Topology optimization of coated structure using moving morphable sandwich bars

An explicit topology optimization method for coated structures is proposed by using moving morphable sandwich bars (MMSBs). An MMSB acting as a composite bar has two different material parts with an inner part of the base material and an exterior layer of the coating material. The geometries of an MMSB are mapped onto two different density fields using a fixed grid and the same shortest distance function. The densities of an element are determined depending on whether the element lies inside or outside the boundaries of the inner bars/the hollowed bars. By treating the coordinates of the ends and thicknesses of the base and coating layers of a sandwich bar as design variables, the sandwich bar can move, morph, change its thicknesses, and overlap with others in a fixed design domain to form optimal shapes of the base and coating structures. The minimum thickness of the base structure as well as the coating layer is independently and precisely controlled in an explicit way by simply adjusting the lower bounds of the thickness variables of the sandwich bars. The uniform thickness control of the coating layer can be obtained without any filtering techniques or additional constraints. The proposed method is also extended for topology optimization of the coated structures with two coating layers. The numerical examples of minimizing structural compliance show that the proposed method works effectively and produces good results with smooth and fast convergence rate.