Skip to main content
SpringerLink
Log in

Unilateral Crack Identification: A Filter-Driven, Iterative, Boundary Element Approach

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

An identification problem for parametric variational inequalities and linear com-plementarity problems is solved here by means of iterative filter techniques. A concrete application in engineering mechanics, the unilateral crack identification problem, is solved. The elastic contact problem is formulated by boundary element-linear complementarity techniques. By means of numerical results and comparison with previous approaches based on optimization and neural networks it is shown that this method is advantageous. In view of the difficulty of the considered bilevel optimization problem, this approach may be of interest for other applications as well.

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. Alessandri, C. and Mallardo, V. (1999), Crack identification in two-dimensional unilateral contact mechanics with the boundary element method. Computational Mechanics 24(2): 100-109.

    Google Scholar 

  2. Antes, H. (1988), Anwendungen der Methode der Randelemente in der Elastodynamik und der Fluiddynamik. B.G. Teubner Verlag, Stuttgart.

    Google Scholar 

  3. Antes, H. and Panagiotopoulos, P.D. (1992), The boundary integral approach to static and dynamic contact problems. Equality and inequality methods. Birkhauser, Basel-Boston-Berlin.

    Google Scholar 

  4. Antes, H. Steinfeld, B. and Trondle, G. (1991), Recent developments in dynamic stress analyses by time domain BEM. Engineering Analysis with Boundary Elements 8(4): 176-184.

    Google Scholar 

  5. Aoki, S., Amaya, K., Sahashi, M. and Nakamura, T. (1997), Identification of Gurson's material constants by using Kalman filter. Computational Mechanics 19: 501-506.

    Google Scholar 

  6. Bittanti, S., Maier, G. and Nappi, A. (1984), Inverse problems in structural elastoplasticity: A Kalman filter approach. In A. Sawczuk and G. Bianchi (eds.), Plasticity Today. Modelling, Methods and Applications, pp. 311-329. Elsevier Applied Science Publishers, London and New York.

    Google Scholar 

  7. Brebbia, C.A. and Dominguez, J. (1989), Boundary Elements. An introductory course. Computational Mechanics Publications and McGraw-Hill Book Co., Southampton.

    Google Scholar 

  8. Brogliato, B. (1997), Nonsmooth mechanics. Models, dynamics and control (2nd edn.). Springer Verlag, Berlin.

    Google Scholar 

  9. Catlin, D.E. (1989), Estimation, control and the discrete Kalman filter. Springer Verlag, Berlin.

    Google Scholar 

  10. Chen, T.-F., Lin, S. and Wang, J.C.Y. (1996), an application of Kalman filter and finite difference scheme to inverse heat conduction problems. Inverse Problems in Engineering 3(1–3): 163-176.

    Google Scholar 

  11. Cividini, A.M., Maier, G. and Nappi, A. (1983), Parameter estimation of a static geotechnical model using a Bayes' approach. Int. J. of Rock Mechanics and Mining Science 20: 215-226.

    Google Scholar 

  12. Cottle, R.W., Pang, J.S. and Stone, R.E. (1992), The linear complementarity problem. Academic Press, Boston.

    Google Scholar 

  13. Dominguez, J. (1993), Boundary elements in dynamics. Computational Mechanics Publications and Elsevier Applied Science, Southampton and New York.

    Google Scholar 

  14. Ferravesi, M., Torini, E. and Vignoli, R. (1996), A solution to the inverse problem in groundwater hydrology based on Kalman filtering. Journal of Hydrology 175(1–4): 567-582.

    Google Scholar 

  15. El Harrouni, K., Ouazar, D., Wrobel, L.C. and Cheng, A.H.-D. (1997), Aquifer parameter estimation by extended Kalman filtering and boundary elements. Engineering Analysis with Boundary Elements 19: 231-237.

    Google Scholar 

  16. Haubrok, D., Steinfeld, B. and Antes, H. (1997), Dynamic contact of elastic bodies with equality and inequality b.e.m. In L. Morino and W.L. Wendland (eds.), Boundary Integral Methods for Nonlinear problems, pages 95-100. Kluwer Academic, Dordrecht, Boston and London.

    Google Scholar 

  17. Hilding, D., Klarbring, A. and Petersson, J. (1999), Optimization of structures in unilateral contact. ASME Applied Mechanics Review 52(4): 139-160.

    Google Scholar 

  18. Kalman, R.E. (1960), A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Engineering 82D: 35-45.

    Google Scholar 

  19. Kalman, R.E. and Bucy, R.S. (1961), Trans. ASME J. Basic Engineering 83D: 95-108.

    Google Scholar 

  20. Lou, K.-N. and Perez, R.A. (1996), A new system identification technique using Kalman filtering and multilayer neural networks. Artificial Intelligence in Engineering 10: 1-8.

    Google Scholar 

  21. Luo, Z.Q., Pang, J.S. and Ralph, D. (1996), Mathematical programs with equilibrium constraints. Cambridge University Press, Cambridge.

    Google Scholar 

  22. Maier, G., Nappi, A. and Cividini, A. (1982), Statistical identification of yield limits in piecewise linear structural models. In G.C. Keramidas and C.A. Brebia (eds), Proc. Int. Conf. on Computational Methods and Experimental Measurements, pages 812-829. Springer Verlag, Berlin.

    Google Scholar 

  23. Pang, J.S., Ferris, M.C. (1997), Engineering and economic applications of complementarity problems. SIAM Review 39(4): 669-713.

    Google Scholar 

  24. Migdalas, A., Pardalos, P.M. and Varbrand, P. (1997), Multilevel optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  25. Mistakidis, E.S. and Stavroulakis, G.E. (1998), Nonconvex optimization in mechanics. Algorithms, heuristics and engineering applications by the F.E.M. Kluwer Academic, Dordrecht, Boston and London.

    Google Scholar 

  26. Murakami, A. and Hasegawa, T. (1993), Inverse problem approach based on the Kalman filtering and its applications. In M. Tanaka and H.D. Bui (eds), IUTAM Conference on Inverse Problems in Engineering Mechanics, Tokyo 1992, pages 529-538. Springer Verlag, Berlin.

    Google Scholar 

  27. Natke, H.G. (1991), Einf uhrung in Theorie und Praxis der Zeitreihen-und Modalanalyse (3rd edn.). Vieweg Verlag, Braunschweig, Wiesbaden.

    Google Scholar 

  28. Oden, J.T. and Kikuchi, N. (1988), Contact problems in elasticity: a study of variational inequalities and finite element methods. SIAM, Philadelphia.

    Google Scholar 

  29. Outrata, J., Kocvara, M. and Zowe, J. (1998), Nonsmooth approach to optimization problems with equilibrium constraints: theory, applications and numerical results. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  30. Panagiotopoulos, P.D. (1985), Inequality problems in mechanics and applications. Convex and nonconvex energy functions. Birkhauser, Basel-Boston-Stuttgart. Russian translation, MIR Publ., Moscow, 1988.

    Google Scholar 

  31. Panagiotopoulos, P.D. (1993), Hemivariational inequalities. Applications in mechanics and engineering. Springer, Berlin-Heidelberg-New York.

    Google Scholar 

  32. Pfeiffer, F. and Glocker, Ch. (1996), Multibody dynamics with unilateral contacts. John Wiley, New York.

    Google Scholar 

  33. Scarpa, F. and Milano, G. (1995), Kalman smoothing technique applied to the inverse heat conduction problem. Numerical Heat Transfer B 28(1): 79-96.

    Google Scholar 

  34. Shimizu, K., Ishizuka, Y. and Bard, J.F. (1996), Nondifferentiable and two-level mathematical programming. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  35. Stavroulakis, G.E. (1995), Optimal prestress of cracked unilateral structures: finite element analysis of an optimal control problem for variational inequalities. Computer Methods in Applied Mechanics and Engineering 123: 231-246.

    Google Scholar 

  36. Stavroulakis, G.E. and Antes, H. (1997), Nondestructive elastostatic identification of unilateral cracks through BEM and neural networks. Computational Mechanics 20(5): 439-451.

    Google Scholar 

  37. Stavroulakis, G.E., Antes, H. and Panagiotopoulos, P.D. (1999), Transient elastodynamics around cracks including contact and friction. Computer Methods in Applied Mechanics and Engineering 177(3/4): 427-440. Special Issue: Computational Modeling of Contact and Friction. J.A.C. Martins and A. Klarbring (eds.).

    Google Scholar 

  38. Tanaka, M., Matsumoto, T. and Oida, S., Identification of unknown boundary shape of rotationally symmetric body in steady heat conduction via BEM and filter theories. In M. Tanaka and G.S. Dulikravich (eds.), Inverse problems in engineering mechanics, pages 121-130. Elsevier Science.

  39. Tanaka, M., Matsumoto, T. and Sakamoto, K., Noise source identification of a railway car model by the boundary element method using sound pressure measurements in 2-D infinite half space. In Proc. of the 3rd Int. Conference on Inverse Problems in Engineering. June 13–18, 1999, Port Ludlow, Washington, USA (to appear).

  40. Tosaka, N., Utani, A. and Takahashi, H. (1995), Unknown defect identification in elastic field by boundary element method with filtering procedure. Engineering Analysis with Boundary Elements 15: 207-215.

    Google Scholar 

  41. Tuan, P.-C., Fong, L.-W. and Huang, W.-T. (1997) Application of Kalman filtering with input estimation technique to online cylindrical inverse heat conduction problems. JSME International Journal Serie B 40(1): 126-133.

    Google Scholar 

  42. Utani, A. and Tosaka, N. (1993), Identification analysis of distributed-parameter systems by using Kalman filter-boundary element method. In M. Tanaka and H.D. Bui (eds.), IUTAM Conference on Inverse Problems in Engineering Mechanics, Tokyo 1992, pages 347-356. Springer Verlag, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mechanics, Carolo Wilhelmina Technical University, Braunschweig, Germany

    G.E. Stavroulakis & H. Antes

Authors
  1. G.E. Stavroulakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Antes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stavroulakis, G., Antes, H. Unilateral Crack Identification: A Filter-Driven, Iterative, Boundary Element Approach. Journal of Global Optimization 17, 339–352 (2000). https://doi.org/10.1023/A:1026550826503

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026550826503

Search

Navigation