An inverse problem in non-linear elastostatics is considered. It concerns the identification of a frictionless unilateral crack in a linear elastic solid on the basis of boundary measurements corresponding to a given static loading. The identification is obtained by means of an iterative process in which an error function is minimised. At every optimization step, the direct problem is modelled by using a single region boundary element formulation with displacement equations on the whole boundary and traction equations on one face of the crack. The arising linear complementarity (LCP) problem is solved by a pivoting technique. The minimisation of the error function is reached by using a standard non-linear optimization technique. The evaluation of the sensitivities is necessary at every optimization step. The effectiveness of the method is demonstrated by some numerical examples.
On identification of unilateral cracks in elastostatics
ALESSANDRI, Claudio;MALLARDO, Vincenzo
1998
Abstract
An inverse problem in non-linear elastostatics is considered. It concerns the identification of a frictionless unilateral crack in a linear elastic solid on the basis of boundary measurements corresponding to a given static loading. The identification is obtained by means of an iterative process in which an error function is minimised. At every optimization step, the direct problem is modelled by using a single region boundary element formulation with displacement equations on the whole boundary and traction equations on one face of the crack. The arising linear complementarity (LCP) problem is solved by a pivoting technique. The minimisation of the error function is reached by using a standard non-linear optimization technique. The evaluation of the sensitivities is necessary at every optimization step. The effectiveness of the method is demonstrated by some numerical examples.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
