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.

基于材料惩罚的传统基于元素的拓扑优化通常针对0/1设计。我们的数值实验表明，将固定网格有限元分析下的边界中间元素的材料属性与材料惩罚模型进行插值时，会高估平滑设计的顺应性。本文提出了一种浮动投影拓扑优化（FPTO）方法，用于使用ersatz材质模型或使用材质惩罚模型的0/1设计来寻求平滑设计。所提出的浮动投影约束结合上下限，启发式地模拟了原始离散优化问题中设计变量的0/1约束。数值示例说明了所提出的基于元素的拓扑优化方法在针对2D和3D一致性最小化问题获得0/1或平滑设计中的能力。所提出的拓扑优化方法可以在固定网格有限元分析的框架下轻松实现，并提供了一种替代的方法来形成结构的显式拓扑，尤其是在采用ersatz材料模型时。