Email this article The boundary integral equation based method for damages detection in multilayered elastic structures
DOI: https://doi.org/10.20528/cjsmec.2016.03.007
View Counter: Abstract | 1677 times | ‒ Full Article | 448 times |
Full Text:
PDFAbstract
For two kinds of defects – delamination and transversal failure in the multilayer composite the damages detection method is proposed. The inverse geometrical problems of crack’s parameters reconstruction were formulated as a sequence of boundary integral equations (BIE). These boundary integral equations were derived on the basis of the principle of works mutuality applied to the problem of the composite specimen stationary oscillations. To solve the integral equations the finite element method, the boundary element method, and the Tikhonov regularization method were used. As complementary information for inverse problems solving the displacement field measured on a mechanical stress free area of the specimen’s surface was served. The numerical examples of the interfacial cracks and transversal failure of the internal layers in the multilayered composite were considered in the framework of two-dimensional elasticity.
Keywords
References
Bannour T, Ben Abda A, Jaoua M (1997). A semi-explicit algorithm for the reconstruction of 3D planar cracks. Inverse Problem, 13, 899-917.
http://dx.doi.org/10.1088/0266-5611/13/4/002
Belokon AV, Eremeev VA, Nasedkin AV, Soloviev AN (2000). The block schemes of a finite element method for dynamic problems of acousto-electro-elasticity. Applied Mathematics & Mechanics, 64(3), 381-393 (in Russian).
Kozlov VA, Mazya VG, Fomin, VG (1991). Iterative method for cauchi problem resolving for elliptic equations. Computational Mathematics and Mathematical Physics, 31, 45-52 (in Russian).
Nowacki W (1970). Teoria Sprezystosci. Panstwowe Wydawnictwo Naukowe, Warszawa (in Polish).
Rjasanow S, Steinbach O (2007). The Fast Solution of Boundary Integral Equations. Springer ed., 284.
Soloviev AN (2002). Identification of interfacial flaws. Proceedings on the VIII International Scientific Conference "Modern Problems of Continuum Media Mechanics", Rostov-on-Don, 1, 163-169.
Tikhonov AN, Arsenin VY (1979). Methods for Non-Correct Problems Resolving. Science ed., Moscow (in Russian).
Vatulyan AO, Soloviev AN (2003). Determination of plane flaws orientation in elastic body. Theoretical an Applied Mechanics, (37), 141-145 (in Russian).
Vatulyan AO, Soloviev AN (2004). On the defects determination in composite elastic body. Defectoscopy, 5, 15-23 (in Russian).
Vatulyan AO, Vorovich II, Soloviev AN (2000). On the one kind of boundary problems in the dynamical elasticity. Applied Mathematics and Mechanics, 64(3), 373-380 (in Russian).
Weikl W, Andra H, Schnack E (2001). An alternating iterative algorithm for the reconstruction of internal cracks in a three-dimensional solid body. Inverse Problem, 17, 1957-1975.
http://dx.doi.org/10.1088/0266-5611/17/6/325
