A level set method for shape and topology optimization of coated structures

Coated structures are commonly used in engineering. The coating material covers the surface of the substrate for protection or to improve certain functionalities. The rising of novel manufacture techniques enables higher design flexibility for such coated structures. This paper presents a level set-based topology optimization method for the design of structures with coating layers. Though a coated structure is composed of two-phase materials, only one level set function is needed in the special case of coating with uniform thickness to describe the distribution of the substrate and the coating layer, thanks to its signed distance property. Without using any intermediate design variables, the proposed method provides a direct interface description between different material phases and geometrical information regarding the coating layer thickness, thus facilitating the sensitivity analysis and numerical implementation. Numerical examples show that the method can be applied to both 2D and 3D problems.