Skip to main content
SpringerLink
Log in

Adaptive multi-analysis strategy for contact problems with friction

Application to aerospace bolted joints

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The objective of the work presented here is to develop an efficient strategy for the parametric analysis of bolted joints designed for aerospace applications. These joints are used in elastic structural assemblies with local nonlinearities (such as unilateral contact with friction) under quasi-static loading. Our approach is based on a decomposition of an assembly into substructures (representing the parts) and interfaces (representing the connections). The problem within each substructure is solved by the finite element method, while an iterative scheme based on the LATIN method (Ladevèze in Nonlinear computational structural mechanics—new approaches and non-incremental methods of calculation, 1999) is used for the global resolution. The proposed strategy consists in calculating response surfaces (Rajashekhar and Ellingwood in Struct Saf 12:205–220, 1993) such that each point of a surface is associated with a design configuration. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestresses) which are introduced into the mechanical analysis. Here, instead of carrying out a full calculation for each point of the surface, we propose to use the capabilities of the LATIN method and reutilize the solution of one problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters) (Boucard and Champaney in Int J Numer Methods Eng 57:1259–1281, 2003). The strategy is adaptive in the sense that it takes into account the results of the previous calculations. The method presented can be used for several types of nonlinear problems requiring multiple analyses: for example, it has already been used for structural identification (Allix and Vidal in Comput Methods Appl Mech Eng 191:2727–2758, 2001).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ladevèze P (1999). Nonlinear computational structural mechanics– new approaches and non-incremental methods of calculation. Springer, Heidelberg

    MATH  Google Scholar 

  2. Rajashekhar M-R and Ellingwood B-R (1993). A new look at the response surface approach for reliability analysis. Struct Saf 12: 205–220

    Article  Google Scholar 

  3. Boucard P-A and Champaney L (2003). A suitable computational strategy for the parametric analysis of problems with multiple contact. Int J Numer Methods Eng 57: 1259–1281

    Article  MATH  Google Scholar 

  4. Allix O and Vidal P (2001). A new multi-solution approach suitable for structural identification problems. Comput Methods Appl Mech Eng 191: 2727–2758

    Article  MathSciNet  Google Scholar 

  5. Benaroya H and Rehak M (1998). Finite element methods in probabilistic structural analysis: a selective review. Appl Mech Rev 41(5): 201–213

    Article  Google Scholar 

  6. Blanzé C, Champaney L and Védrine P (2000). Contact problems in the design of a superconducting quadrupole prototype. Eng Comput 17(2/3): 136–153

    MATH  Google Scholar 

  7. Blanzé C, Champaney L, Cognard J-Y and Ladevèze P (1995). A modular approach to structure assembly computations. Application to contact problems. Eng Comput 13(1): 15–32

    Google Scholar 

  8. Zhong Z and Mackerle J (1992). Static contact problems: a review. Eng Comput 9: 3–37

    Article  MathSciNet  Google Scholar 

  9. Wriggers P (1995). Finite element algorithms for contact problems. Arch Comput Methods Eng 2: 1–49

    Article  MathSciNet  Google Scholar 

  10. Kikuchi N (1982) Penalty/finite element approximations of a class of unilateral contact problems. In: Penalty method and finite element method. ASME, New York

  11. Armero F and Petz E (1998). Formulation and analysis of conserving algorithms for dynamic contact/impact problems. Comput Methods Appl Mech Eng 158: 269–300

    Article  MATH  Google Scholar 

  12. Alart P and Curnier A (1991). A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92: 253–375

    Article  MathSciNet  Google Scholar 

  13. Arora J-S, Chahande A-I and Paeng J-K (1991). Multiplier methods for engineering optimization. Int J Numer Methods Eng 32: 1485–1525

    Article  MathSciNet  MATH  Google Scholar 

  14. Klarbring A (1992) Mathematical programming and augmented lagrangian methods for frictional contact problems. In: Curnier A (ed) Proceedings of the Contact Mechanics International Symposium, Presses Polytechniques et Universitaires Romandes, pp 409–422

  15. Radi B, Baba O-A and Gelin J-C (1998). Treatment of the frictional contact via a Lagrangian formulation. In: Rodin, E-Y and Shillor, M (eds) Mathematical and Computer Modelling, vol 28., pp 407–412. Pergamon Press, Oxford

    Google Scholar 

  16. Chabrand P, Dubois F and Raous M (1998). Various numerical methods for solving unilateral contact problems with friction. In: Rodin, E-Y and Shillor, M (eds) Mathematical and Computer Modelling, vol 28., pp 97–108. Pergamon Press, Oxford

    Google Scholar 

  17. Arrow K-J, Hurwicz L and Uzawa H (1998). Studies in nonlinear programming. University Press, Stanford

    Google Scholar 

  18. Simo J-C and Laursen T-A (1992). An augmented lagrangian treatment of contact problems involving friction. Comput Struct 42: 97–116

    Article  MathSciNet  MATH  Google Scholar 

  19. Champaney L, Cognard J-Y and Ladevze P (1999). Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions. Comput Struct 73: 249–266

    Article  MATH  Google Scholar 

  20. Cocu M, Pratt E and Raous M (1996). Formulation and approximation of quasistatic frictional contact. Int J Eng Sci 34: 783–798

    Article  MathSciNet  MATH  Google Scholar 

  21. Hild P (2002). On finite element uniqueness studies for Coulomb’s frictional contact model. Int J Appl Math Comput Sci 12: 41–50

    MathSciNet  MATH  Google Scholar 

  22. Lions P-L (1990) On the Schwartz alternating method III: a variant for non-overlapping subdomains. In: Chan T, Glowinski R, Périaux J, Windlun O (eds) Proceedings of the 3rd Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia, pp 202–223

  23. Glowinski R, Le Tallec P (1990) Augmented lagrangian interpretation of the non-overlapping Schwarz alternating method. In: Glowinski R, Périaux J, Widlund O-B (eds) Proceedings of the 3rd Conference on Domain Decomposition Methods, SIAM, Philadelphia, pp 224–231

  24. Zavarise G and Wriggers P (1999). A super linear convergent augmented lagragian procedure for contact problems. Eng Comput 16(1): 88–119

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LMT-Cachan, (ENS Cachan/CNRS/Universite Paris 6/UniverSud Paris), 61 av. du President Wilson, 94230, Cachan, France

    L. Champaney & P. -A. Boucard

  2. EADS-IW, 18, rue Marius Terce-BP 13050, 31025, Toulouse Cedex 03, France

    S. Guinard

Authors
  1. L. Champaney
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. -A. Boucard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Guinard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. -A. Boucard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Champaney, L., Boucard, P.A. & Guinard, S. Adaptive multi-analysis strategy for contact problems with friction. Comput Mech 42, 305–315 (2008). https://doi.org/10.1007/s00466-007-0213-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-007-0213-7

Keywords

Search

Navigation