An integrated optimization method of multi-hierarchy variables for rudder structures with radial force transfer paths

The optimization of structures with beam-like force transfer paths for flight vehicles is closely dependent on the hierarchy decomposition and interaction effects of variables. In this work, the variable of a rudder structure with radial beams is decomposed into conventional hierarchies of topology and size and a new unconventional hierarchy of angle, which is a representational variable with implicit expression for radial beam direction. A unified code form is proposed for discrete variable, i.e., topology and continuous variables, i.e., angle and size, and then an integrated optimization method of multi-hierarchy variables is developed based on the genetic algorithm and the interaction effects between different hierarchies are fully considered. A two-hierarchy optimization model of topology and size and a three-hierarchy optimization model of topology, size and angle are then constructed, respectively. The statics problem with objective of minimum structural mass and constraints of stress and displacement, and the static aeroelastic problem with objective of minimum influence quantity and constraints of structural mass, stress and displacement are solved. The results show that the three-hierarchy optimization model is more efficient than the two-hierarchy one with structural mass reduction of 18.9 % and aeroelastic influence quantity reduction of 4.3 %.