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.