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Numerical Model for Elastic Contact Simulation

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Abstract

Recently, interest has been growing among the engineering community to develop predictive models for the effect of joints on the tribology of jointed structures. The ability to predict contact forces and force-displacement relations of joints is key in enabling simulations to predict forced response and wear of jointed structures. Only for a limited number of contact geometries has a solution in closed-form been found, and it is available in literature. The finite element method has been used to a great extent to solve problems of elastic bodies in contact, but the iterative solution of large models is very demanding. This work deals with the development of a numerical procedure that utilizes the stiffness matrices of the bodies in contact modeled with the finite element method. The matrices are reduced with a lossless static reduction, and their small dimensions make the iterative solution of the contact problem very fast. Results are compared with contact models found in literature and the sample results agree well with corresponding exact solutions.

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References

  1. Hertz H (1882) Über die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik 92:156–171

    MATH  MathSciNet  Google Scholar 

  2. Signorini A (1933) Sopra alcune questioni di elastostatica, Atti della Società Italiana per il Progresso delle Scienze (in Italian)

    Google Scholar 

  3. Signorini A (1959) Questioni di elasticità non linearizzata e semilinearizzata. Rendiconti di Matematica e delle sue applicazioni 18:95–139 (in Italian)

    MathSciNet  Google Scholar 

  4. Fichera G (1964) Problemi elastostatici con vincoli unilaterali: il problema di signorini con ambigue condizioni al contorno, Memorie della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali (in Italian) 7(2): 91–140

    Google Scholar 

  5. Duvaut G, Lions J (1972) Les inéquations en mécanique et en physique. Dunod, Paris

    MATH  Google Scholar 

  6. Kalker JJ (1977) Variational principles of contact elastostatics. J Inst Math Appl 20(2):199–219

    Article  MathSciNet  Google Scholar 

  7. Duvaut G, Lions JL (1971) Elasticité avec frottement. J de Mécanique 10:409–420

    MATH  MathSciNet  Google Scholar 

  8. Kalker JJ (1979) The computation of three-dimensional rolling contact with dry friction. Intern J Numer Meth Eng 14(9):1293–1307

    Article  Google Scholar 

  9. Cattaneo C (1938) Sul contatto di due corpi elastici, Accademia dei Lincei, Rendiconti (in Italian), Serie 6(27): 342–348, 434–436, 474–478

    Google Scholar 

  10. Mindlin RD, Deresiewicz H (1953) Elastic spheres in contact under varying oblique forces. ASME Trans J Appl Mech 20:327–344

    MATH  MathSciNet  Google Scholar 

  11. Deresiewicz H (1957) Oblique contact of nonspherical elastic bodies. J Appl Mech 24(4):623–624

    Google Scholar 

  12. Ciavarella M, Hills D, Monno G (1998) The influence of round edges on the indentation by a flat punch. Proc Inst Mech Eng Part C J Mech Eng Sci 212:319–328

    Article  Google Scholar 

  13. Conry TF, Seireg A (1971) A mathematical programming method for design of 190 elastic bodies in contact. J Appl Mech 38:387–392

    Article  Google Scholar 

  14. Chan S, Tuba IS (1971) A finite element method for contact problems of solid bodies – Part I. Theory and validation. Int J Mech Sci 13:615–625

    Article  MATH  Google Scholar 

  15. Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380–380

    Article  MATH  Google Scholar 

  16. Johnson KL (1985) Contact Mechanics. Cambridge: Cambridge University Press

    Google Scholar 

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Correspondence to D. Botto .

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© 2016 The Society for Experimental Mechanics, Inc.

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Botto, D., Lavella, M. (2016). Numerical Model for Elastic Contact Simulation. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15221-9_37

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  • DOI: https://doi.org/10.1007/978-3-319-15221-9_37

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15220-2

  • Online ISBN: 978-3-319-15221-9

  • eBook Packages: EngineeringEngineering (R0)

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