Topology Optimization of Conformal Structures on Manifolds Using Extended Level Set Methods (X-LSM) and Conformal Geometry Theory

ABSTRACT

The free-form surface, also termed manifold, is a smooth 3D skin that contains aesthetic value and presents functionalities. With the integration of mathematics, computer-aided design, and construction techniques, people can bring the free-form surface into reality. However, how to achieve an optimal layout on the free-form surface is still an open topic. In this talk, I will first introduce my research efforts on topology optimization on the freeform surface using the extended level set method and conformal mapping theory. Next, I will present my work on optimizing a typical adaptive surface- the origami structure, which can transform from flattening 2D status to a complex 3D design at a given crease pattern. In terms of fabricating thin shell surfaces, I will briefly introduce our surface weaving method, which can directly construct a 3D surface by weaving two groups of computed strips. The future research directions and applications will be discussed at the end.