Dynamic Scaling of a Wing Structure Model Using Topology Optimization

Abstract

In this paper, a dynamic scaling methodology is introduced to devise reduced scaled models of aircraft with the objectives of minimizing the development cost and exploring the design space. A promising way to accomplish this is using Topology Optimization (TO) for Additive Manufacturing (AM). Here, TO is employed to design a reduce scale model by matching its natural frequencies and mode shapes to those of a full scale model. Different TO strategies based on density approach are tested with the goal of achieving a dynamically scaled structure that can be manufactured. To achieve this goal, the TO solution should be free from intermediate densities, which is observed for some TO strategies but not all. When no penalization factor is applied: (i) the relative difference between natural frequencies is less than 1% and (ii) the estimated Modal Assurance Criteria (MAC) metric to evaluate the correlation between mode shapes is close to the ideal identity matrix. These results demonstrate the effectiveness of the dynamic scaling methodology. However, when using a penalization factor to avoid intermediate densities, the dynamic behavior correlation between full and scaled models degrades. This trend is more visible in the MAC metric, where off-diagonal terms above 20% and diagonal terms below 90% appear.

Keywords

• dynamic scaling
• topology optimization
• additive manufacturing
• modal parameters
• wing structure