Shape optimization of curved slots on 3-D surface

In the aeronautic and aerospace thin-walled structures, hole shape designs are very popular to achieve the weight reduction, structural reparation, cooling and other purposes and have important influences on the structural weight, performances and fatigue life. Due to the fact that the hole shape optimization has to ensure the movement of the hole contour always located on the specific 3D surface, it is difficult to define reasonably the geometric design variables and the automatic design procedure of engineering simulation by means of existing design methodologies.

The research group of Professor ZHANG WeiHong at Northwestern Polytechnical University, China has been dedicated to advanced optimization methods of aeronautic and aerospace lightweight structures for a long time. Recently, WANG Dan, Ph. D student, Professor ZHANG WeiHong, her supervisor and other research staffs deeply investigated the above problem in the paper “Shape optimization of 3D curved slots and its application to the squirrel-cage elastic support design”, which was published in SCIENCE CHINA Physics, Mechanics & Astronomy, (http://phys.scichina.com/) Volume 10, 2010.

The squirrel-cage elastic support is one of the most important components of an aero-engine rotor system. A proper structural design will favor the static and dynamic performances of the system. This elastic support is a typical thin-walled structure of cylindrical surface on which a certain number of milling slots are distributed in a periodic way. Previous works related to the squirrel-cage elastic support design were mainly experience-based and focused on the vibration reduction and structure resistance analysis. However, practical applications indicate that the transition of a small circular arc on the rectangular slots will lead to an important stress concentration which will further initiate fatigue cracks and even sometimes break the cage strips. Yet, no related references exist about shape optimization of holes on such 3D surfaces.

A new parametrical mapping method is proposed by the research team of Professor ZHANG Weihong. The essential idea is to define geometrical design variables in the 2D reference coordinate system for the description of 3D curved contours. Mathematical demonstrations show that this approach ensures that the curved contours are automatically located on the prescribed 3D surface. As a result, the 3D design problem is equivalently transformed into a 2D parametric problem. Finally, slot shape optimization of the aero-engine squirrel-cage elastic supports is successfully performed by this approach. Three kinds of slot contour shapes, i.e., one-directional symmetrical shapes, bi-directional symmetrical shapes and elliptical shapes are used to test the approach. It concludes that the spindly slot shape with two narrow ends and one large width at the center is a new valid design. The stress concentration in the squirrel-cage elastic supports can be effectively reduced without increasing the structural weight or changing the structural rigidity.

In fact, the parametrical mapping method is a universal approach that combines perfectly the philosophies of computational geometry and shape optimization and it can be thus applied to shape design optimization of holes on other types of surfaces.

This work is supported by the National Science Fund for Distinguished Young Scholars of China (Grant No. 10925212), National Science Foundation of China (Grant Nos. 50775184, 90916027) and Aviation Science Foundation of China (Grant No. 2008ZA53007).

See the article:
Wang D, Zhang W H, Wang Z P, etc. Shape optimization of 3D curved slots and its application to the squirrel-cage elastic support design. Sci China Phys Sci, 2010, 53: 1895 — 1900

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