Implementation of topological derivative in the moving morphable components approach

We propose a new topology optimization approach based on the moving morphable components (MMC) framework with an explicitly described a layout through a finite number of components. The position and shape values of each component were defined as design variables. In this study, a method was developed by utilizing topological derivative. Instead of performing a discrete sensitivity analysis based on finite element methods, a topological derivative was used to calculate the first derivative of an objective function with respect to the shape and position of the components. The obtained derivative was validated via discrete sensitivity analysis. The topological derivative formulation has been well developed in recent years for different structural and non-structural problems. Utilizing this powerful tool enabled the MMC approach to easily solve various types of topology optimization problems. Herein, the presented method is illustrated through several topology optimization problems such as stress-based and thermo-mechanical topology optimization.