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This paper addresses manufacturing constraints by means of a unified projection-based approach restricting the range of solutions to the topology optimization problem. A domain of design variables is considered, which is projected in a pseudo-density domain to obtain the solution. The relation between domains is defined by the projection and variable mappings according to each manufacturing constraint of interest. The following constraints are considered: minimum member size, minimum hole size, symmetry, extrusion, pattern repetition, turning, casting, forging, and rolling.

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Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

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