Level set-based topology optimization for variable thickness coated structures
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In a broad range of applications, structures are coated to gain enhanced reliability and durability under extreme operating conditions. Resulting structures are composed of multiple materials, i.e., a substrate material and a coating material. In contrast to standard multi-material structures, coated structures are designed to exhibit a specific material arrangement; the coating can only be applied on top of the substrate. This requirement drastically limits the possible geometries of coated structures and poses an interesting manufacturing challenge. Over the years, topology optimization has gained popularity as a method to systematically create structures with enhanced performance while respecting design requirements. Considerable research efforts have focused on the development of topology optimization frameworks to design structures with uniform thickness coating. To increase the potential for enhanced performance and to maximize the material efficiency, structures with variable thickness coating layers are desirable. In this work, we propose a level set-based topology optimization framework that allows for variable thickness coating. The geometry of coated structures is described using the level set method. Hereby, multiple level set functions are used to describe the multi-material structure layouts. The mechanics response of coated structures is predicted using the XIGA and considering small strain linear elasticity. To generate adequately coated structures, geometric constraints, independent of the underlying physics, are formulated. These constraints require the evaluation of the distance from boundaries and interfaces that can be obtained through the heat method. The constraints enforce a lower and upper bound on the thickness of the coating layer, a lower bound on the minimum feature size of the substrate material, and give control over the connectivity of the substrate material. To illustrate the capabilities of the proposed formulation, academic two- and three-dimensional optimization problems considering compliance minimization are investigated. The generated designs show the clear emergence of variable thickness coated structures, e.g., thick coating layers in critical areas and thin coating layers in low load bearing areas. The obtained designs emphasize the efficiency and flexibility of the proposed approach to tackle different problems in terms of design domains, boundary conditions and material selection.