<p>In this paper, the authors propose&nbsp;a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on freeform surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method significantly simplifies the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The performance of the proposed method is demonstrated through two examples of heat conduction on manifolds.</p><p>governing the act of governing; exercising authority More (Definitions, Synonyms, Translation)</p>

Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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