Elastic wind tunnel model design via eigenvector-based level-set topology optimization

ifasd2024 Tracking Number 85

The objective of this study is to develop a numerical method for designing elastic wind tunnel models suitable for additive manufacturing. To assess dynamic aeroelastic phenomena in wind tunnels, the scaled model must be elastic and emulate the dynamic characteristics of full-scale aircraft [1]. Realizing structural properties at scaled size based on the scaling law is challenging. When scaling down the full-scale components to the scaled model, changes in some structural properties occur [1]. Also, practical constraints may hinder directly scaling down internal structure of full-scale aircraft. Therefore, redesign of the internal structure is necessary. However, the process of redesigning the internal structure is complicated. In this study, we propose a numerical method for designing the internal structure that can be 3D printed. In this work, a Level-set topology optimization method [2] is developed to generate the internal structure of elastic wind tunnel model, which has equivalent mass, eigenvalues, and eigenvectors to its full-scale aircraft. In this method, the internal structure's boundary is implicitly represented by a level-set function. For structural analysis, an automatic differentiation algorithm is integrated into the extended finite element method [3] to enable gradient-based optimization. The proposed method was tested on a simple geometry case. The result showed that the proposed method can iteratively optimize the structure to satisfy each objective function, i.e., the mass, eigenvalues, and eigenvectors. Future modifications will allow consideration of static deflection and multi-objective optimization. The proposed method can take eigenvectors as the objective function. Although there is some research on topology optimization using eigenvalues as the objective function [4], there are few research using eigenvectors as the objective function. The necessity to calculate all eigenvectors to derive one eigenvector derivative vector in machine precision has traditionally been impractical [5]. This study introduces a new approximation method to efficiently optimize structures to meet eigenvector targets. In conclusion, the proposed method can design the 3D-printable elastic wind tunnel models, considering mass, eigenvalues, and eigenvectors as objective functions. Ongoing modifications aim to integrate static analysis results and handle multi-objective optimization.