Application of Betti’s reciprocal work theorem to the location of cracks in three-dimensional elasticity
| dc.contributor.author | Ioakimidis, Nikolaos | |
| dc.date.accessioned | 2023-11-11T07:40:09Z | |
| dc.date.available | 2023-11-11T07:40:09Z | |
| dc.date.issued | 1990-04 | |
| dc.description.abstract | In this note, the solution of the problem of location of a crack C of arbitrary shape inside a finite three-dimensional isotropic elastic medium D is proposed through a combination of experimental and numerical methods and on the basis of the classical Betti’s reciprocal work theorem. More explicitly, the position, shape and orientation of the crack C can be characterized by a set of n unknown quantities a_j. Next, for the aforementioned medium D under consideration both the tractions t_i0 (generally known in advance) and the displacements u_i0 on the whole boundary S of D can become available by using one of the methods of experimental stress analysis. Next, a number m of loadings t_ik is assumed applied on the surface S of D and the corresponding displacements u_ik on the same surface S are computed by using an appropriate numerical method such as here the boundary element method. Under these circumstances and by appropriately using Betti’s reciprocal work theorem we can derive a system of m nonlinear algebraic equations with respect to the n unknown quantities a_j (evidently with m greater than or equal to n). The approximate solution of this system permits the computation of the unknown quantities a_j and, therefore, the determination of the position, shape and orientation of the crack C inside D. Generalizations of the present experimental–computational approach to more complicated crack problems, problems of arrays of cracks, holes, inclusions, etc. inside D are also easily possible. | |
| dc.identifier.doi | https://doi.org/10.1007/BF01185962 | |
| dc.identifier.uri | https://hdl.handle.net/10889/26193 | |
| dc.language.iso | en | |
| dc.publisher | Kluwer Academic Publishers | |
| dc.title | Application of Betti’s reciprocal work theorem to the location of cracks in three-dimensional elasticity | |
| oaire.citation.endPage | R77 | |
| oaire.citation.issue | 4 | |
| oaire.citation.startPage | R75 | |
| oaire.citation.title | International Journal of Fracture | |
| oaire.citation.volume | 42 | |
| oaire.version | http://purl.org/coar/version/c_b1a7d7d4d402bcce |