具有中等组分不同网状结构功能梯度构件的三维动力特性分析

THREE-DIMENSIONAL DYNAMIC CHARACTER ANALYSIS OF FGM STRUCTURES WITH DIFFERENT MEDIUM COMPONENT NET STRUCTURES

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。该文建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。此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材料构件的各种材料细观构造得到反映。通过细观元技术,对具有中等组分不同网状结构功能梯度构件进行三维动力特性分析,并给出其三维固有频率及振型的三维分布,特别是给出了不同网格结构功能梯度板件应力振型的平面等值线图差异。结果表明:不同细观网格结构对功能梯度材料结构三维动力响应有较明显影响。

Functionally graded material has complex microstructures, and its internal structure is more complicated than the homogeneous material＇s. Therefore, the analytic solution for dynamic analyses of functionally graded structure is difficult to obtain. A new microelement method for the dynamic analyses of functionally graded structures was suggested to establish quantitative relation between the macro-character and microstructures of functionally graded materials, and the mechanism, that different combination and variation of materials have different macro-character, can be founded. This microelement method can fully realize the transition from material micro-constitution to macro-response of structure, and its computational elements and degrees of freedom are the same as that of the normal finite element method. Moreover, in this method, any microconstitutions of functionally graded materials will be reflected without increasing the degrees of freedom. In this paper, the three-dimensional dynamic characters of functionally graded plates with different medium components net structures are analyzed, and the three-dimensional dimensionless values of natural frequencies and the three-dimensional distributions of mode shapes of the functionally graded plates are given. Especially, the stress modes in the plane contour charts of functionally graded plates with different medium components net structures are compared in this paper. The results show that micro-net structures have great influences on the three-dimensional dynamic response of functionally graded structures.