Definitions
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...
References
Abrate S (2001) Modeling of impacts on composite structures. Composite Struct 51:129–138
McConnel AJ (1957) Application of tensor analysis. Dover Publications, New York
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/10.1115/1.3005096
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/BF01176816
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/10.1177/0583102407080410
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-x
Rossikhin YA, Shitikova MV, Shamarin VV (2011) Dynamic response of spherical shells impacted by falling objects. Int J Mech 5(3):166–181
Thomas TY (1961) Plastic flow and fracture in solids. Academic Press, New York
Timoshenko SP (1936) Theory of elastic stability. McGrow-Hill, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2019 Springer-Verlag GmbH Germany, part of Springer Nature
About this entry
Cite this entry
Rossikhin, Y., Shitikova, M. (2019). Ray Expansions in Impact Interaction Problems. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_99-1
Download citation
DOI: https://doi.org/10.1007/978-3-662-53605-6_99-1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53605-6
Online ISBN: 978-3-662-53605-6
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering