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Asymptotic models of integrally-strained slender structures for high-fidelity nonlinear aeroelastic analysis.

机译:用于高保真非线性气动弹性分析的整体应变细长结构的渐近模型。

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A three-step methodology is presented for high-fidelity modeling of slender structures with embedded actuators and sensors. The solution to the three-dimensional problem of solid electromechanics in the slender domain is sought through the identification of two different scales in the system. The variational formulation of the problem is then asymptotically approximated at each level, defining, first, a linearized local problem at the cross section under the assumption of small local strains and, then, a geometrically-nonlinear long-scale problem along the dominant dimension. Each problem is solved independently and their combined solution provides an asymptotic approximation to the electroelastic field in the original domain. This approach can be used to define the solid part in a fluid-structure interaction problem. The proposed formulation can model anisotropic non-homogeneous slender structures with embedded piezoelectric actuators and sensors, hygrothermal effects, and arbitrary geometrical definitions of the cross section (thin-walled or solid, closed- or open-cell) and the reference line (initially curved and twisted). In addition to this, a Ritz-based method is used to define a modal approximation to the local cross-sectional warping displacements to account for particular deformation shapes (e.g., airfoil camber bending in a wing). Numerical results are used to illustrate the formulation. They include comparison with three-dimensional finite-element models, conventional beam theories, and analytical results. The formulation yields numerically-efficient low-order structural models, and this is illustrated by the nonlinear structural response analysis of a complete flexible aircraft. The integration of the models in high-fidelity aeroelastic analysis is finally exemplified by steady-state results on a very flexible swept wing in transonic flow.
机译:提出了一种三步方法,用于带有嵌入式执行器和传感器的细长结构的高保真建模。通过识别系统中两个不同的尺度,寻求解决细长域中的固体机电三维问题的方法。然后在每个级别上渐近逼近问题的变分形式,首先在假设局部应变较小的情况下,在横截面上定义线性化局部问题,然后沿支配维度定义几何非线性长尺度问题。每个问题都是独立解决的,它们的组合解决方案为原始域中的电弹性场提供了渐近近似。此方法可用于定义流体-结构相互作用问题中的实体零件。拟议的公式可以模拟具有嵌入式压电致动器和传感器,湿热效应以及横截面(薄壁或实心,闭孔或开孔)和参考线(初始弯曲)的任意几何定义的各向异性非均匀细长结构和扭曲)。除此之外,基于Ritz的方法用于定义局部横截面翘曲位移的模态近似值,以说明特定的变形形状(例如机翼中的机翼外倾弯曲)。数值结果用于说明配方。它们包括与三维有限元模型,常规梁理论和分析结果的比较。该公式产生了数值有效的低阶结构模型,这可以通过完整的柔性飞机的非线性结构响应分析来说明。最后,在跨音速流中一个非常灵活的后掠翼上的稳态结果证明了模型在高保真气动弹性分析中的集成。

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