中文摘要：

热载荷作用下，由于热障涂层（thermal barrier coatings，TBCs）各层材料的热不匹配以及材料参数的温度相关等因素，会使热障涂层界面区域存在复杂的应力应变场，影响系统安定性，并导致涂层开裂和剥落．将热障涂层外凸和内凹微观界面结构简化为多层圆筒模型，借助经典机动安定定理，利用特雷斯卡（Tresca）屈服准则和增量破坏准则处理对时间的积分问题，避免了常规安定性分析的数学规划问题，建立了热障涂层安定极限分析方法，将材料屈服强度随温度变化关系简化为双线性关系，利用补偿变换的方法简化求解过程，对典型热障涂层安定性进行了研究．结果表明，利用基于圆筒的安定极限分析方法，能够方便求解安定极限，便于工程应用：热障涂层安定极限值明显高于弹性设计值，且界面外凸区域安定极限高于内凹区域极限值，结构首先在内凹处失效；圆筒模型基体曲率和涂层厚度越大，结构安定极限越高，分析结果与试验结果一致；所建立的热障涂层安定分析方法，对进一步研究考虑蠕变因素影响的热障涂层安定性具有重要意义．

英文摘要：

Due to thermal expansion misfit and temperature dependent material parameters among layers of thermal bar- rier coatings （TBCs）, the interfacial stress-strain fields become more complicated under thermal loading, which affecting the TBCs stability and spalling failure directly. In this study, the convex and concave microscopic structure around TBCs interface is simplified as multi-cylinder model, with the classic shakedown theorem, Tresca yield criterion and incremental failure criterion, an analytical method of TBCs shakedown analysis is established, in addition, avoiding the time integral and mathematical programming. The variation between material yield strength and temperature is simplified as bilinear relationship, and the stability of typical TBCs is analyzed by using the method of compensation transformation to sim- plify the solving process. The results show that the stability limit can be obtained facility by using the analytical model of shakedown analysis based on the cylinder model. Stability limit of TBCs was significantly higher than the elastic limit, and the regional stability limit in convex area is higher than concave area around the interface, which indicates that failure prior to occur in concave area. The larger the radius of curvature of the substrate and the thickness of TBCs, the higher the stability limit, and those analysis results are consistent with the experimental results. The shakedown analysis method of TBCs built in this study has a great significant influence on the further research on stability of TBCs considering the creep.