Explicit topography design for complex shell structures based on embedded spline components

The slender property of shell structures causes the magnitude difference between in-plane and out-of-plane stiffness. Inspired by such a geometry-induced anisotropy phenomenon, this paper proposes a novel design approach to improve the stiffness of complex shell structures. The optimization algorithm is constructed based on two technical pillars, i.e., the explicit moving morphable components (MMC) framework and the computational conformal mapping (CCM) technique. Owing to the MMC framework, the proposed approach can describe complex topography fields with local details via relatively few design variables, theoretically decreasing the computation burden. Towards shell structures in practice, of which the geometry models are usually flexible and complex, we leverage the CCM technique to parameterize the middle surfaces to obtain a unified and robust algorithm architecture. Representative examples with complex geometry models are provided to validate the proposed design method's effectiveness, efficiency, and universality.