Inverse problem

Finite element method

Mathematics

Boundary (topology)

Structural engineering

Algorithm

Mathematical optimization

Basis (linear algebra)

Engineering

Mathematical analysis

Optimization problem

Heuristic

Extended finite element method

Set (abstract data type)

Programming language

Geometry

Computer science

Scheme (mathematics)

Computational Mechanics

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.

Multiple crack detection in 3D using a stable XFEM and global optimization