Advertisement

Integrated layout and topology optimization design of multi-component systems under harmonic base acceleration excitations

  • Tao Liu
  • Ji-Hong ZhuEmail author
  • Wei-Hong ZhangEmail author
  • Hua Zhao
  • Jie Kong
  • Tong Gao
Research Paper
  • 35 Downloads

Abstract

The integrated optimization of component layout and structural topology is studied in this paper to improve the dynamic performance of the multi-component structure systems under harmonic base acceleration excitations. Considering linear systems, including multi-point constraints interconnecting the components and structures as an integrity, the dynamic responses and the corresponding design sensitivities are analytically derived based on the mode acceleration method. To obtain precise dynamic response, structural real damping characteristics are measured using vibration experiments, which are relevant to the structural dynamic response, especially when the excitation frequencies fall into the resonant frequency band. Further verifications are done by the comparison of Rayleigh damping, constant damping ratio, and hysteretic damping model with experimental results of structures achieved by resin-based additive manufacturing. In this way, structural real damping characteristics are taken into account in the integrated optimization. Numerical examples and vibration testing results are presented to show the validity of the optimization procedure and its potential application in engineering.

Keywords

Topology optimization Component layout optimization Base acceleration excitation Vibration experiment Damping model 

Notes

Acknowledgments

This work is supported by the National Key Research and Development Program (2017YFB1102800), the NSFC for the Excellent Young Scholars (11722219), and Key Project of the NSFC (51790171, 5171101743, 51735005).

References

  1. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer Science & Business Media, BerlinzbMATHGoogle Scholar
  3. Besselink B, Tabak U, Lutowska A et al (2013) A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J Sound Vib 332:4403–4422CrossRefGoogle Scholar
  4. Clough RW, Penzien J (2003) Dynamics of structures. Copyright of Computers & Structures, USAzbMATHGoogle Scholar
  5. Cornwell (1983) On the application of the mode-acceleration method to structural engineering problems. Earthq Eng Struct Dyn 11:679–688CrossRefGoogle Scholar
  6. Deng S, Suresh K (2015) Multi-constrained topology optimization via the topological sensitivity. Struct Multidiscip Optim 51(5):987–1001MathSciNetCrossRefGoogle Scholar
  7. Felippa CA (2004) Introduction to finite element methods. In: Course notes. Department of Aerospace Engineering Sciences, University of Colorado at Boulder available at http://kis.tu.kielce.pl/mo/COLORADO_FEM/colorado/IFEM.Ch10.pdf. Accessed 30 Jan 2019
  8. Fox RL, Kapoor MP (1968) Rates of change of eigenvalues and eigenvectors. AIAA J 6:2426–2429CrossRefzbMATHGoogle Scholar
  9. Gao HH, Zhu JH, Zhang WH et al (2015) An improved adaptive constraint aggregation for integrated layout and topology optimization. Comput Methods Appl Mech Eng 289:387–408MathSciNetCrossRefGoogle Scholar
  10. Guo X, Cheng GD (2010) Recent development in structural design and optimization. Acta Mech Sinica 26:807–823MathSciNetCrossRefzbMATHGoogle Scholar
  11. Guo X, Zhang WS, Zhong WL (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(8):081009CrossRefGoogle Scholar
  12. JOG CSS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253:687–709CrossRefGoogle Scholar
  13. Kang Z, Wang YQ (2013) Integrated topology optimization with embedded movable holes based on combined description by material density and level sets. Comput Methods Appl Mech Eng 255:1–13MathSciNetCrossRefzbMATHGoogle Scholar
  14. Kang Z, Zhang X, Jiang S et al (2012) On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidiscip Optim 46:51–67MathSciNetCrossRefzbMATHGoogle Scholar
  15. Kang Z, Wang YG, Wang YQ (2016) Structural topology optimization with minimum distance control of multiphase embedded components by level set method. Comput Methods Appl Mech Eng 306:299–318MathSciNetCrossRefGoogle Scholar
  16. Kim TS, Kim YY (2000) Mac-based mode-tracking in structural topology optimization. Comput Struct 74:375–383CrossRefGoogle Scholar
  17. Liu P, Kang Z (2018) Integrated topology optimization of multi-component structures considering connecting interface behavior. Comput Methods Appl Mech Eng 341:851–887MathSciNetCrossRefGoogle Scholar
  18. Liu GR, Quek SS (2003) The finite element method: a practical course. Elsevier, Butterworth-Heinemann, OxfordzbMATHGoogle Scholar
  19. Liu H, Zhang WH, Gao T (2015) A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct Multidiscip Optim 51:1321–1333MathSciNetCrossRefGoogle Scholar
  20. Liu T, Guessasma S, Zhu J et al (2018) Microstructural defects induced by stereolithography and related compressive behaviour of polymers. J Mater Process Technol 251:37–46CrossRefGoogle Scholar
  21. Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121:259–280MathSciNetCrossRefzbMATHGoogle Scholar
  22. Niu B, He X, Shan Y et al (2018) On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation. Struct Multidiscip Optim 57(6):2291–2307MathSciNetCrossRefGoogle Scholar
  23. Olhoff N, Du J (2005) Topological design of continuum structures subjected to forced vibration. In: Proceedings of 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, BrazilGoogle Scholar
  24. Olhoff N, Du J (2016) Generalized incremental frequency method for topological design of continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency. Struct Multidiscip Optim 54(5):1113–1141MathSciNetCrossRefGoogle Scholar
  25. Olhoff N, Niu B (2016) Minimizing the vibrational response of a lightweight building by topology and volume optimization of a base plate for excitatory machinery. Struct Multidiscip Optim 53:567–588MathSciNetCrossRefGoogle Scholar
  26. Qian Z, Ananthasuresh GK (2004) Optimal embedding of rigid objects in the topology design of structures. Mech based Des Struct Mach 32:165–193CrossRefGoogle Scholar
  27. Shu L, Wang MY, Fang Z et al (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330:5820–5834CrossRefGoogle Scholar
  28. Sigmund O, Jensen JS (2003) Systematic design of phononic band–gap materials and structures by topology optimization. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 361(1806):1001–1019MathSciNetCrossRefzbMATHGoogle Scholar
  29. Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48:1031–1055MathSciNetCrossRefGoogle Scholar
  30. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22:116–124CrossRefGoogle Scholar
  31. Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Proceedings of the first world congress of structural and multidisciplinary optimization, vol 28, pp 9–16Google Scholar
  32. Thorby D (2008) Structural dynamics and vibration in practice: an engineering handbook. Butterworth-Heinemann, UKGoogle Scholar
  33. Torvik PJ (2011) On estimating system damping from frequency response bandwidths. J Sound Vib 330:6088–6097CrossRefGoogle Scholar
  34. Wang Y, Luo Z, Zhang X et al (2014) Topological design of compliant smart structures with embedded movable actuators. Smart Mater Struct 23:045024CrossRefGoogle Scholar
  35. Xu Y, Zhu J, Wu Z et al (2018) A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization.  https://doi.org/10.1007/s42114-018-0032-7
  36. Yang KK, Zhu JH, Wu MQ et al (2018) Integrated optimization of actuators and structural topology of piezoelectric composite structures for static shape control. Comput Methods Appl Mech Eng 334:440–469MathSciNetCrossRefGoogle Scholar
  37. Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199:1744–1763MathSciNetCrossRefzbMATHGoogle Scholar
  38. Zhang Q, Zhang WH, Zhu JH et al (2012) Layout optimization of multi-component structures under static loads and random excitations. Eng Struct 43:120–128CrossRefGoogle Scholar
  39. Zhang WS, Zhong WL, Guo X (2015) Explicit layout control in optimal design of structural systems with multiple embedding components. Comput Methods Appl Mech Eng 290:290–313MathSciNetCrossRefGoogle Scholar
  40. Zhou Y, Zhang WH, Zhu JH et al (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1–32MathSciNetCrossRefGoogle Scholar
  41. Zhu JH, Zhang WH, Beckers P (2009) Integrated layout design of multi-component system. Int J Numer Methods Eng 78:631–651CrossRefzbMATHGoogle Scholar
  42. Zhu JH, Zhang WH, Xia L (2015) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng 23:595–622MathSciNetCrossRefzbMATHGoogle Scholar
  43. Zhu JH, Guo WJ, Zhang WH et al (2016) Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems. Struct Multidiscip Optim 51:21–45MathSciNetGoogle Scholar
  44. Zhu JH, He F, Liu T et al (2018) Structural topology optimization under harmonic base acceleration excitations. Struct Multidiscip Optim 57:1061–1078MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State IJR Center of Aerospace Design and Additive Manufacturing, School of Mechanical EngineeringNorthwestern Polytechnical UniversityXianChina
  2. 2.MIIT Laboratory of Metal Additive Manufacturing and Innovative Design, NPU-QMUL Joint Research InstituteNorthwestern Polytechnical UniversityXianChina
  3. 3.Institute of Intelligence Material and Structure, Unmanned System TechnologiesNorthwestern Polytechnical UniversityXianChina
  4. 4.Shaanxi Key Laboratory of Macromolecular Science and Technology, School of ScienceNorthwestern Polytechnical UniversityXianChina

Personalised recommendations