The aim of the proposed work is to develop and to test a solution technique for non destructive 2D identification problems. With reference to some recent experiences, the Authors present a numerical BEM procedure for identifying internal cracks or inclusions on the basis of boundary measurements at some sensor points for given static loadings. The procedure is then extended to the identification of the inclusion, with prescribed area, corresponding to the maximum structural stiffness under prescribed loading. The contact between the faces of the crack or between matrix and inclusion is supposed to be unilateral and frictionless and the involved materials are considered linear elastic. The problem is stated as a first-order minimisation problem where the design variables represent the size and the shape of the crack or of the inclusion and the error function gradient is computed by implicit differentiation. The error function evaluates the difference between the computed and observed displacements at some sensor points of the external boundary if dealing with the nondestructive identification problems, the strain energy accumulated by the matrix-inclusion system if dealing with the optimisation problem. In the latter case the inclusion is modelled either as rigid or as deformable body. Some simple but meaningful examples are presented and discussed in detail in order to show the applicability of the proposed technique.
On crack and inclusion identification with BEM in unilateral contact mechanics
MALLARDO, Vincenzo;ALESSANDRI, Claudio
1999
Abstract
The aim of the proposed work is to develop and to test a solution technique for non destructive 2D identification problems. With reference to some recent experiences, the Authors present a numerical BEM procedure for identifying internal cracks or inclusions on the basis of boundary measurements at some sensor points for given static loadings. The procedure is then extended to the identification of the inclusion, with prescribed area, corresponding to the maximum structural stiffness under prescribed loading. The contact between the faces of the crack or between matrix and inclusion is supposed to be unilateral and frictionless and the involved materials are considered linear elastic. The problem is stated as a first-order minimisation problem where the design variables represent the size and the shape of the crack or of the inclusion and the error function gradient is computed by implicit differentiation. The error function evaluates the difference between the computed and observed displacements at some sensor points of the external boundary if dealing with the nondestructive identification problems, the strain energy accumulated by the matrix-inclusion system if dealing with the optimisation problem. In the latter case the inclusion is modelled either as rigid or as deformable body. Some simple but meaningful examples are presented and discussed in detail in order to show the applicability of the proposed technique.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
