Identification of Defects in an Elastic Body by Means of the Boundary Measurements

Abstract:

Article Preview

A problem of identification of a single defect (a crack, a cavity or an inclusion) in an anisotropic, linear elastic body using boundary measurements is considered. An analytical solution of the problem of ellipsoidal defect identification in an infinite elastic solid is presented in the conditions when arbitrary constant stresses are applied at the infinity and the loads and displacements are known on a closed surface, containing the defect inside. The problem is solved using reciprocity gap functional method. The obtained analytical solution is used for solving the problem of ellipsoidal defect identification in a bounded elastic body by means of the results of one static test. It is assumed that the loads and displacements are measured on the external boundary of the body. Numerical examples illustrating efficiency of the developed method are considered. Stability of the results relative to the noise in the data and variation of the defect shape is studied.

Info:

Periodical:

Edited by:

Robert V. Goldstein, Dr. Yeong-Maw Hwang, Yeau Ren Jeng and Cho-Pei Jiang

Pages:

101-110

Citation:

E.I. Shifrin and P. S. Shushpannikov, "Identification of Defects in an Elastic Body by Means of the Boundary Measurements", Key Engineering Materials, Vol. 528, pp. 101-110, 2013

Online since:

November 2012

Export:

Price:

$38.00

[1] W.D. Keat, M.C. Larson, M.A. Verges, Inverse method of identification for three-dimensional subsurface cracks in a half-space, Int. J. Fract. 92 (1998) 253-270.

[2] M. Engelhardt, M. Schanz, G.E. Stavroulakis, H. Antes, Defect identification in 3-D elastostatics using a genetic algorithm, Optim. Eng. 7 (2006) 63-79.

DOI: https://doi.org/10.1007/s11081-006-6591-4

[3] H. Ben Ameur, M. Burger, B. Hackl, Cavity identification in linear elasticity and thermoelasticity, Math. Meth. Appl. Sci. 30 (2007) 625-647.

DOI: https://doi.org/10.1002/mma.772

[4] M. Khodadd, M. Dashti Ardakani, Investigating the effect of different boundary conditions on the identification of a cavity inside solid bodies, Int. J. Advanced Design and Manufacturing Technology. 4 (2011) 9-17.

[5] H. Ammari, H. Kang, G. Nakamura, K. Tanuma, Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion, J. Elasticity. 67 (2002) 97-129.

[6] S. Andrieux, A. Ben Abda, H. Bui, Reciprocity principle and crack identification, Inverse. Probl. 15 (1999) 59-65.

DOI: https://doi.org/10.1088/0266-5611/15/1/010

[7] R.V. Goldstein, E.I. Shifrin, P.S. Shushpannikov, Application of invariant integrals to the problems of defect identification, Int. J. Fract. 147 (2007) 45-54.

DOI: https://doi.org/10.1007/s10704-007-9125-y

[8] E.I. Shifrin, P.S. Shushpannikov, Identification of a spheroidal defect in an elastic solid using a reciprocity gap functional, Inverse. Probl. 26 (2010) 055001.

DOI: https://doi.org/10.1088/0266-5611/26/5/055001

[9] E.I. Shifrin, Ellipsoidal defect identification in an elastic body from the results of a uniaxial tension (compression) test, Mech. Sol. 45 (2010) 417-426.

DOI: https://doi.org/10.3103/s002565441003012x

[10] E.I. Shifrin, P.S. Shushpannikov, Identification of an ellipsoidal defect in an elastic solid using boundary measurements, Int. J. Solids and Struct. 48 (2011) 1154-1163.

DOI: https://doi.org/10.1016/j.ijsolstr.2010.12.016

[11] A. Morassi, E. Rosset, Detecting rigid inclusions, or cavities, in an elastic body, J. Elasticity. 73 (2003) 101-126.

DOI: https://doi.org/10.1023/b:elas.0000029955.79981.1d

[12] G. Alessandrini, A. Bilotta, G. Formica, A. Morassi, E. Rosset, E. Turco, Evaluating the volume of a hidden inclusion in an elastic body, J. Comput. Appl. Math. 198 (2007) 288-306.

DOI: https://doi.org/10.1016/j.cam.2005.09.024

[13] J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. A241 (1957) 376-396.

[14] R.J. Asaro, Somigliana dislocations and internal stresses: with application to second phase hardening, Int. J. Engineering Science. 13 (1975) 271-286.

DOI: https://doi.org/10.1016/0020-7225(75)90035-x

[15] E.S. Fisher, C.J. Renken, Single-crystal elastic moduli and the hcp-bcc transformation in Ti, Zr and Hf, Phys. Rev. A 135 (1964) 482-494.

DOI: https://doi.org/10.1103/physrev.135.a482