基于超椭圆方程和序列响应面法的回转壳开孔形状优化

含有多种功能开孔的轻质回转壳结构是航空航天结构系统内的常用支撑构件,其开孔形状直接影响结构的静动态性能。以回转壳结构为对象,基于超椭圆方程和坐标映射变换推导了回转壳开孔边界的参数化表达,开展了开孔形状动力学优化研究。为提高结构优化计算的精度、效率和收敛性,提出了准等弧长方法和基于均匀设计的序列响应面近似建模方法(SRSM),以分别实现空间超椭圆曲线的精确逼近、减少结构有限元分析成本和加快迭代收敛。以非支配排序遗传算法Ⅱ(NSGA-Ⅱ)作为响应面模型求解算法,结合有限元分析构建了回转壳开孔形状优化设计流程,开展了最大化结构一二阶频率带隙的典型回转壳结构开孔形状优化设计。结果表明,基于超椭圆方程和序列响应面法的开孔优化方法获得了有效改进结构动态特性的回转壳开孔形状,对开展计算耗时工程结构形状优化设计具有一定应用价值。

Shape optimization of openings on rotation shells based on super-elliptic function and sequential response surface method

Rotation shell structures with closed functional openings are widely used as lightweight and rotary components in aeronautic and aerospace engineering. The opening's geometrical shape has great effects on structural static and dynamic performances. A parameterized geometry model to optimize the opening shape is presented based on the parametrical mapping method in this paper, by considering the opening boundary as super-elliptic function. In order to improve the accuracy, efficiency and convergence of structural optimization, isoperimetric controlling approach is employed to precisely fit space super-elliptic boundary curve for geometrical modeling, and a sequential response surface approximate method (SRSM) is proposed to reduce finite element analysis cost and accelerate the iterative convergence. Overall structural optimization procedure is constructed to carry out opening shape optimization with maximizing the difference between the first and second order frequencies in rotation shell structure. Non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) is implemented to obtain global optimum as the SRSM sub-optimizer. Numerical results indicate that the dynamic performance of rotation shell could be enhanced remarkably by opening shape optimization using the presented optimization method combined with super-elliptic function and SRSM. The optimization procedure exhibits the application value in the computation-intensive shape optimization of engineering structures.