论文标题
基于固定网格元素的拓扑优化的平滑或0/1设计
On smooth or 0/1 designs of the fixed-mesh element-based topology optimization
论文作者
论文摘要
基于材料惩罚的传统基于元素的拓扑优化通常旨在实现0/1设计。我们的数值实验表明，当固定网格有限元分析下边界中间元素的材料中间元素的材料特性被用物质惩罚模型插值时，平滑设计的合规性被高估了。本文提出了一种使用ERSATZ材料模型或使用材料惩罚模型的0/1设计寻求平滑设计的浮动投影拓扑优化（FPTO）方法。所提出的浮动投影约束与上限和下界结合在原始离散优化问题中模拟设计变量的0/1限制。数值示例证明了提出的基于元素的拓扑优化方法在获得2D和3D合规性最小化问题的平滑设计方面具有能力。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，并提供了形成结构显式拓扑的另一种方法，尤其是在采用Ersatz材料模型时。
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.
