On Necessary and Sufficient Conditions for Wedging in Two Contact Node System

  • Sangkyu Kim
  • Yong Hoon JangEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


A necessary and sufficient condition for wedging in two node system is explored. When external loading is zero, wedging is possible if and only if the constraint vectors consisting of contact stiffness and coefficient of friction, directing either admissible or inadmissible region, are positive linear dependent. This condition is validated by comparing with the conventional necessary condition.


Wedging Necessary and Sufficient Condition Positively Linear Dependence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We are pleased to acknowledge support from the National Research Foundation of Korea (NRF) funded by the Korea government (MSIP) (Y.H. Jang and S.K Kim, Grant No. 2018R1A2B6008891).


  1. 1.
    Klarbring, A.: Examples of non-uniqueness and non-existence of solutions to quasi-static contact problems with friction. Ingenieur-Archiv, 60, 529–541, (1990).Google Scholar
  2. 2.
    Ahn, Y. J., Bertocchi, E., and Barber, J. R.: Shakedown of coupled two dimensional discrete frictional systems. Journal of the Mechanics and Physics of Solids, 56, 3433–3440, (2008).Google Scholar
  3. 3.
    Ahn, Y. J.: Discontinuity of quasi-static solution in the two-node coulomb frictional system. International Journal of Solids and Structures, 47, 2866–2871, (2010).Google Scholar
  4. 4.
    Andersson, L-E. Barber, J. R., and Ahn, Y-J.: Attractors in frictional systems subjected to periodic loads. SIAM Journal of Applied Mathematics, 73, 1097–1116, (2013).Google Scholar
  5. 5.
    Andersson, L-E. Barber, J. R., and Ponter, A. R. S.: Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions. International Journal of Solids and Structures, 51, 3710–3714, (2014).Google Scholar
  6. 6.
    Barber, J.R., Hild, P., 2006. On wedged configurations with Coulomb friction. In: Wriggers, Peter, Nackenhorst, Udo (eds.), ANALYSIS AND SIMULATION OF CONTACT PROBLEMS, pp. 205–213. Springer-Verlag, Berlin. (2006).Google Scholar
  7. 7.
    Klarbring, A. Contact, friction, discrete mechanical structures and discrete frictional systems and mathematical programming. In P. Wriggers and P. Panagiotopoulos (eds), NEW DEVELOPMENTS IN CONTACT PROBLEMS, pp. 55-100. Springer, Wien, (1999)..Google Scholar
  8. 8.
    Davis. C.: Theory of positive linear dependence, American Journal of Mathematics, 76:733-746, (1954).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringYonsei UniversitySeoulRepublic of Korea

Personalised recommendations