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 explains why they are less common in the literature.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 [1]; and a novel sharp method, based on the immersed boundary-body conformal enrichment (IB-BCE) approach [2], 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. For each method, several strategies are investigated in order to increase the method’s robustness and to reduce its sensitivity to initial conditions. Although the diffuse method is more robust than its sharp counterpart, it was found that the method could still converge to a sub-optimal outcome when the design parameters are initialized incorrectly. We show that this sensitivity to initial conditions can generally be tackled by a gradual increase of the blending exponent in the SIMP power law during the optimization loop, and that the method’s robustness can be enhanced by filtering either the cost function gradient or the design parameters directly. Regarding the sharp approach, some parametrization forms of the level set field, e.g.&nbsp;radial basis functions (RBFs), were tested in order to extend the zone of influence of individual design parameters and to accelerate the rate of convergence of the method. Furthermore, regularization strategies such as perimeter restriction and gradient control were found efficient in addressing some of the robustness issues. It is shown, however, that these approaches are not suitable for every problem, and that each of them requires a certain tuning of parameters.[1] M. P. Bendsøe, Optimal shape design as a material distribution problem, Structural Optimization, 1(4) (1989) 193-202.[2] F. Ilinca, and J.-F. Hétu, An immersed boundary–body conformal enrichment method for thermal flow problems, Computers &amp; Fluids, 88 (2013) 616-628.

A Comparative Study Between a Sharp and a Diffuse Topology Optimization Method for Thermal Problems

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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