轮盘概念设计中拓扑和形状同时优化方法

为了减小人为选择参数对优化结果的影响,针对航空发动机轮盘概念设计阶段的结构优化问题,提出了拓扑和形状同时优化(STSO)法.该方法是在变密度(SIMP)法的基础上,通过分析优化目标和约束的灵敏度,用序列二次规划优化(SQP)法进行求解.接着,以板壳结构为例,对比分析了STSO法和分步优化法的结果,说明了拓扑和形状同时优化方法的优点.最后,将同时优化方法应用于轮盘结构概念设计,对比分析了使用拓扑和形状同时优化方法与单独拓扑优化方法进行轮盘结构优化的结果,探讨了不同振型对应的频率约束对优化结果的影响.结果表明,不同振型对应的频率约束下优化结果的结构形式呈现多样性;相较于单独拓扑优化方法,STSO法收敛速度较快、结果也更精确;但是由于形状优化变量取值范围选取不当,有可能会出现网格畸变过大,而导致STSO法所得的结果无效. 

Simultaneous topology and shape optimization method in conceptual design of disk

To minimize the effects of artificially chosen variables on optimization results, simultaneous topology and shape optimization (STSO) method was proposed for structural optimization of aero-engine disk at the conceptual design phase. This method was based on solid isotropic material with penalization (SIMP) method, by analyzing the sensitivities of the optimized object and constraints, sequential quadratic programming (SQP) optimized method was used to solve the problem. Then, taking shell structure for instant, the results of STSO method and multi-step optimization method were comparatively analyzed, which confirmed the advantage of STSO method. At last, the STSO method was utilized to design a conceptual disk structure. Results of disk structural optimization of STSO method were compared to that of the sole topology optimization method. Influence of frequency constraints of different vibration modes on optimization results was discussed. The results show that the structural forms of optimization results of frequency constraints of different vibration modes vary a lot. Convergence rate of STSO method is faster than that of solo topology optimization, and the consequences of STSO method are more accurate. Meanwhile, the results of STSO method may be invalid for excessive mesh distortion caused by the wrong choice of the value range of shape optimization variables.