An Enhanced Modal Approach for Large Deformation Modeling of Wing-Like Structures

Abstract

A new modal-based method that captures the geometric nonlinear effects that arise in the regime of large deformations of wing-like structures is presented. The most limiting factors of the modal approach are the linear force-displacement relationship and the representation of the nodal displacement field based on normal modes. The proposed extension includes stiffness terms that cubically depend on the generalized coordinates. The structural deformation is calculated not only by normal modes but also by higher order mode components that account for the foreshortening effect at beam-type structures. The approach is applied to a cantilever slender wing. Static and dynamic results are presented together with results from a commercial finite element solver and from the UM/NAST aeroelastic solver from the University of Michigan. The numerical study highlights the capability of the new approach to capture nonlinear effects while keeping the simplicity of the modal approach.

Nonlinear Aeroelastic Trim of Very Flexible Aircraft Described by Detailed Models

“…The core module coupling MSC Nastran SOL 400 with the VLM code is validated by analyzing the nonlinear aeroelastic static response of a highly flexible 16 m wing [23] and of the X-HALE risk reduction vehicle (RRV) [24] at a prescribed freestream velocity and angle of attack. The analyses are performed by assuming clamped boundary conditions at the root for the wing and at the wing centerline for the X-HALE.…”

“…The nonlinear aeroelastic static response of the 16 m wing is studied for incompressible flow, ρ ∞ 1.225 kg∕m 3 , V ∞ 40 m∕s, α 3, 4, 5 deg, and by neglecting weight. The results are compared with solutions from 1) the UM/NAST solver based on strip-theory aerodynamics corrected with weighting factors [23], 2) the UM/NAST solver based on VLM aerodynamics [22], and 3) the MSC Nastran SOL 400/VLM solver of the DLR toolbox [14].…”

“…The deflections from UM/NAST with strip theory are smaller than those obtained considering VLM aerodynamics, with a relative wing-tip difference that increases from 1.85 to 2% with the angle of attack. This behavior is motivated by considering that the weighting factors used to correct the strip-theory aerodynamic load distribution are evaluated on the rigid undeformed configuration [23].…”

Aeroelastic Stability of High-Speed Cylindrical Vehicles

“…These shape bases are often composed of free-vibration modes and can be enhanced by including static loading shapes which capture deformation due to specific loading conditions of interest 5 or higherorder mode shapes which capture geometric nonlinearities. [18][19][20] Consider the undamped full-order structural dynamic equations ,…”

Effects of Geometric Nonlinearities on the Fidelity of Aeroelasticity Loads Analyses of Very Flexible Airframes

“…The cost of direct integration of finite element equations is often directly proportional to the size of the system. While the method of modal superposition, where the system is reduced from the size of the entire physical system to a select number of modes, is very common in linear dynamic response analysis [36]- [38], a key difference with nonlinear analyses is that the stiffness matrix, and thus, the mode shapes and natural 27 frequencies, are often dependant on the applied load and current state of deformation. On the other hand, Bathe showed that even the eigenvectors and eigenvalues derived from a linear modal decomposition can be used to accurately model the effect of nonlinearities using an iterative solution methodology [23], [24].…”