一种基于附加重力场的铸件拓扑优化方法

针对铸件结构拓扑优化问题,提出了一种新的铸造脱模约束形式.首先,在变密度拓扑优化的框架下,提出了相对密度描述的优化解的逆结构概念;之后,对该逆结构施加附加重力载荷并固定脱模方向的边界;最后,利用该问题的位移解构造铸造约束.通过对逆结构的最大柔顺性施加单一约束,即可避免优化结构出现不可铸造的特征(包括内部孔洞和侧凹),从而保证了铸件结构拓扑优化解的可制造性.二维和三维数值算例验证了该方法的有效性.研究表明,这种积分函数表达的铸件脱模约束本质上为单一约束,具有优化问题求解方便的优点.

An additional gravity field method for topology optimization of cast parts

In this paper, a new form of casting constraints is proposed to optimize a casting structure. First, under the framework of variable density topology optimization, a concept of inverse structure of topology optimized structure described by the relative density is proposed. Then, a gravity load on the inverse structure is applied and the boundaries in the demolding directions are fixed. Finally, the casting constraints are constructed using the displacement field solution of the inverse structure. By applying a single constraint to the maximum compliance of the inverse structure, non-castable features (including internal cavities and undercuts) can be avoided in the optimized structure, thus ensuring the manufacturability of the optimized casting part. Numerical examples in 2D and 3D design domains verify the effectiveness of the method. The numerical results indicate that the proposed casting constraint expressed by an integral function is in nature a single constraint, and facilitates solution of the topology optimization problems.