On smooth or 0/1 designs of the fixed-mesh element-based topology optimization

•A simple element-based topology optimization is proposed.•The linear ersatz material model is suitable for the fixed-mesh smooth design.•A new mechanism for the formation of structural topology is introduced.•The proposed algorithm can achieve a smooth or pure 0/1 design as desired.•A smooth design is better than a 0/1 design in aesthetics and performance. The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary intermediate elements under the fixed-mesh finite element analysis are interpolated with a material penalization model. This paper proposes a floating projection topology optimization (FPTO) method for seeking a smooth design using the ersatz material model or a 0/1 design using a material penalization model. The proposed floating projection constraint combining with the upper and lower bounds heuristically simulates 0/1 constraints of design variables in the original discrete optimization problem. Numerical examples demonstrate the capability of the proposed element-based topology optimization approach in obtaining 0/1 or smooth designs for 2D and 3D compliance minimization problems. The proposed topology optimization approach can be easily implemented under the framework of the fixed-mesh finite element analysis and provides an alternative way to form explicit topologies of structures, especially when the ersatz material model is adopted.