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The purpose of this work is to identify simultaneously two irregular interfacial boundaries configurations between the components of three connected domains using a discrete number of displacement measurements obtained by a simple tension test. A unique combination of a global optimization method, i.e., the imperialist competitive algorithm and two local optimization methods, i.e., the conjugate gradient method and Simplex method along with the inverse application of the boundary elements method are employed in an inverse software package. A fitness function, which is the summation of squared differences between calculated displacements and measured displacements at identical locations on the outer boundary, is minimized. Due to the complexity and the ill-posed nature of this identification problem, imperialist competitive algorithm is used to find the best initial guesses of the unknown interface boundaries in order to be used by the local optimization techniques, i.e., conjugate gradient method and then Simplex method to accurately converge to the optimal shape of two irregular interfacial boundaries between the components of an inhomogeneous body. Several examples are selected, and the accuracy of the obtained results is discussed. The effect of experimental measurement errors and the influence of material properties of the sub regions on the identification process are also investigated.

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.

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.

The boundary elements method (BEM), manipulated genetic algorithm (MGA), conjugate gradient method (CGM), and cubic spline interpolation (CSI) are implemented to identify the shape of a cavity located inside a 2D solid body using displacements measured from a biaxial tension test. A fitness function which is defined as the squared differences between the computed and measured displacements is minimized. The BEM is used to solve the direct 2D elastostatics problem for the boundary displacements. The MGA is used as a robust explorer to find the best circular initial guess needed by the CGM to achieve convergence. The CSI is finally employed to draw the best curve through the points found by the CGM which depict the boundary of the cavity. Several example problems with different shapes of the cavity such as elliptic, pear, heart and egg shaped are solved. The effects of the size of cavity and measurement errors on the estimation process are investigated.