Skip to main content
SpringerLink
Log in

Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity

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

Abstract

A methodology for analyzing the large static deformations of geometrically nonlinear structural systems in the presence of both system parameters uncertainties and model uncertainties is presented. It is carried out in the context of the identification of stochastic nonlinear reduced-order computational models using simulated experiments. This methodology requires the knowledge of a reference calculation issued from the mean nonlinear computational model in order to determine the POD basis (Proper Orthogonal Decomposition) used for the mean nonlinear reduced-order computational model. The construction of such mean reduced-order nonlinear computational model is explicitly carried out in the context of three-dimensional solid finite elements. It allows the stochastic nonlinear reduced-order computational model to be constructed in any general case with the nonparametric probabilistic approach. A numerical example is then presented for a curved beam in which the various steps are presented in details.

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. Capiez-Lernout E, Soize C (2008) Robust design optimization in computational mechanics. ASME J Appl Mech 75(2): 021001-1–021001-11

    Article  MathSciNet  Google Scholar 

  2. Capiez-Lernout E, Soize C (2008) Robust updating of uncertain damping models in structural dynamics for low- and medium-frequency ranges. Mech Syst Signal Process 22(8): 1774–1792

    Article  Google Scholar 

  3. Crisfield M (1997) Non-linear finite element analysis of solids and structures. Essentials, vol 1. Wiley, Chichester

    Google Scholar 

  4. Hodges D, Shang X, Cesnik C (1996) Finite element solution of nonlinear intrinsic equations for curved composite beams. J Am Helicopter Soc 41(4): 313–321

    Article  Google Scholar 

  5. Hollkamp JJ, Gordon RW (2008) Reduced-order models for nonlinear response prediction: implicit condensation and expansion. J Sound Vib 318(4–5): 1139–1153

    Article  Google Scholar 

  6. Huang H, Han Q (2010) Research on nonlinear postbuckling of functionally graded cylindrical shells under radial loads. Comput Struct 92(6): 1352–1357

    Article  MathSciNet  Google Scholar 

  7. Lee SH (ed) (1992) MSC/Nastran handbook for nonlinear analysis, version 67

  8. Lindgaard E, Lund E, Rasmussen K (2010) Nonlinear buckling optimization of composite structures considering “worst” shape imperfections. Int J Solids Struct 47(22-23): 3186–3202

    Article  MATH  Google Scholar 

  9. Mignolet MP, Soize C (2008) Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems. Comput Methods Appl Mech Eng 197: 3951–3963

    Article  MATH  MathSciNet  Google Scholar 

  10. Murthy, R, Wang, X, Mignolet, MP Uncertainty-based experimental validation of nonlinear reduced order models. In: Proceedings of the RASD 2010, Southampton, 12–14 July 2010

  11. Muryavov A, Rizzi S (2003) Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures. Comput Struct 81: 1513–1523

    Article  Google Scholar 

  12. Pai P, Nayfeh A (1994) A fully nonlinear-theory of curved and twisted composite rotor blades accounting for warpings and 3-dimensional stress effects. Int J Solids Struct 31(9): 1309–1340

    Article  MATH  Google Scholar 

  13. Sampaio R, Soize C (2007) Remarks on the efficiency of pod for model reduction in non-linear dynamics of continuous elastic systems. Int J Numerical Methods Eng 72(1): 22–45

    Article  MATH  MathSciNet  Google Scholar 

  14. Schenk C, Schuëller G (2003) Buckling analysis of cylindrical shells with random geometric imperfections. Int J Nonlinear Mech 38(7): 1119–1132

    Article  MATH  Google Scholar 

  15. Schenk C, Schuëller G (2007) Buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections. Comput Methods Appl Mech Eng 196(35–36): 3424–3434

    Article  MATH  Google Scholar 

  16. Sirovich L (1987) Turbulence and the dynamics of coherent structures. Q Appl Math 45(3): 561–571

    MATH  MathSciNet  Google Scholar 

  17. Soize C (2000) A nonparametric model of random uncertainties for reduced matrix models in structural dynamics. Probab Eng Mech 15(3): 277–294

    Article  Google Scholar 

  18. Soize C (2005) A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics. J Sound Vib 288(3): 623–652

    Article  MathSciNet  Google Scholar 

  19. Soize C (2005) Random matrix theory for modeling random uncertainties in computational mechanics. Comput Methods Appl Mech Eng 194(12–16): 1333–1366

    Article  MATH  MathSciNet  Google Scholar 

  20. Soize C, Capiez-Lernout E, Durand JF, Fernandez C, Gagliardini L (2008) Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation. Comput Mech Methods Appl Mech Eng 98(1): 150–163

    Article  Google Scholar 

  21. Tang D, Dowell E (1996) Nonlinear response of a non-rotating rotor blade to a periodic gust. J Fluids Struct 10(7): 721–742

    Article  Google Scholar 

  22. Yvonnet J, Zahrouni H, Potier-Ferry M (2007) A model reduction method for the post-buckling analysis of cellular microstructures. Comput Methods Appl Mech Eng 197: 265–280

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Modélisation et Simulation Multi Échelle, MSME UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77455, Marne-la-Vallée Cedex 02, France

    E. Capiez-Lernout & C. Soize

  2. SEMTE, Faculties of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, 85287-6106, USA

    M. P. Mignolet

Authors
  1. E. Capiez-Lernout
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Soize
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. P. Mignolet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Capiez-Lernout.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Capiez-Lernout, E., Soize, C. & Mignolet, M.P. Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity. Comput Mech 49, 87–97 (2012). https://doi.org/10.1007/s00466-011-0629-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-011-0629-y

Keywords

Search

Navigation