19, 85-92. https://doi.org/10.1007/s001580050088.
  17. Kumar, P. (2023), "TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads", Struct. Multidisc. Optim., 66(4), 97. https://doi.org/10.1007/s00158-023-03533-9.
  18. Kumar, P., Frouws, J.S. and Langelaar, M. (2020), "Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method", Struct Multidisc Optim, 62, 1637-1655. https://doi.org/10.1007/s00158-019-02442-0.
  19. Li, D., Kim, I.Y. (2018), "Multi-material topology optimization for practical lightweight design", Struct. Multidiscipl. Optimiz., 58, 1081-1094. https://doi.org/10.1007/s00158-018-1953-z
  20. Liao, J., Huang, G., Chen, X., Yu, Z. and Huang, Q. (2021), "A guide-weight criterion-based topology optimization method for maximizing the fundamental eigenfrequency of the continuum structure", Struct. Multidiscipl. Optimiz.. https://doi.org/10.1007/s00158-021-02971-7.
  21. Lieu, X.Q. and Lee J. (2017a), "Multiresolution topology optimization using isogeometric analysis", Int. J. Numer. Meth. Eng., 112, 2025-2047. https://doi.org/10.1002/nme.5593.
  22. Lieu, X.Q. and Lee, J. (2017b), "A multi-resolution approach for multi-material topology optimization based on isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 323, 272-302. https://doi.org/10.1016/j.cma.2017.05.009.
  23. Luo, Y., Li, Q. and Liu, S. (2019), "A projection-based method for topology optimization of structures with graded surfaces", Int. J. Numer. Meth. Eng., 118, 654-677. https://doi.org/10.1002/nme.6031.
  24. Paulino, G.H. and Silva, E.C.N. (2005), "Design of functionally graded structures using topology optimization", Mater. Sci. Forum, 492-493, 435-440. www.scientific.net/MSF.492-493.435. https://doi.org/10.4028/www.scientific.net/MSF.492-493.435
  25. Pedersen, N.L. (2000), "Maximization of eigenvalue using topology optimization", Struct. Multidiscipl. Optimiz., 20, 2-11. https://doi.org/10.1007/s001580050130.
  26. Silva, E.C.N. and Paulino, G.H. (2004), "Topology optimization applied to the design of functionally graded material (FGM) structures", In: Proceedings of 21st international congress of theoretical and applied mechanics (ICTAM), Warsaw, 15-21. https://doi.org/10.12989/scs.2021.41.3.385.
  27. Stolpe, M. and Svanberg, K. (2001), "An alternative interpolation scheme for minimum compliance topology optimization", Struct. Multidisc. Optim., 22, 116-124. https://doi.org/10.1007/s001580100129.
  28. Svanberg, K. (1987), "The method of moving asymptotes - A new method for structural optimization", Int. J. Numer. Meth. Eng., 24, 359-373. https://doi.org/10.1002/nme.1620240207.
  29. Talischi, C., Paulino, G.H. and Pereira A. (2012), "PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes", Struct. Multidiscipl. Optimiz., 45, 329-357. https://doi.org/10.1007/s00158-011-0696-x
  30. Wachspress, E.L. (1975), "A Rational Finite Element Basis", Academic Press.
  31. Wang, B., Bai, J., Lu, S. and Zuo, W. (2023), "Structural topology optimization considering geometrical and load nonlinearities", Comput. Struct., 289, 107190. https://doi.org/10.1016/j.compstruc.2023.107190.
  32. Yap, H.K., Ng, H.Y. and Yeow, C.H. (2016), "High-force soft printable pneumatics for soft robotic applications", Soft Robotics, 3(3), 144-158. https://doi.org/10.1089/soro.2016.0030.
  33. Zolfagharian, A., Kouzani, A.Z., Khoo S.Y., Moghadam A.A.A., Gibson I. and Kaynak A. (2016), "Evolution of 3D printed soft actuators", Sensors Actuators A: Physic., 250, 258-272. https://doi.org/10.1016/j.sna.2016.09.028.