功能梯度材料结构的非线性稳定性理论研究

Due to its material properties through the thickness, mechanical behavior of structures made of functionally graded materials under applied loading is often different from that of structures made of traditional materials. This project is concerned with investigating in nonlinear stability theory of functionally graded material structures in the frame of geometric nonlinear theory. Unusual nonlinear mechanical behavior of functionally graded material structures are investigated in this project, which reveal the intrinsic mechanism of effect of material properties on the mechanical behavior for functionally graded material structures. In this investigation, we focus on the following problems: 1. a functionally graded structure subjected to applied load may be have many deformed configurations, 2. the effect of the pre-buckling coupling deformation on the buckling of the functionally graded material structures are studied quantificationally, 3. based on the geometric nonlinear theory, a nonlinear stability theory used for the functionally graded material structures is established by investigating the whole procedure in deformation of the structures subjected to applied loads and taking the effects of the pre-buckling coupling into account in the analysis. The above mentioned works are challenging problems in field of nonlinear mechanical behavior of functionally graded material structures, so, the achievements of the project are expected to enrich the theory of stability and thermoelastic mechanics for functionally graded material structures and to provid theoretical foundation for application and safe design of functionally graded material structures.

由于功能梯度材料本身的材料特性，使得其结构在外因素下的力学响应，常常异于传统材料结构。本项目将在几何非线性理论框架下，拟就功能梯度材料结构的非线性稳定性等问题展开研究，分析外因素下功能梯度结构异于均匀材料结构的力学行为, 揭示功能梯度材料性能变化对这类结构力学行为影响的内在机理。本项目主要针对以下问题展开研究：1. 外因素下，功能梯度结构可能产生的多构形问题；2. 定量分析前屈曲耦合变形对功能梯度结构屈曲的影响；3.从结构的全局变形入手，基于变形的几何非线性理论，并计及前屈曲耦合变形的影响，建立适合功能梯度结构的非线性稳定分析理论。以上问题是功能梯度材料结构非线性力学行为研究领域中富有挑战性的课题，其研究结果无疑会丰富功能梯度结构热弹性力学理论以及结构稳定理论，并为功能梯度材料结构的应用和安全性设计提供理论基础。

由于功能梯度材料本身的材料特性，使得其结构在外因素下的力学响应，常常异于传统材料结构。基于此，本项目研究了以下几个方面的问题：(1) 研究了均匀、非均匀热载荷下梯度材料梁结构的稳定性、大挠度弯曲和过屈曲问题，给出了相关问题闭合形式的精确解。并通过这些解研究了功能梯度结构的多个构形问题。研究结果表明：热载荷作用下，夹紧FGM梁发生过屈曲变形，而简支梁则发生较为复杂的热弯曲变形，而且在同一热载荷作用下，简支FGM梁将会产生多构形问题。(2)研究了纵横机械载荷作用下梁非线性静态响应，并给出了问题的闭合形式解。并发现，纵横载荷作用下均匀材料梁的非线性力学行为，十分类似于单一热载荷作用下两端简支的功能梯度梁的弯曲行为。(3)研究了机械或热载荷作用下，梯度多孔材料圆板的线性、非线性静动态力学行为。(4)研究了机械载荷作用下梯度多孔材料梁的非线性弯曲、过屈曲行为。(5)研究了非完善界面和粘弹性加载对一类石英晶体微天平振动响应的影响。.本项目的研究结论揭示了功能梯度材料的材料性能变化对这类结构力学行为影响的内在机理，为功能梯度材料结构的应用和安全性设计提供了必要的理论基础。