功能梯度材料薄板的热气动弹性数值分析方法及特性研究

对高超声速环境中功能梯度薄板的热气动弹性问题的有限元数值分析方法和特性进行了研究。在考虑了沿板厚方向上非线性温度分布影响基础上，建立了更为精确的功能梯度薄板的热气弹耦合力学模型。采用Eckert参考温度法模拟气动加热效应，进而使用有限元方法求解热传导方程，得到薄板内部的热应力以及物性参数分布，并求解功能梯度材料薄板的控制方程，得到薄板在热应力-气动力-弹性力耦合下的振动特性。结果表明，所提出的基于有限元的数值分析方法能够有效处理该问题的复杂性，并且发现气动加热效应能够使薄板发生热屈曲或者提前进入振动状态，此外还发现当无量纲气动力位于某一“过渡区”内时，薄板行为对初值异常敏感。最后，建立的功能梯度薄板热气弹耦合模型以及相关数值求解方法，能够有效地研究高超声速环境中功能梯度材料薄板的振动行为，相关数值结果对功能梯度薄板的热气弹研究也具有借鉴意义。

Numerical Analysis Method and Aerothermoelastic Behaviorsof Temperature Dependent Functional Graded Panels

Numerical analysis based on finite element method and aerothermoelastic behaviors of temperature dependent Functional Graded Panels (FGP) in supersonic or hypersonic flows are investigated in this study. Considering the nonlinear distribution of temperature along the thickness direction of the panel, a more available aerothermoelastic model of FGP is established. The aerodynamic heating effect is simulated by use of Eckert’s reference temperature method, then thermal stresses and physical properties of the panel are obtained by solving the Heat Conduction Equation by use of the Finite Element Method. Finally, solving the governing equation of FGP by  use of the Finite Element Method, the vibration behaviors due to aerothermoelasticity are studied. From the simulation results, it can be found that, the numerical analysis is effective and efficient, and the effects of aerodynamic heating can make the panel turn into thermal buckling state or vibrating state easily. And it is also found that, the panel behaviors are very sensitive to the initial condition when the non dimensional aerodynamic force is in a certain ‘transition region’. As a conclusion, it can be drawn that the model and numerical method presented in this study could be used to study the aerothermoelastic behaviors of FGP accurately and feasibly.