Mathematical method for prediction aeroelastic phenomena and multidisciplinary optimization lifting surfaces of flight vehicle at preliminary stage design

Every year, the air transportation market increases the requirements for aircraft performance in order to obtain greater profits. Satisfaction of this requirement is the main purpose for aircraft manufacturer. One of the ways to achieve this purpose is improving the design process by developing and implementing new approaches and tools for modelling different phenomena (in considered case – Aeroelastic phenomena) inherent to flight vehicles. The purpose of this report is to present a modern mathematical method that allows modelling static and dynamic Aeroelastic Phenomena by a symbolic operation, in contrast to the numerical methods that are widely used today. The theory of this method based on science analogies approach which allow to present interaction (considering 6 DOF) between aeroelastic forces in analytical formulation, using modern Computer Algebra System tools and as results exclude iteration calculations which inherent inversing and eigenvalue extraction of large dimension matrixes. Approach of this method based on reduced order modelling principle and main idea is presenting lifting surface (wing, blade, etc.) as a principal scheme which look as parallel, serial and star connection of three types of elements: aerodynamical, elastic and inertial. Each element describes by respective matrixes of parameters with maximum dimension of 6×6 for 6 DOFs (3 translations 3 rotations). Analysis is performing by transformation scheme (connection nodes condensation) and finding equivalent matrix of “Aeroelasticity” using recurrent equations for each type of connection (analogical with electrical circuit). Described method was validate by modelling: Wing load distribution, Divergence, Effectiveness of control surface and Flutter. Finally, gotten Math model describes dependences between design variables and aeroelastic characteristic in explicit symbolic form which allow performs wide fast parametric investigation at preliminary stage design. Additional this model will be useful for structure optimization process using analytical methods and for machine learning and will allow expand using artificial intelligence in aerospace structure design.