Shape optimization method for axisymmetric disks based on mesh deformation and smoothing approaches

Axisymmetric disk structures with complex contour curves are widely used in aero-engines. The shape optimization is generally carried out to reduce the stress level of axisymmetric disks. In this article, a shape optimization method for axisymmetric disks based on radial basis function (RBF) mesh deformation and Laplace smoothing approaches is proposed. This method can obtain the optimized reduced control points selection of mesh deformation under the influence of design space based on greedy algorithm. RBF mesh deformation is used to change the axisymmetric contour shape. And after deformation, the local mesh quality is monitored and improved by Laplace smoothing. In this article, two illustrative examples used in aero-engines are carried out to validate the effectiveness of the proposed method, including an independent optimization of a turbine disk and a collaborative optimization of a turbine disk with a deflector for minimizing the maximum equivalent stress. To improve the computational efficiency, a two-dimensional (2D) axisymmetric FE model is established. Compared with initial results, optimized results in two examples obtained by the proposed optimization method reduce the maximum von Mises stress by 8.02% and 9.25%, respectively. It can be concluded that the proposed method has significant potential in the shape optimization design of axisymmetric disks.

具有复杂轮廓曲线的轴对称盘结构在航空发动机领域应用广泛。为降低轴对称盘的应力水平，通常需开展形状优化工作。本文提出了一种基于径向基函数（Radial Basis Function, RBF）网格变形与拉普拉斯平滑方法的轴对称盘形状优化方案。该方法基于贪心算法，在设计空间约束下获取经优化的精简网格变形控制点选取方案；通过径向基函数网格变形修改轴对称盘的轮廓形状，变形完成后再利用拉普拉斯平滑方法监测并优化局部网格质量。本文开展两项航空发动机领域的典型算例以验证所提方法的有效性，分别为涡轮盘独立形状优化，以及带导流器的涡轮盘协同优化，两者均以最小化最大冯·米塞斯等效应力（von Mises stress）为优化目标。为提升计算效率，本文建立了二维（2D）轴对称有限元（Finite Element, FE）模型。相较于初始结果，通过所提优化方法得到的两个算例的优化结果，其最大冯·米塞斯等效应力分别降低了8.02%与9.25%。研究表明，所提方法在轴对称盘的形状优化设计中具有显著的应用潜力。