The aim of the proposed work is to develop and to test a solution technique for non destructive identification. With reference to some recent experiences [1-5], the Authors present a numerical procedure for identifying the position and the size of an inclusion on the basis of boundary measurements at some sensor points for given static loadings. The matrix and the inclusion are supposed linear elastic and in frictionless unilateral contact at the interface. The problem is stated as a 2D optimisation problem where the design variables are the co-ordinates of the centre and the area of the hole-inclusion system. The measure of the difference between the computed and observed displacements at some sensor points of the external boundary is minimised in order to provide the geometrical configuration of the inclusion. The minimisation is performed by using a first-order non-linear unconstrained optimisation technique in which the cost function gradient is computed by the implicit differentiation method. Most published work deals with cavity and crack identification in different fields [3-9]. In this paper, a circular inclusion is considered within a linear elastic solid subject to given boundary load and displacement conditions. The direct static frictionless unilateral contact problem, formulated in terms of boundary variational inequalities with contact tractions as physical variables, is discretised by means of the standard Boundary Element Method (BEM) based on collocations and solved as a Linear Complementarity Problem (LCP) with a non-symmetric coefficient matrix. The choice of boundary element techniques is generally acknowledged as more appropriate for this kind of inverse problems since only a small number of data, the ones concerning the hole-inclusion surfaces, need to be stored and adapted along the required repetitive procedure. Quadratic boundary elements are used with the example presented. For the presence of the unilateral constraints, the error function is a non-convex and nondifferentiable function of the matrix-inclusion parameters and its sensitivity can be calculated only along given directions
Identification of inclusions in unilateral contact with the matrix
MALLARDO, Vincenzo;ALESSANDRI, Claudio
1999
Abstract
The aim of the proposed work is to develop and to test a solution technique for non destructive identification. With reference to some recent experiences [1-5], the Authors present a numerical procedure for identifying the position and the size of an inclusion on the basis of boundary measurements at some sensor points for given static loadings. The matrix and the inclusion are supposed linear elastic and in frictionless unilateral contact at the interface. The problem is stated as a 2D optimisation problem where the design variables are the co-ordinates of the centre and the area of the hole-inclusion system. The measure of the difference between the computed and observed displacements at some sensor points of the external boundary is minimised in order to provide the geometrical configuration of the inclusion. The minimisation is performed by using a first-order non-linear unconstrained optimisation technique in which the cost function gradient is computed by the implicit differentiation method. Most published work deals with cavity and crack identification in different fields [3-9]. In this paper, a circular inclusion is considered within a linear elastic solid subject to given boundary load and displacement conditions. The direct static frictionless unilateral contact problem, formulated in terms of boundary variational inequalities with contact tractions as physical variables, is discretised by means of the standard Boundary Element Method (BEM) based on collocations and solved as a Linear Complementarity Problem (LCP) with a non-symmetric coefficient matrix. The choice of boundary element techniques is generally acknowledged as more appropriate for this kind of inverse problems since only a small number of data, the ones concerning the hole-inclusion surfaces, need to be stored and adapted along the required repetitive procedure. Quadratic boundary elements are used with the example presented. For the presence of the unilateral constraints, the error function is a non-convex and nondifferentiable function of the matrix-inclusion parameters and its sensitivity can be calculated only along given directionsI documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
