Explicit design optimization of air rudders for maximizing stiffness and fundamental frequency

In aerospace engineering, there is a growing demand for lightweight design through topology optimization. This paper presents a novel design optimization method for stiffened air rudders, commonly used for aircraft attitude control, based on the Moving Morphable Component (MMC) method. The stiffeners within the irregular enclosed design domain are modeled as MMCs and discretized by shell elements, accurately capturing their geometry and evolution during optimization process using explicit parameters. In order to maximize the stiffness and fundamental frequency of the rudder structures, numerical analysis algorithms were developed with shape sensitivity analysis conducted. To comply with the manufacturing requirement, a minimum thickness is prescribed for the stiffeners, and the thickness and density penalty schemes are proposed to meet the minimum thickness constraint and prevent the occurrence of spurious modes respectively. The method's effectiveness was demonstrated through optimization examples of a typical trapezoidal air rudder, illustrating the significance of stiffener's distribution on design objectives. The explicit modeling characteristics allow for directly importing the optimization results into CAD systems, significantly enhancing the engineering applicability.