• Igor V. AndrianovEmail author
  • Jan AwrejcewiczEmail author
  • Vladyslav V. DanishevskyyEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 77)


“Similar ideas could be applied for many different applications” - this ritual phrase appears in majority of conclusions of many papers and monographs, and this is valid also in our case.


  1. 1.
    Findlin, A.Ya. 2007. Peculiarities of the use of computational methods in applied mathematics 108 (on global computerization and common sense). In Blekhman, I.I., A.D. Myshkis, and Ya.G. Panovko. 2007. Applied Mathematics: Subject, Logic, Peculiarities of approaches. With Examples from Mechanics. Moscow: URSS, 350–358 (in Russian).Google Scholar
  2. 2.
    Andrianov, I.V., A.A. Diskovsky, and E. Syerko. 2017. Optimal design of a circular diaphragm using the homogenization approach. Mathematics and Mechanics of Solids 22(3): 283-3030.Google Scholar
  3. 3.
    Andrianov, I.V., J. Awrejcewicz, and A.A. Diskovsky. 2013. Sensitivity analysis in design of constructions made of functionally graded materials. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227 (1): 19–28.Google Scholar
  4. 4.
    Andrianov, I.V., V.I. Bolshakov, V.V. Danishevs’kyy, and D. Weichert. 2008. Higher order asymptotic homogenization and wave propagation in periodic composite structures. Proceedings of the Royal Society of London A 464: 1181–1201.CrossRefzbMATHGoogle Scholar
  5. 5.
    Fleck, N.A., V.S. Deshpande, and M.F. Ashby. 2010. Micro-architectured materials: past, present and future. Proceedings of the Royal Society of London A 466 (2121): 2495–2516.CrossRefGoogle Scholar
  6. 6.
    Ghosh, S., and M. Arroyo. 2013. An atomistic-based foliation model for multilayer graphene materials and nanotubes. Journal of the Mechanics and Physics of Solids 61: 235–253.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kalamkarov, A.L., and A.V. Georgiades. 2002. Modeling of smart composites on account of actuation. Thermal Conductivity and Hygroscopic Absorption, Composites, Part B 33 (2): 141–152.Google Scholar
  8. 8.
    Lurie, K.A. 2007. An introduction to the mathematical theory of dynamic materials. Berlin: Springer.zbMATHGoogle Scholar
  9. 9.
    Perrins, W.T., and R.C. McPhedran. 2010. Metamaterials and the homogenization of composite materials. Metamaterials 4: 24–31.CrossRefGoogle Scholar
  10. 10.
    Suresh, S., and A. Mortensen. 1998. Fundamentals of functionally graded materials. London: Institute of Materials.Google Scholar
  11. 11.
    Chen, W.-Q. 2014. The renaissance of continuum mechanics. Journal of Zhejiang University—Science A (Applied Physics and Engineering) 15 (4): 231–240.Google Scholar
  12. 12.
    Willis, J.R. 1983. The overall elastic response of composite materials. Journal of Applied Mechanics 50: 1202–1209.Google Scholar
  13. 13.
    Ferguson, E.S. 1993. How engineers lose touch. Invention and Technology 8 (3): 16–24.Google Scholar
  14. 14.
    Gleik, J. 1987. Chaos: Making a new science. Viking: Penguin.Google Scholar
  15. 15.
    Andrianov, I.V., and L.I. Manevitch. 2002. Asymptotology: Ideas, methods, and applications. Dordrecht, Boston, London: Kluwer Academic Publishers.CrossRefGoogle Scholar
  16. 16.
    Tayler, A.B. 2001. Mathematical models in applied mechanics. Oxford: Clarendon Press.zbMATHGoogle Scholar
  17. 17.
    Andrianov, I., and J. Awrejcewicz. 2013. Methods of asymptotic analysis and synthesis in nonlinear dynamics and mechanics of solids. Moscow-Izhevsk: Institute of Computer Researches. (in Russian).Google Scholar
  18. 18.
    Andrianov, I.V., J. Awrejcewicz, V.V. Danishevs’kyy, and A.O. Ivankov. 2014. Asymptotic methods in the theory of plates with mixed boundary conditions. Chichester: Wiley.CrossRefzbMATHGoogle Scholar
  19. 19.
    Andrianov, I.V., J. Awrejcewicz, and L.I. Manevitch. 2004. Asymptotical mechanics of thin-walled structures: A handbook. Berlin, Heidelberg: Springer-Verlag.CrossRefGoogle Scholar
  20. 20.
    Nayfeh, A.H. 1981. Introduction to Perturbation Techniques. New York: Wiley & Sons.Google Scholar
  21. 21.
    Bauer, S.M., S.B. Filippov, A.L. Smirnov, P.E. Tovstik, and R. Vaillancourt. 2015. Asymptotic methods in mechanics of solids. Birkhäuser.Google Scholar
  22. 22.
    Hinch, E.J. 1991. Perturbation methods. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  23. 23.
    Villaggio, P. 2013. Crisis of mechanics literature? Meccanica 48: 765–767.CrossRefzbMATHGoogle Scholar
  24. 24.
    Christensen, R.M. 2005. Mechanics of composite materials. Mineola, New York: Dover Publications.Google Scholar
  25. 25.
    Hashin, Z. 1983. Analysis of composite materials—a survey. Journal of Applied Mechanics 50: 481–505.CrossRefzbMATHGoogle Scholar
  26. 26.
    Milton, G.W. 2002. The theory of composites. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  27. 27.
    Pobedrya, B.Ye. 1984. Mechanics of composite materials. Moscow: MGU.zbMATHGoogle Scholar
  28. 28.
    Torquato, S. 2002. Random heterogeneous materials. Microstructure and Macroscopic Properties. New York: Springer.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institut für Allgemeine MechanikRWTH Aachen UniversityAachenGermany
  2. 2.Automation, Biomechanics and MechatronicsLodz University of TechnologyŁódźPoland
  3. 3.School of Computing and MathematicsKeele UniversityKeeleUK

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