Elastic contact problems involving Euler-Bernoulli beams or Kirchhoff plates generally involve concentrated contact forces. Linear elasticity (e.g. finite element) solutions of the same problems show that finite contact regions are actually developed, but these regions have dimensions that are typically of the order of the beam thickness. Thus if beam theory is appropriate for a given structural problem, the local elasticity fields can be explored by asymptotic methods and will have fairly general (problem independent) characteristics. Here we show that the extent of the contact region is a fixed ratio of the beam thickness which is independent of the concentrated load predicted by the beam theory, and that the distribution of contact pressure in this region has a universal form, which is well approximated by a simple algebraic expression.
Bibliographical noteFunding Information:
We are pleased to acknowledge support from the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Y.H. Jang and J.H. Kim, Grant No. 2012R1A1A2042106 ), and the Ministry of Science ICT and Future Planning (Y.-J. Ahn, Grant No. 2014R1A1A1004186 ).
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics