基于映射的拓扑优化最大尺寸控制方法

拓扑优化方法经过几十年的发展，已成功应用于机械工程、航空航天、电磁等领域的构型设计中。然而，由于制造工艺的限制，拓扑优化结果通常无法直接应用，需根据工艺要求进行修改，因此在拓扑优化模型中考虑制造约束成为重要的研究方向。其中，尺寸控制广泛存在于大部分制造工艺中，主要包括最小尺寸控制与最大尺寸控制。该文提出了一种基于映射的拓扑优化最大尺寸控制方法，构造了一种新的映射模型，对结构中不满足最大尺寸约束的中心单元密度进行惩罚，在不引入任何约束条件的情况下实现了对结构最大尺寸的控制。此外，该文将该方法中的惩罚转变为一个全局约束条件后与具有最小尺寸控制功能的拓扑优化鲁棒列式相结合，实现了对构件的最大最小尺寸协同控制。数值算例表明了该方法的有效性。

A NOVEL PROJECTION BASED METHOD FOR IMPOSING MAXIMUM LENGTH SCALE IN TOPOLOGY OPTIMIZATION

During the past decades, various topology optimization methods have been developed to design the optimal structure in many fields such as mechanical engineering, aerospace and electromagnetism. However, the optimized topologies are often considered as conceptual because they ignore the manufacturing constraints in the topology optimization model. As one of the important manufacturing constraints, a great effort has been devoted to the issue of length scale control which includes minimum length scale control and maximum length scale control in topology optimization. In this paper, a novel projection based method for imposing maximum length scale in topology optimization is presented. In this method, a new penal formulation for the density of the center element which violates the maximum length scale constraints is proposed and the maximum length scale control can be achieved without additional constraints. Furthermore, a combination of the new method and the robust formulation which is able to control the minimum length scale is realized by changing the penal formulation into a global constraint. By this way, simultaneous control of the minimum length scale and maximum length scale is achieved. Some numerical examples that consider the length scale control in topology optimization are presented to show the validity of this method.