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Aerothermoelastic analysis of imperfect FG cylindrical shells in supersonic flow

机译：超音速流中不完善的FG圆柱壳的气动热弹性分析

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摘要

The supersonic panel flutter of functionally graded cylindrical shells under thermal loadings is investigated by considering the effects of various axisymmetric and asymmetric geometric imperfections. The problem is formulated using a nonlinear first-order shear deformation theory of shells with the first-order aerodynamic piston theory. The temperature is assumed to vary in the thickness direction according to the steady-state heat conduction equation. The semi-analytical finite element method (FEM), based on the field consistency redistribution approach is used to obtain discretized nonlinear aeroelastic equations. In the process of FEM, the imperfection functions are also discretized and efficiently approximated by the Hermitian polynomials in order to facilitate the required integrations. For analysis purpose, the deformations and stresses induced by the temperature rise are first computed by solving the nonlinear static aerothermoelastic equations using the Newton-Raphson method. The pseudo-arclength continuation method is also employed to detect the possible snap-through of the shell. The linearized stability equation about the equilibrium state is then used for determining the flutter boundaries. Numerous parametric studies are conducted to examine the effects of temperature rise and imperfections on the flutter boundaries, which show considerable effects of imperfections on changing the trend of variation of the flutter pressure with temperature.
机译：通过考虑各种轴对称和非对称几何缺陷的影响，研究了功能梯度圆柱壳在热载荷下的超音速面板颤振。该问题是根据壳体的非线性一阶剪切变形理论和一阶气动活塞理论来解决的。假定温度根据稳态热传导方程在厚度方向上变化。基于场一致性重新分布方法的半解析有限元方法（FEM）用于获得离散化的非线性气动弹性方程。在有限元过程中，缺陷函数也被离散化，并通过埃尔米特多项式有效地近似，以便于进行所需的积分。为了分析的目的，首先通过使用牛顿-拉夫森（Newton-Raphson）方法求解非线性静态气动热弹性方程来计算由温度升高引起的变形和应力。伪弧长延续方法也用于检测壳体的可能咬接。然后使用关于平衡状态的线性化稳定性方程式来确定颤动边界。进行了大量的参数研究，以研究温度升高和缺陷对颤振边界的影响，这表明缺陷对颤振压力随温度的变化趋势的变化具有相当大的影响。

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