Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory

In this paper, we propose a new method to systematically address the issue of structural shape and topology optimization on free-form surfaces. A free-form surface, also termed manifold, is conformally mapped onto a 2D rectangle domain where the level set function is defined. With the conformal mapping, the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar. Keeping this intrinsic...