Designing Metasurfaces with Topology Optimization and

Conformal Mapping Theory

A computational framework for computational design and additive manufacturing of free-form periodic metasurfaces is explored. The proposed scheme rests on the level-set based topology approach and the conformal mapping theory. A metamaterial with pre-specified performance is created using a level-set based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle when mapping the 2D design to a 3D surface. With the embedded geometric information, the proposed level-set based optimization methods not only can act as a motivator for design synthesis, but also can be seamlessly hooked with additive manufacturing with no need of CAD reconstructions. The current computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces in different fields of interest. The performance of the proposed scheme is illustrated through two benchmark examples where a negative-Poisson's-ratio unit cell pattern, and a stiff and light inner structure are mapped to 3D free-form surfaces and fabricated through additive manufacturing.

Negative Poisson’s ratio metamaterial design on a 3D human face

Reinforced Surface

Representative publications:

Journal:

Panagiotis Vogiatzis, Ming Ma, Shikui Chen and Xianfeng Gu, “Computational Design and Additive Manufacturing of Periodic Conformal Metasurfaces by Synthesizing Topology Optimization with Conformal Mapping”, Computer Methods in Applied Mechanics and Engineering, 328 (2018): 477-497.

Conference:

Panagiotis Vogiatzis, Ming Ma, Shikui Chen and Xianfeng David Gu, “Computational Design and Additive Manufacturing of Periodic Conformal Metasurfaces by Synthesizing Topology Optimization with Conformal Mapping”, ASME Proceedings of IDETC/CIE, August 6-9, 2017, Cleveland, Ohio, USA.

Designing a stiff and light 3D metamaterial design

Reinforced Stanford bunny