不同功能梯度材料组分板件的跨尺度动力特性分析  

Span-scale Dynamic Character Analysis of FGM Plates with Variant Material Components

作　　者：程红梅[1] 曹志远[2] 仲政[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116 [2]同济大学航空航天与力学学院,上海200092

出　　处：《中国矿业大学学报》2008年第5期719-724,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金重点项目(10432030);中国矿业大学科技基金项目(OK080308)资助

摘　　要：从制备时给定材料组分分布出发计算功能梯度板件宏观三维动力特性.利用细观元法对具有复杂细观构造的构件进行宏观单元剖分,每个宏观单元内部含有复杂的微结构构造.根据宏观元内细观构造及各组成材料分布情况,进一步将宏观元细分为密集的细观元,通过协调条件使细观元结点上力学量转换为宏观单元上结点自由度变量,建立三维动力分析数学模型.该方法可实现材料细观结构到构件宏观响应的直接过渡分析,而计算单元与自由度又等同一般常规有限元,却使得组成功能梯度板件的各种材料组分分布得到反映.利用细观元法对由不同材料组分分布及不同材料复合而成的功能梯度板件进行三维动力分析,分别给出了其三维固有频率及振型的三维分布.结果表明:不同材料组分复合对功能梯度材料结构三维宏观动力响应有较大影响.Three-dimensional dynamic characteristics can be immediately calculated from the material component distribution determined in the process of material production. Structures with a complex micro-constitution were divided into macro-elements using a micro-element method. According to the micro-structures and the distributions of the material components, the micro-element method establishes dense micro-elements in each macro-element and trans- lates the degrees of freedom of the nodes of all micro-elements into nodes of the same normal finite elements by the compatibility conditions. In the end, the three-dimensional mathematical model could be established. This micro-element method can entirely realize the transition from the micro-constitution to the macro-response of the material structure. Its computational elements and degrees of freedom are the same as those from the normal finite element method. In this method, any material component distribution of functionally graded plates will be reflected without increasing the degrees of freedom. The functionally graded plates with different com- ponent constitutions or different composite materials are dynamically analyzed by the micro-ele- ment method. The three-dimensional dimensionless values of the natural frequency and the three-dimensional distributions of mode shape are given. The results show that the different material components have considerable effect on the three-dimensional dynamic macro-respon-ses of functionally graded structures.

关 键 词：功能梯度材料 细观元法 组分 三雏动力特性 固有频率 振型 

分 类 号：O316[理学—一般力学与力学基础]