Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Ray Expansions in Impact Interaction Problems

  • Yury A. Rossikhin
  • Marina V. ShitikovaEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_99-1



The impact interaction problems are those connected with the shock interactions of bodies subjected to the contact law.

Preliminary Remarks

The problems connected with the analysis of the shock interaction of thin bodies (rods, beams, plates, and shells) with other bodies have widespread application in various fields of science and technology. The physical phenomena involved in the impact event include structural responses, contact effects, and wave propagation. These problems are topical not only from the point of view of fundamental research in applied mechanics but also with respect to their applications. Because these problems belong to the problems of dynamic contact interaction, their solution is connected with severe mathematical and calculation difficulties. To overcome this impediment, a rich variety of approaches and methods have been suggested, and the overview of current...

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


  1. Abrate S (2001) Modeling of impacts on composite structures. Composite Struct 51:129–138CrossRefGoogle Scholar
  2. McConnel AJ (1957) Application of tensor analysis. Dover Publications, New YorkGoogle Scholar
  3. Rossikhin YA, Shitikova MV (1995a) Ray method for solving dynamic problems connected with propagation on wave surfaces of strong and weak discontinuities. Appl Mech Rev 48(1):1–39. https://doi.org/10.1115/1.3005096CrossRefGoogle Scholar
  4. Rossikhin YA, Shitikova MV (1995b) The ray method for solving boundary problems of wave dynamics for bodies having curvilinear anisotropy. Acta Mech 109(1–4): 49–64. https://doi.org/10.1007/BF01176816MathSciNetCrossRefGoogle Scholar
  5. Rossikhin YA, Shitikova MV (2007a) Transient response of thin bodies subjected to impact: wave approach. Shock Vibr Digest 39(4):273–309. https://doi.org/10.1177/0583102407080410CrossRefGoogle Scholar
  6. Rossikhin YA, Shitikova MV (2007b) The method of ray expansions for investigating transient wave processes in thin elastic plates and shells. Acta Mech 189(1–2): 87–121. https://doi.org/10.1007/S00707-006-0412-xCrossRefGoogle Scholar
  7. Rossikhin YA, Shitikova MV, Shamarin VV (2011) Dynamic response of spherical shells impacted by falling objects. Int J Mech 5(3):166–181Google Scholar
  8. Thomas TY (1961) Plastic flow and fracture in solids. Academic Press, New YorkzbMATHGoogle Scholar
  9. Timoshenko SP (1936) Theory of elastic stability. McGrow-Hill, New YorkGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Research Center on Dynamics of Solids and StructuresVoronezh State Technical UniversityVoronezhRussia

Section editors and affiliations

  • Marina V. Shitikova
    • 1
  1. 1.Research Center on Dynamics of Solids and StructuresVoronezh State Technical UniversityVoronezhRussia