  In the present paper, an integrated paradigm for topology optimization on
complex surfaces with arbitrary genus is proposed. The approach is constructed
based on the two-dimensional (2D) Moving Morphable Component (MMC) framework,
where a set of structural components are used as the basic units of
optimization, and computational conformal mapping (CCM) technique, with which a
complex surface represented by an unstructured triangular mesh can be mapped
into a set of regular 2D parameter domains numerically. A multi-patch stitching
scheme is also developed to achieve an MMC-friendly global parameterization
through a number of local parameterizations. Numerical examples including a
saddle-shaped shell, a torus-shape shell and a tee-branch pipe are solved to
demonstrate the validity and efficiency of the proposed approach. It is found
that compared with traditional approaches for topology optimization on 2D
surfaces, optimized designs with clear load transmission paths can be obtained
with much fewer numbers of design variables and degrees of freedom for finite
element analysis (FEA) via the proposed approach.
