Reduced order modeling analysis for flexible wing using a co-rotational beam element

ifasd2024 Tracking Number 83

The objective of this paper is to develop a reduced order modelling (ROM) method suitable for aeroelastic analysis with high efficiency and sufficient fidelity. The method is applied for solving the static aeroelastic problems of highly flexible wing containing geometric nonlinearities. The structural ROM method is based on equations derived from the Galerkin approach to solve the geometric nonlinear dynamics in a weak form, in which the explicit calculation of nonlinear stiffness is not practical. Based on dynamic response data samples, nonlinear stiffness coefficients in structural dynamics equation are identified based on the fast Fourier transform (FFT) and the harmonic balance nonlinearity identification technique. And dynamic response data samples can be gained by the commercially finite element (FE) software, however, for aeroelastic analysis, the computational cost usually takes a lot. In this paper, we adopt the co-rotational (CR) finite element to shorten the simulation time and better deal with different load cases. The total and updated Lagrangian formulations for geometrically nonlinear analysis are used in most commercially available FE software. Their accuracy is enough for the engineering application, but are numerically quite demanding and may exhibit convergence issues. However, the CR finite element is computationally more efficient for the case of large displacements and/or large rotations in a geometrically nonlinear analysis, as the rigid part is purged from the total motion. More specifically, the main idea of CR theory is to decompose the motion of the element into rigid body and pure deformational parts, through the use of co-rotational frame which continuously rotates and translates with the element. In this paper, the CR beam element is adopted for the structural simulation of wing. The fidelity of the method (ROM with CR) is verified against ROM with MSC Nastran (a widely-used multidisciplinary structural analysis solver), on a high aspect ratio wing. Compared to solutions figured out by ROM with MSC Nastran, the result of ROM with CR shows high efficiency and adequate accuracy. The final paper will include detailed simulated results of ROM with CR and comparison with MSC Nastran.