通过拓扑优化得到的结构优化构型往往因存在内部封闭孔洞而导致难以满足工艺约束。为实现对拓扑优化结果的特定形状控制，面向空天装备中的轴对称结构，基于变密度法提出了一种双向密度分布函数。首先，通过将设计变量由每个单元的伪密度转化为双向密度分布函数的控制参数，拓扑优化过程中结构材料将沿特定方向变化，最终的伪密度场分布也将随着双向密度分布函数具体表达形式的不同而改变。然后，使用一种线性加权过滤方法对设计变量进行过滤以获得更加光滑的材料边界。进而，针对结构质量和最大von Mises应力响应，分别开展了二者对设计变量的敏度分析，并搭建了在质量约束下，结构最大von Mises应力最小化的拓扑优化框架。同时，为避免拓扑优化过早陷入局部最优解，在迭代过程中针对灰度单元控制参数和应力P-范数系数采用延拓更新的方式。最后，使用典型空天轴对称结构航空发动机轮盘开展算例验证，在满足质量约束的前提下，材料分布在优化过程中朝着应力最小化的方向逐步演化，得到的拓扑优化构型材料/孔洞界面清晰、应力分布均匀、材料利用率高，证明了所提方法的有效性。

The structure optimization configuration obtained by topology optimization is often difficult to meet the manufacturing constraints due to the existence of internal closed holes. To control the specific shape of topology optimization results， a bidirectional density distribution function is proposed based on variable density method for axisymmetric structures in aerospace equipment. By converting the design variables from the pseudo density of each element to the control parameters of the bidirectional density distribution function， the structural materials will change along a specific direction in the process of topology optimization. The final pseudo density field distribution will also change with the specific expression of bidirectional density distribution function. Then， a linear weighted filtering method is used to filter the design variables to obtain a smoother material boundary. Furthermore， the sensitivity analysis of the structural mass and the maximum von Mises stress response to the design variables is carried out respectively， and the topology optimization framework of minimizing the maximum von Mises stress of the structure under the mass constraint is established. Meanwhile， to avoid the topology optimization from falling into the local optimal solution too early， the extension updating method is adopted for the grey element control parameters and the stress P-norm coefficient in the iterative process. Finally， typical aero-engine disks with aerospace axisymmetric structure are used to carry out the example verification. Under the premise of meeting the quality constraints， the material distribution gradually evolves towards the direction of stress minimization in the optimization process. The obtained topology optimization configuration has clear solid space interface， uniform stress distribution and high material utilization rate， demonstrating the effectiveness of the proposed method.