Axisymmetric and two-dimensional crack identification using boundary elements and coupled quasi-random downhill simplex algorithms

• Published in: Engineering analysis with boundary elements Vol. 34; no. 6; pp. 611 - 618
• Main Authors: Amoura, N., Kebir, H., Rechak, S., Roelandt, J.M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.06.2010; Elsevier
• Subjects: Algorithms; Axisymmetric; Boundaries; Boundary element method; Cracks; Dual boundary element method; Exact sciences and technology; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Inverse problem; Mathematical analysis; Mathematical models; Mathematics; Measurement and testing methods; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Physics; Regularization; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Two dimensional; Dual boundary element method; Fracture mechanics; Regularization; Inverse problem; Probabilistic approach; Rupture; Modeling; Axial symmetry; Strain sensors; Deformation measurement; Defect characterization; System identification; Boundary element method; Crack
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2010.02.002

In this paper, a crack identification method is developed for axisymmetric and two-dimensional structures. The dual boundary element method is coupled with a quasi-random sequence and the downhill simplex algorithm to minimize the error function, which is expressed as the difference between strains at the boundary sensor points in the guessed crack shape and ones measured in the actual crack identity. The measures are randomly perturbed and the residual norm is regularized to provide an efficient and numerically stable algorithm that leads to stabilized solutions. The accuracy of this method is investigated in the identification of single two-dimensional and axisymmetric cracks on several cases. Through the treated examples, we showed that the quasi-random sequence presents a solid tool, allowing the choice of the optimal initial solution necessary to the convergence of the downhill simplex algorithm.