An explicit optimization model for integrated layout design of planar multi-component systems using moving morphable bars

Layout design of multi-component systems has received ever-increasing attention over recent years. However, most of the current literature on the layout design of multi-component systems conducted are all carried out in an implicit way. In this paper, an explicit optimization model based on the moving morphable bars method is proposed. To this aim, topology description functions are used to describe the geometrical shapes of embedded components, while moving bars act as supporting structure that connects these embedded components. Different from traditional optimization methods, the geometric parameters used to describe the size, shape, location and orientation of the moving bars and embedded components are considered as design variables in this work. To avoid remeshing the grids and improve the efficiency of computation, the moving bars and embedding components are mapped into two density fields on a fixed grid using a smoothed Heaviside function. A discrete material interpolation scheme developed for orientation optimization problem is extended for the first time to the material parameterization of multi-component systems. Moreover, a single explicit constraint based on the volume and perimeter of embedded components is proposed for avoiding overlaps between the embedded components, and between each component and the design domain boundary. Several numerical examples are performed to show the effectiveness and flexibility of the presented optimization model in handling layout optimization of structures with multi-phase embedded components.