Abstract
Characterization of the interior of an inhomogeneous body using displacement measurements obtained by conducting a simple tension test was investigated. A homogeneous elastic solid body is assumed to have another solid body with arbitrary shape hidden inside it. The shape and physical properties of this inclusion were unknown. The Boundary Element Method (BEM) coupled with a mete heuristic Genetic Algorithm (GA) and Conjugate Gradient Method (CGM) was used in this characterization problem. A fitness function, which is the summation of squared differences between the measured displacements and calculated displacements at the same locations on the boundary, is minimized using GA and CGM. GA is used to find a good initial estimate of the unknown parameters and the CGM was used as the hybrid function to get converged values of the unknown parameters. For the cases that the fitness function fluctuates severely, a regularization function was added to CGM in order to dampen the fluctuations.
Highlights
Geometric and material properties of an inclusion using Boundary Element Method (BEM) and implementation of regularization function[8], In this study, the feasibility of characterizing the internal structure of an inhomogeneous body solely on the basis of surface measurements will be explored
In particular we will examine the problem of determining the location, shape and physical properties i.e., the Young's modulus and Poisson's ratio of an inclusion in a body of arbitrary shape using measurements of displacement at a discrete number of points on the surface of the body only
Local optimization techniques in inverse elasticity problems using BEM[9], estimation of geometric shape of an irregular boundary between a numbers of solid elastic bodies using surface temperatures[10], are among some of the investigations done in this field
Summary
Geometric and material properties of an inclusion using BEM and implementation of regularization function[8], In this study, the feasibility of characterizing the internal structure of an inhomogeneous body solely on the basis of surface measurements will be explored. Several questions arise in this inverse application temperature measurements[2], estimation of the optimal of the BEM, which have not been adequately addressed sizes and locations of coolant flow passages for a user- in previous investigations. Among these are (1) what specified steady distribution of surface temperatures and fluxes[3], investigation of a spatially regularized solution of inverse elasticity problem using the BEM[4], effect will the inevitable errors in experimental measurements have on the ability to estimate the sought parameters and (2) what is the influence of the estimation of thermal and mechanical properties along inclusion size on the estimation process?. The success of the technique demonstrated here shows great promise for application in the area of non-destructive evaluation
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