Skip to main content
SpringerLink
Log in

Multiscale Computational Method for Dynamic Thermo-Mechanical Problems of Composite Structures with Diverse Periodic Configurations in Different Subdomains

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

In this paper, a novel multiscale computational method is presented to simulate and analyze dynamic thermo-mechanical problems of composite structures with diverse periodic configurations in different subdomains. In these composite structures, thermo-mechanical coupled behaviors at microscale have an important impact on the macroscopic displacement and temperature fields. Firstly, the novel second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on multiscale asymptotic analysis. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing the SOTS solutions. Furthermore, the error estimate for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method, finite difference method and decoupling method. Finally, some numerical examples are shown, which demonstrate the feasibility and effectiveness of the SOTS numerical algorithm we proposed. In this paper, a unified two-scale computational framework is established for dynamic thermo-mechanical problems of composite structures with diverse periodic configurations in different subdomains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Chen, F., Liu, H., Zhang, S.T.: Coupled heat transfer and thermo-mechanical behavior of hypersonic cylindrical leading edges. Int. J. Heat Mass Transf. 122, 846–862 (2018)

    Article  Google Scholar 

  2. Tsalis, D., Chatzigeorgiou, G., Charalambakis, N.: Effective behavior of thermo-elastic tubes with wavy layers. Compos. Part B Eng. 99, 173–187 (2016)

    Article  Google Scholar 

  3. Cui, J.Z.: The two-scale expression of the solution for the structure with several sub-domains of small periodic configurations. Workshop Sci. Comput. 99, 27–30 (1996)

    Google Scholar 

  4. Cui, J.Z., Shan, Y.J.: Computational Techniques for Materials, Composites and Composite Structures, pp. 255–264. Civil-Comp Press, Edinburgh (2000)

    Book  Google Scholar 

  5. Cui, J.Z.: Proceedings on Computational Mechanics in Science and Engineering, pp. 33–43. Peking University Press, Beijing (2001)

    Google Scholar 

  6. Terada, K., Kurumatani, M., Ushida, T., Kikuchi, N.: A method of two-scale thermo-mechanical analysis for porous solids with micro-scale heat transfer. Comput. Mech. 46, 269–285 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yang, Z.H., Cui, J.Z.: The statistical second-order two-scale analysis for dynamic thermo-mechanical performances of the composite structure with consistent random distribution of particles. Comput. Mater. Sci. 69, 359–373 (2013)

    Article  Google Scholar 

  8. Wang, X., Cao, L.Q., Wong, Y.S.: Multiscale computation and convergence for coupled thermoelastic system in composite materials. SIAM Multiscale Model. Simul. 13, 661–690 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Savatorova, V.L., Talonov, A.V., Vlasov, A.N.: Homogenization of thermoelasticity processes in composite materials with periodic structure of heterogeneities. Z. Angew. Math. Mech. 93, 575–596 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, S., Yang, D.S., Zhang, H.W., Zheng, Y.G.: Coupling extended multiscale finite element method for thermoelastic analysis of heterogeneous multiphase materials. Comput. Struct. 121, 32–49 (2013)

    Article  Google Scholar 

  11. Nasution, M.R.E., Watanabe, N., Kondo, A., Yudhanto, A.: Thermo-mechanical properties and stress analysis of 3-D textile composites by asymptotic expansion homogenization method. Compos. Part B Eng. 60, 378–391 (2014)

    Article  Google Scholar 

  12. Wu, Y.T., Nie, Y.F., Yang, Z.H.: Comparison of four multiscale methods for elliptic problems. CMES-Comput. Model. Eng. Sci. 99, 297–325 (2014)

    MathSciNet  MATH  Google Scholar 

  13. Dong, H., Nie, Y.F., Yang, Z.H., Wu, Y.T.: The numerical accuracy analysis of asymptotic homogenization method and multiscale finite element method for periodic composite materials. CMES-Comput. Model. Eng. Sci. 111, 395–419 (2016)

    Google Scholar 

  14. Oleinik, O.A., Shamaev, A.S., Yosifian, G.A.: Mathematical Problems in Elasticity and Homogenization, pp. 13–38. North-Holland, Amsterdam (1992)

    MATH  Google Scholar 

  15. Xing, Y.F., Du, C.Y.: An improved multiscale eigenelement method of periodical composite structures. Compos. Struct. 118, 200–207 (2014)

    Article  Google Scholar 

  16. Francfort, G.A.: Homogenization and linear thermoelasticity. SIAM J. Math. Anal. 14, 696–708 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang, Z.H., Cui, J.Z., Wu, Y.T., Wang, Z.Q., Wan, J.J.: Second-order two-scale analysis method for dynamic thermo-mechanical problems in periodic structure. Int. J. Numer. Anal. Model. 12, 144–161 (2015)

    MathSciNet  MATH  Google Scholar 

  18. Yang, Z.Q., Cui, J.Z., Sun, Y., Liang, J., Yang, Z.H.: Multiscale analysis method for thermo-mechanical performance of periodic porous materials with interior surface radiation. Int. J. Numer. Methods Eng. 105, 323–350 (2016)

    Article  MathSciNet  Google Scholar 

  19. Feng, Y.P., Cui, J.Z.: Multi-scale analysis and FE computation for the structure of composite materials with small periodic configuration under condition of coupled thermoelasticity. Int. J. Numer. Methods Eng. 60, 1879–1910 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ma, Q., Cui, J.Z.: Second-order two-scale analysis method for the quasi-periodic structure of composite materials under condition of coupled thermo-elasticity. Adv. Mater. Res. 629, 160–164 (2013)

    Article  Google Scholar 

  21. Chatzigeorgiou, G., Efendiev, Y., Charalambakis, N., Lagoudas, D.C.: Effective thermoelastic properties of composites with periodicity in cylindrical coordinates. Int. J. Solids Struct. 49, 2590–2603 (2012)

    Article  Google Scholar 

  22. Li, Z.H., Ma, Q., Cui, J.Z.: Second-order two-scale finite element algorithm for dynamic thermoCmechanical coupling problem in symmetric structure. J. Comput. Phys. 314, 712–748 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  23. Dong, H., Cui, J.Z., Nie, Y.F., Yang, Z.H.: Second-order two-scale computational method for damped dynamic thermo-mechanical problems of quasi-periodic composite materials. J. Comput. Appl. Math. 343, 575–601 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. Dong, H., Nie, Y.F., Cui, J.Z., Yang, Z.H., Wang, Z.Q.: Second-order two-scale analysis method for dynamic thermo-mechanical problems of composite structures with cylindrical periodicity. Int. J. Numer. Anal. Model. 15, 834–863 (2018)

    MathSciNet  MATH  Google Scholar 

  25. Dong, H., Cui, J.Z., Nie, Y.F., Ma, Q., Yang, Z.H.: Multiscale computational method for thermoelastic problems of composite materials with orthogonal periodic configurations. Appl. Math. Model. 60, 634–660 (2018)

    Article  MathSciNet  Google Scholar 

  26. Cioranescu, D., Donato, P.: An Introduction to Homogenization, pp. 221–238. Oxford University Press, Oxford (1999)

    MATH  Google Scholar 

  27. Dong, Q.L., Cao, L.Q.: Multiscale asymptotic expansions methods and numerical algorithms for the wave equations in perforated domains. Appl. Math. Comput. 232, 872–887 (2014)

    MathSciNet  MATH  Google Scholar 

  28. Dong, Q.L., Cao, L.Q.: Multiscale asymptotic expansions methods and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients. Appl. Numer. Math. 59, 3008–3032 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Dong, Q.L., Cao, L.Q., Wang, X., Huang, J.Z.: Multiscale numerical algorithms for elastic wave equations with rapidly oscillating coefficients. Appl. Math. Comput. 336, 16–35 (2018)

    MathSciNet  Google Scholar 

  30. Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures, pp. 165–173. American Mathematical Society, Rhode Island (2011)

    MATH  Google Scholar 

  31. Cao, L.Q.: Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains. Numer. Math. 103, 11–45 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  32. Cao, L.Q., Luo, J.L.: Multiscale numerical algorithm for the elliptic eigenvalue problem with the mixed boundary in perforated domains. Appl. Numer. Math. 58, 1349–1374 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang, X., Wang, T.S., Liu, Y.: Computational Dynamics, pp. 94–118. Tsinghua University Press, Beijing (2007)

    Google Scholar 

  34. Lin, Q., Zhu, Q.D.: The Preprocessing snd Preprocessing for the Finite Element Method, pp. 48–71. Shanghai Scientific & Technical Publishers, Shanghai (1994)

    Google Scholar 

Download references

Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (No. JB180703), the National Natural Science Foundation of China (Nos. 51739007, 11471262 and 11501449), the National Basic Research Program of China (No. 2012CB025904), the State Scholarship Fund of China Scholarship Council (File No. 201606290191), and also supported by the Key Technology Research of FRP-Concrete Composite Structure and Center for high performance computing of Northwestern Polytechnical University.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Hao Dong

  2. School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071, People’s Republic of China

    Xiaojing Zheng

  3. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Junzhi Cui

  4. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, 710129, People’s Republic of China

    Yufeng Nie & Zihao Yang

  5. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Zhiqiang Yang

Authors
  1. Hao Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaojing Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junzhi Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yufeng Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhiqiang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zihao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hao Dong or Zhiqiang Yang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, H., Zheng, X., Cui, J. et al. Multiscale Computational Method for Dynamic Thermo-Mechanical Problems of Composite Structures with Diverse Periodic Configurations in Different Subdomains. J Sci Comput 79, 1630–1666 (2019). https://doi.org/10.1007/s10915-018-00904-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-018-00904-z

Keywords

Search

Navigation