梯度多孔材料结构的非线性力学行为研究

Due to its material properties through the thickness, mechanical behavior of structures made of graded porous materials under applied loading is often different from that of structures made of traditional materials. This project is concerned with investigating in mechanical behavior of graded porous material structures in the frame of continuum mechanics theory. Nonlinear mechanical behavior, such as large deflection bending,buckling and postbuckling, of graded porous material structures are investigated in this project, which reveal the intrinsic mechanism of effect of graded porous material properties on the mechanical behavior for the structures. In this investigation, we focus on the following problems: 1. a graded porous 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 graded porous structures are studied quantificationally, 3. based on the geometric nonlinear theory, postbuckling responses of the graded porous structures are analysed 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 graded porous structures, so, the achievements of the project are expected to provid theoretical foundation for application and safe design of graded porous structures.

由于梯度泡沫材料本身的材料特性，使得其结构在外因素下的力学响应异于传统材料结构。本项目将在连续介质力学理论框架下，拟就梯度泡沫材料结构的非线性力学行为问题展开研究，分析外因素下梯度泡沫结构的弯曲、屈曲以及过屈曲等力学行为, 揭示梯度泡沫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，梯度泡沫材料结构的大挠度弯曲问题；2. 定量分析前屈曲耦合变形对梯度泡沫材料结构屈曲的影响；3.从结构的全局变形入手，研究梯度泡沫材料结构的过屈曲问题，并建立适合梯度泡沫材料结构的非线性稳定分析理论。以上问题是轻质非均匀材料结构非线性力学行为研究领域中富有挑战性的课题，其研究结果无疑会为梯度泡沫材料结构的应用和安全性设计提供理论基础。

本项目旨在研究梯度泡沫材料结构的弯曲、屈曲以及过屈曲等力学行为，揭示梯度泡沫材料性能变化对这类结构力学行为影响的内在机理。主要研究了各类因素下梯度多孔材料梁、圆板、矩形板以及圆柱壳的线性和非线性问题以及前屈曲耦合变形对功能梯度梁稳定性的影响等。主要研究成果包括：1、提出了一类可用于分析功能梯度多孔材料板弯曲、屈曲和自由振动行为的简单精化板理论；2、给出了热以及机械载荷作用下功能梯度梁弯曲、过屈曲以及振动问题的闭合形式解或数值解；3、使用辛方法获得了功能梯度梁和圆柱壳的屈曲临界载荷和弹塑性分界面；4、定量得到了热载荷下前屈曲耦合变形对功能梯度简支梁非线性变形和稳定性的影响；5、分析了磁场/压应力对压磁材料和弹性材料组成的非均匀板中厚度扭转波传播特性/捕获的厚度扭转波特性的影响，并获取了具有周期光栅的功能梯度材料板中兰姆波的传播特性。.本项目的研究结论从机理上解释了材料性能变化对功能梯度材料结构力学行为的影响，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。