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 引用本文: 安效民 徐敏. 一种几何大变形下的非线性气动弹性求解方法[J]. 力学学报, 2011, 43(1): 97-104.
Xiao-min An Xu Min. An improved geometrically nonlinear algorithm and its application for nonlinear aeroelasticity[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 97-104.
 Citation: Xiao-min An Xu Min. An improved geometrically nonlinear algorithm and its application for nonlinear aeroelasticity[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 97-104.

## An improved geometrically nonlinear algorithm and its application for nonlinear aeroelasticity

• 摘要: 非线性气动弹性的时域求解中, 涉及到非线性的流体动力学(CFD)和非线性的结构动力学(CSD)耦合问题. 基于Co-rotational理论, 推导了三维壳单元几何非线性下的切线刚阵和内力公式, 针对推进过程中的能量守恒, 引入预估-校正推进格式, 发展了一种近似能量守恒的非线性动态响应算法; 基于1/2时间步的交错耦合格式, 结合带有几何守恒律的双时间推进求解雷诺平均N-S方程的求解器, 发展了非线性气动弹性求解的高精度耦合格式. 通过结构几何大变形下的静力和动力分析验证了所发展的结构非线性求解器, 并通过AGARD445.6机翼的非线性气动弹性响应分析, 说明了所发展耦合求解方法的实用性.

Abstract: The coupled algorithm between computational fluid dynamics(CFD) and computational structural dynamics (CSD) referring to nonlinearaeroelasticity are studied in time domain. Based on CR (Corotational)theory, the expressions of tangent stiffness equations and internal forcesof 3D shell element under geometric nonlinear structure are derived, thenintroducing a predictor-corrector procedure, a nonlinear dynamic solutionalgorithm is developed based on approximate energy conservation during thedynamic process. Combined with dual-time marching scheme and geometricconservation law, which are included in the solver of Reynolds averagedNavier-Stokes equation, an coupled algorithm is improved for nonlinearaeroelasticity based on the staggered process with mid-steps. The developednonlinear structural solver is performed on static and dynamic analysis andvalidated by the results of experiments and references. With the applicationon nonlinear aeroelastic respones simulation of AGARD 445.6 wing, it showsthat the improved coupled algorithm has a better stability andpracticability for nonlinear analysis.

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