| Résumé | For the past two decades, topology optimization has become increasingly prized by the industry for its key role in product design. The objective behind topology optimization is to find the optimal material distribution in order to minimize a certain cost function. In structural applications for instance, one can seek to minimize the compliance of a part (i.e. to maximize its stiffness) while constraining its volume, whereas in heat transfer applications the minimization of maximal or average temperature is often desired. Most topology optimization methods can be categorized in either of the following two main families: diffuse approaches, where the transition between different states is gradual, i.e. where one state is dispersed into another by a local fraction; and sharp approaches, where the states are separated by a precise interface which serves as a frontier between monolithic states. Despite their attractive features, sharp methods generally lack the robustness of diffuse ones and are more complex to implement. This work deals with the comparison of two distinct topology optimization approaches, which were both implemented in our in-house finite element solver: a traditional diffuse, density-based, method, constructed upon the so-called simplified isotropic material with penalization (SIMP) approach; and a novel sharp method, based on the immersed boundary-body conformal enrichment approach, where the interface separating the two materials is defined by a level set function. The two optimization methods are compared in various heat transfer problems. In particular, it is shown that regularization strategies such as perimeter restriction and level set gradient control were found efficient in addressing some of the sharp method’s robustness issues, but that these approaches are not suitable for every problem and require a certain tuning of parameters. |
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