Tools for the numerical solution of inverse problems in structural mechanics: review and research perspectives

Abstract

In this work, the author gives a review of the state of the art on the computational strategies developed for the analysis of inverse problems. Starting from the definition of the inverse problem, and focusing the intrinsic difficulties in their solution, various computational tools developed for their solution are presented and discussed. This allows an aware choice of the most effective strategies with respect to the problem to be dealt with. Successively, some selected inverse problems are briefly sketched and their numerical solution is thoroughly discussed. This allows to enlighten the main problems to overcome and the attainable accuracy. Finally, new and challenging inverse problems are addressed, discussing thoroughly some current and classical results, in order to outline future perspectives.

Keywords:

• Inverse problems
• Cauchy’s problem
• damage identification
• reconstruction problems
• model updating

Notes

1 The norm considered in the whole paper is the Euclidean norm.

2 Even if there are other modern techniques of measurements, which are more accurate in some cases, only photogrammetric measurements are currently available. Furthermore, the sketched procedure can be easily adapted to other kinds of measurements.