TY - CONF
A1 - Lahmer, Tom
A1 - Ghorashi, Seyed Shahram
A2 - Gürlebeck, Klaus
A2 - Lahmer, Tom
A2 - Werner, Frank
T1 - XFEM-BASED CRACK IDENTIFICATION APPLYING REGULARIZING METHODS IN A MULTILEVEL APPROACH
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - Many structures in different engineering applications suffer from cracking. In order to make reliable prognosis about the serviceability of those structures it is of utmost importance to identify cracks as precisely as possible by non-destructive testing. A novel approach (XIGA), which combines the Isogeometric Analysis (IGA) and the Extended Finite Element Method (XFEM) is used for the forward problem, namely the analysis of a cracked material, see [1]. Applying the NURBS (Non-Uniform Rational B-Spline) based approach from IGA together with the XFEM allows to describe effectively arbitrarily shaped cracks and avoids the necessity of remeshing during the crack identification problem. We want to exploit these advantages for the inverse problem of detecting existing cracks by non-destructive testing, see e.g. [2]. The quality of the reconstructed cracks however depends on two major issues, namely the quality of the measured data (measurement error) and the discretization of the crack model. The first one will be taken into account by applying regularizing methods with a posteriori stopping criteria. The second one is critical in the sense that too few degrees of freedom, i.e. the number of control points of the NURBS, do not allow for a precise description of the crack. An increased number of control points, however, increases the number of unknowns in the inverse analysis and intensifies the ill-posedness. The trade-off between accuracy and stability is aimed to be found by applying an inverse multilevel algorithm [3, 4] where the identification is started with short knot vectors which successively will be enlarged during the identification process.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
UR - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2771
UR - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27717
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -