  This paper proposes a level set-based method for optimizing shell structures
with large design changes in shape and topology. Conventional shell
optimization methods, whether parametric or nonparametric, often only allow
limited design changes in shape. In the proposed method, the shell structure is
defined as the isosurface of a level set function. The level set function is
iteratively updated based on the shape sensitivity on the surface mesh.
Therefore, the proposed method can represent an arbitrary manifold surface
while dealing with topological changes, for example, from a spherical surface
to a toroidal surface. We applied the proposed method to the mean compliance
minimization problems of 3D shell structural designs for dome, bending plate
and cantilever beam examples to demonstrate its efficacy of the proposed
method.
