功能梯度结构的热-力冲击动态屈曲行为

Functionally graded material (FGM) structures are widely used in unusual working environment with the high-temperature thermal or mechanical impact loadings, etc. To achieve a theoretical basis for the impact resistance optimizaiton design and stability analysis of FGM structures, this project is focused on the dynamic-stability of FGM structures under thermo-mechanical impact loadings. Based on the non-linear theory of plates and shells and thermo-elasticity, the dynamic governing equations are derived by considering the various factors gradually, such as the correlation of the material physical performance parameters versus temperature and geometry, the initial geometrical imperfection of structures, thermoelastic coupling and wave effects, etc. By using efficient numerical methods, the nonlinear partial differential control equations with multi-variables coupling are solved, and the critical loadings are obtained by selecting a reasonable and feasible dynamic buckling criterion. Furethermore, the post-buckling behaviors of structures are analyzed preliminarily. The innovations of this project in the structure stability field are profoundly manifested by considering the thermal impact loading, thermoelastic coupling and thermal wave effects, etc. This study will reveal the relationships of the dynamic instability versus thermo-mechanical impact characteristics, the geometry and imperfection parameters, the graded properties of materials and temperature, thermoelastic coupling and thermal wave effects, etc. Meanwhile, the corresponding analysis method will be developed to reveal the impact failure mechanism of the FGM structures, with obtaining the dominant factors affecting the impact instability. And the optimal component distribution law of FGM will be obtained as well. The study is helpful to the design and stability analysis of FGM structures.

功能梯度材料(FGM)结构常服役于高温热冲击或机械冲击等超常工作环境中。为给该结构的抗冲击优化设计与稳定性分析提供理论基础，本项目研究FGM结构在热－力冲击载荷作用下的动力稳定性。基于几何非线性板壳理论和热弹性理论，考虑材料物理性能参数与温度和几何的相关性、结构的初始缺陷、热弹耦合、波动效应等建立动力学控制方程。采用行之有效的数值方法，对该多变量耦合的非线性偏微分控制方程进行求解，选取合理可行的冲击屈曲判别准则获得临界载荷，并进行初步的后屈曲分析。项目的主要创新之处体现在基于广义耦合热弹性理论，考虑冲击载荷、热-弹耦合和波动效应研究FGM结构的非线性动态屈曲机理，并发展相关的分析方法。通过研究可揭示一类非均匀结构动力失稳与冲击特性、结构几何与缺陷、材料的梯度特性和温度相关性、热弹耦合和波动效应等之间的关系，给出影响FGM结构冲击稳定性的主要因素和最优组分分布规律，揭示冲击失效机理。

功能梯度材料(Functionally graded materials，简称FGM)及其结构常服役于高温热冲击或机械冲击等超常工作环境中。为给该结构的抗冲击优化设计与稳定性分析提供理论基础，本项目研究功能梯度结构在热－力冲击载荷作用下的动力稳定性问题。主要完成三方面研究内容：（1）功能梯度梁的动态特性及其热冲击稳定性：求解获得了热冲击作用时功能梯度材料内部的瞬态温度场、热轴力及热弯矩；建立了功能梯度梁热冲击屈曲问题研究的辛求解方法，获得该梁的各阶临界载荷与屈曲模态；精确考虑轴线伸长变形，研究了功能梯度梁在随动分布载荷作用下的后屈曲问题；在此基础上还研究了沿轴线切向分布随动载荷作用下功能梯度材料简支梁在过屈曲前后的自由振动特性。（2）功能梯度圆板和环板的动力特性及热冲击动态屈曲和后屈曲研究：基于几何非线性板理论和热弹性理论，考虑材料物理性能参数与位置的相关性、结构的初始缺陷、热弹耦合效应建立动力学控制方程，采用理论分析与数值计算相结合求得了动态响应、临界温度和后屈曲路径。研究发现功能梯度圆板和环板的屈曲对于初始缺陷的大小较为敏感，随缺陷增大，屈曲发生的时间提前，但屈曲温度变化不大。（3）功能梯度圆柱壳的动力响应及稳定性研究：基于经典壳理论，采用微分求积法获得热冲击作用下该结构的瞬态位移及热应力；在Hamilton体系下采用辛方法研究了该结构在热冲击载荷与端部扭转冲击载荷分别作用时的动态屈曲，其中考虑了应力波效应的影响，求解获得了轴对称屈曲和非轴对称屈曲两种情况的临界载荷与屈曲模态。研究发现，屈曲模态与材料无关，另外可以通过适当调整功能梯度材料的组分含量来改变结构的屈曲温度、降低内部热应力。. 本项目的研究揭示了一类非均匀结构动力失稳与冲击特性、结构几何与缺陷、材料的梯度特性和温度相关性、热弹耦合和波动效应等之间的关系，给出了影响功能梯度结构冲击稳定性的主要因素和最优组分分布规律，揭示了冲击失效机理。

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