| Citation: | XU Q Y，MENG Y，LI S. Strain-based geometrically nonlinear beam modeling and analysis[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（8）：2039-2049 （in Chinese） doi: 10.13700/j.bh.1001-5965.2021.0627
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Under the action of aerodynamic forces, flexible wings undergo large deformations, for which geometric nonlinearity cannot be ignored. By taking advantage of their slenderness, flexible wings can be modeled as beams. This paper developed the dynamic equilibrium equations of nonlinear beams based on the geometrically exact beam theory and Hamilton principle. Different from the classical displacement-based finite element, this work took the generalized strains as interpolated variables and obtained the generalized mass matrix, damping matrix, stiffness matrix and force vectors, based on which a strain-based nonlinear beam model was proposed. The nonlinear dynamic equations were then solved by Newmark method combined with Newton-Raphson iterations with typical examples investigated from both static and dynamic perspectives. Next, the results were compared with those calculated by finite-element software, which proved that the strain-based beam model has better convergence with the comparable accuracy. The method was further verified by static ground tests of a large-aspect-ratio wing model, during which laser displacement sensor and fiber optic sensing technology were utilized to measure the structural deformation. The excellent agreement between numerical results calculated by the proposed method and the test results further validated the accuracy of the strain-based formulation.
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