Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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CONTACT FORCE MODEL FOR A BEAM WITH DISCRETELY SPACED GAP SUPPORTS AND ITS APPROXIMATED SOLUTION

  • Received : 2010.11.12
  • Accepted : 2011.04.11
  • Published : 2011.10.31
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Abstract

This paper proposes an approximated contact force model to identify the nonlinear behavior of a fuel rod with gap supports; also, the numerical prediction of interfacial forces in the mechanical contact of fuel rods with gap supports is studied. The Newmark integration method requires the current status of the contact force, but the contact force is not given a priori. Taylor's expansion can be used to predict the unknown contact force; therefore, it should be guaranteed that the first derivative of the contact force is continuous. This work proposes a continuous and differentiable contact force model with the ability to estimate the current state of the contact force. An approximated convex and differentiable potential function for the contact force is described, and a variational formulation is also provided. A numerical example that considers the particularly stiff supports has been studied, and a fuel rod with hardening supports was also examined for a realistic simulation. An approximated proper solution can be obtained using the results, and abrupt changes from the contacting state to non-contacting state, or vice versa, can be relieved. It can also be seen that not only the external force but also the developed contact force affects the response.

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References

  1. A.J. Molnar, K.M. Vashi, C.W. Gay, "Application of Normal Mode Theory and Pseudoforce Methods to Solve Problems with Nonlinearity", J. Pressure Vessel Tech. 151-156, (1976).
  2. S.W. Shaw, P.J. Holmes, "A Periodically Forced Piecewise Linear Oscillator", J. Sound and Vibration 90(1), 129-155, (1983). https://doi.org/10.1016/0022-460X(83)90407-8
  3. L. Johansson, "Beam Motion with Unilateral Contact Constraints and Wear of Contact Sites", J. Pressure Vessel Tech. 119, 105-110, (1997). https://doi.org/10.1115/1.2842252
  4. Xi Tan, R.J. Rogers, "Simulation of Friction in Multi- Degree-of-Freedom Vibration Systems", J. Dynamic Systems, Measurement, and Control 120, 144-146, (1998). https://doi.org/10.1115/1.2801312
  5. N.P. Hoffmann, "Linear Stability of Steady Sliding in Point Contacts with Velocity Dependent and LuGre Type Friction", J. Sound and Vibration 301, 1023-1034, (2006).
  6. M.A. Savi, S. Divenyi, L.F.P. Franca, H.I. Weber, "Numerical and Experimental Investigations of the Nonlinear Dynamics and Chaos in Non-smooth Systems", J. Sound and Vibration 301, 59-73, (2006).
  7. L. Baillet, S. D'Errico, B. Laulagnet, "Understanding the Occurrence of Squealing Noise Using the Temporal Finite Element Method", J. Sound and Vibration 292, 443-460, (2005).
  8. J. Knudsen, A. R. Massih, "Vibro-Impact Dynamics of a Periodically Forced Beam", J. Pressure Vessel Tech. 122, 210-221, (2000). https://doi.org/10.1115/1.556175
  9. Y.B. Gessesse, M.H. Attia, M.O.M. Osman, "On the Mechanics of Crack Initiation and Propagation in Elasto-Plastic Materials in Impact Fretting Wear", J. Tribology 126, 393-403, (2004).
  10. F. Axisa, J. Antunes, B. Villard, "Overview of Numerical Methods for Predicting Flow-Induced Vibration", J. Pressure Vessel Tech. 110, 6-14, (1988). https://doi.org/10.1115/1.3265570
  11. J.A. Turner, "Non-linear Vibrations of a Beam with Cantilever-Hertzian Contact Boundary Conditions", J. Sound and Vibration 275, 177-191, (2004). https://doi.org/10.1016/S0022-460X(03)00791-0
  12. M.A. Hassan, D.S. Weaver, M.A. Dokainish, "The Effects of Support Geometry on the Turbulence Response of Loosely Supported Heat Exchanger Tubes", J. Fluids and Structures 18, 529-554, (2003). https://doi.org/10.1016/j.jfluidstructs.2003.08.011
  13. M.A. Hassan, D.S. Weaver, M.A. Dokainish, "A New Tube/Support Impact Model for Heat Exchanger Tubes", J. Fluids and Structures 21, 561-577, (2005). https://doi.org/10.1016/j.jfluidstructs.2005.07.016
  14. K. Blakely, W.B. Walton, "Modeling of Nonlinear Elastic Structures Using MSC/NASTRAN", MSC World User's Conference, (1983).
  15. J. N. Reddy, "An Introduction to Nonlinear Finite element Analysis", Oxford, (2005).
  16. G. Duvaut, J.L. Lions, "Inequalities in Mechanics and Physics", Springer-Velag, (1976).
  17. N. Kikuchi, J.T. Oden, "Contact Problems in Elasticity; A Study of Variational Inequalities and Finite element Methods", SIAM, (1988).
  18. A. Dimarogonas, "Vibration for Engineer", Prentice Hall, (1996).
  19. M.K. Au-Yang, "Flow-Induced Vibration of Power and Process Plant Components", Professional Engineering Publishing, (2001).
  20. C.E. Taylor, M.J. Pettigrew, F. Axisa, B. Villard, "Experimental Determination of Single and Two-phase Cross Flow-Induced Forces on Tube Rows", J. Pressure Vessel Tech. 110, 22-28, (1988). https://doi.org/10.1115/1.3265563
  21. N.W. Mureithi, S.J. Price, M.P. Paidoussis, "The Post-hopfbifurcation Response of a Loosely Supported Cylinder in an Array Subjected to Cross-flow-part I: Experimental Results", J. Fluids and Structures 8(8), 833-852, (1994). https://doi.org/10.1006/jfls.1994.1060
  22. T.J.R. Hughes, "The Finite Element Method", Dover Publications, (1987).
  23. O. Axelsson, "Finite Element Solution of Boundary Value Problems", Academic Press, (1984).