A study of the optimal measurement placement for parameter identification of orthotropic composites by the boundary element method

Abstract

This paper concentrates on the design of the optimal measurement placement for the parameter identification of two-dimensional orthotropic composites, which is modeled by the boundary element. From the analysis of the well-posedness of the parameter identification processes using the Levenberg–Marquardt method, a performance indicator and an estimation of the maximum bias of identified parameters are deduced. Based on these results, a method for selecting the optimal measurement placement is proposed. The validity of this method is illustrated by some numerical examples. These examples reveal that the measurement placement has significant influence on identification results. Furthermore, an iterative process of selecting measurement placement is suggested for practical implementation.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34:439–452

    Article  MATH  Google Scholar 

  2. 2.

    Ayorinde EO (1995) Elastic constants of thick orthotropic composite plates. J Compos Mater 29:1025–1039

    Google Scholar 

  3. 3.

    Brebbia CA, Telles JCF, Wrobel LC (1984) Boundary element techniques–-theory and applications in engi. Springer Verlag, Berlin

  4. 4.

    Cunha J, Piranda J (1999) Application of model updating techniques in dynamics for the identification of elastic constants of composite materials. Composites: Part B 30:79–85

    Google Scholar 

  5. 5.

    Cunha J, Piranda J (2000) Identification of stiffness properties of composite tubes from dymanic tests. Exp Mech 40:211–218

    Article  Google Scholar 

  6. 6.

    Deobald LR, Gibson RF (1988) Determination of elastic constants of orthotropic plates by a modal analysis/Rayleigh-Ritz technique. J Sound Vibration 124:269–283

    Article  Google Scholar 

  7. 7.

    Fadale TD, Nenarokomov AV, Emery AF (1995) Two approaches to optimal sensor locations. J Heat Trans 117:373–379

    Article  Google Scholar 

  8. 8.

    Frederiksen PS (1997) Experimental procedure and results for the identification of elastic constants of thick orthotropic plates. J Compos Materials 31:360–382

    Google Scholar 

  9. 9.

    Frederiksen PS (1998) Parameter uncertainty and design of optimal experiments for the estimation of elastic constants. Int J Solids Struct 35:1241–1260

    Article  MATH  Google Scholar 

  10. 10.

    Fällström K-E (1991) Determing material properties in anisotropic plates using Rayleigh's method. Poly Compos 12:306–314

    Article  Google Scholar 

  11. 11.

    Fällström K-E, Jonsson M (1991) A nondestructive method to determine material properties in anisotropic plates. Poly Compos 12:293–305

    Article  Google Scholar 

  12. 12.

    Griffel DH (2002) Applied functional analysis. Dover publications, New York

  13. 13.

    Haftka RT, Scott EP, Cruz JR (1998) Optimization and experiments: a survey. Appl Mech Rev 51:435–448

    Article  Google Scholar 

  14. 14.

    Huang LX, Sun XS, Liu YH, Cen ZZ (2004) Parameter identification for two-dimensional orthotropic material bodies by the boundary element method. Eng Anal Bound Elem 28:109–121

    Article  MATH  Google Scholar 

  15. 15.

    Kavanagh KT (1972) Extension of classical experimental techniques for characterizing composite-material behavior. Exp Mech 12:50–56

    Article  Google Scholar 

  16. 16.

    Kavanagh KT (1973) Experiment versus analysis: computational techniques for the description of static material response. Int J Numer Meth Eng 5:503–515

    Article  Google Scholar 

  17. 17.

    Kavanagh KT, Clough RW (1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7:11–23

    Article  MATH  Google Scholar 

  18. 18.

    Mota Soares CM, Moreira de Freitas M, Araújo AL, Pedersen P (1993) Identification of material properties of composite plate specimens. Compos Struct 25:277–285

    Article  Google Scholar 

  19. 19.

    Moussu F, Nivoit M (1993) Determination of elastic constants of orthotropic plates by a modal analysis/method of superposition. J Sound Vib 165:149–163

    Article  MATH  Google Scholar 

  20. 20.

    Pedersen P, Frederiksen PS (1992) Identification of orthotropic material moduli by a combined experimental/numerical method. Measurement 10:113–118

    Article  Google Scholar 

  21. 21.

    Rikards R, Chate A, Gailis G (2001) Identification of elastic properties of laminates based on experiment design. Int J Solids Struct 38:5097–5115

    Article  MATH  Google Scholar 

  22. 22.

    Rus G, Gallego R (2002) Optimization algorithms for identification inverse problems with the boundary element method. Eng Anal Bound Elem 26:315–327

    Article  MATH  Google Scholar 

  23. 23.

    Wang WT, Kam TY (2000) Material characterization of laminated composite plates via static testing. Compos Struct 50:347–352

    Article  Google Scholar 

  24. 24.

    Xiang ZH, Swoboda G, Cen ZZ (2003) Optimal layout of displacement measurements for parameter identification process in geomechanics. Int J Geomech 3:205–216

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Z. Z. Cen.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Huang, L., Xiang, Z., Sun, X. et al. A study of the optimal measurement placement for parameter identification of orthotropic composites by the boundary element method. Comput Mech 38, 201–209 (2006). https://doi.org/10.1007/s00466-005-0741-y

Download citation

Keywords

  • Parameter identification
  • Optimal measurement placement
  • Boundary element method
  • Orthotropic composites