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An inverse elasticity problem is solved to identify the irregular boundary between the components of a multiple connected domain using displacement measurements obtained from an uniaxial tension test. The boundary elements method (BEM) coupled with the particle swarm optimization (PSO) and conjugate gradient method (CGM) are employed. Due to the ill-posed nature of this inverse elasticity problem, and the need for an initial guess of the unknown interfacial boundary when local optimization methods are implemented, a Meta heuristic procedure based on the PSO algorithm is presented. The CGM is then employed using the best initial guess obtained by the PSO to reach convergence. This procedure is highly effective, since the computational time reduces considerably and accuracy of the results is reasonable. Several example problems are solved and the accuracy of obtained results is discussed. The influence of material properties and the effect of measurement errors on the estimation process are also addressed.

The boundary element method and the techniques of parameter estimation are coupled to identify the internal structure of an inhomogeneous body using a discrete number of surface measurements. In this study, a body of some arbitrary but given shape is subjected to uniaxial tension. The body is assumed to contain an inclusion of circular shape but of unknown location, size, Poisson's ratio and shear modulus. The simultaneous estimation of these parameters is to be accomplished by measuring displacements at surface locations where tractions have been specified and/or measuring tractions at selected surface locations where displacement has been specified. The parameter estimation technique with line search is used for optimization.

Temperature measurements from the exterior boundary of a two-dimensional solid body containing an inclusion, under steady state conditions, are used to estimate the thermal conductivity and the shape of the inclusion. The particle swarm optimization algorithm (PSO), coupled with the boundary elements method, is used in this identification problem. A fitness function which is the summation of the squared differences between the measured and calculated temperatures at the locations on the exterior boundary is minimized. To avoid trapping into the local optimum points, the PSO algorithm which is a global optimization method is used instead of local optimization methods. The credibility of the PSO algorithm and its effectiveness in solving inverse problems is investigated. The effect of measurement errors and the size of the inclusion on the estimation process will be addressed.