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In the present paper, an integrated paradigm for topology optimization oncomplex surfaces with arbitrary genus is proposed. The approach is constructedbased on the two-dimensional (2D) Moving Morphable Component (MMC) framework,where a set of structural components are used as the basic units ofoptimization, and computational conformal mapping (CCM) technique, with which acomplex surface represented by an unstructured triangular mesh can be mappedinto a set of regular 2D parameter domains numerically. A multi-patch stitchingscheme is also developed to achieve an MMC-friendly global parameterizationthrough a number of local parameterizations. Numerical examples including asaddle-shaped shell, a torus-shape shell and a tee-branch pipe are solved todemonstrate the validity and efficiency of the proposed approach. It is foundthat compared with traditional approaches for topology optimization on 2Dsurfaces, optimized designs with clear load transmission paths can be obtainedwith much fewer numbers of design variables and degrees of freedom for finiteelement analysis (FEA) via the proposed approach.

Topology optimization on complex surfaces based on the moving morphable component (MMC) method and computational conformal mapping (CCM)