功能梯度材料构件三维分析的细观元模型

提出一种新颖的功能梯度构件分析的细观元法,给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度及组分变化特性,而其计算单元与自由度又与常规有限元一样,是一种针对功能梯度构件分析的有效数值方法。算例表明了细观元法对不同情况下功能梯度构件分析的适应性与精度。

Micro-element model for three-dimensional analysis of functionally graded structures

A new micro-element method for the analysis of functionally graded structures was suggested,and the method model,basic computational equations,features and functions are given in this paper.In order to reflect the graded change of material properties,the micro-element method set up the dense microelements in the normal finite element of the structure,and translated the freedom degrees of all microelement's nodes into ones of the same normal finite element by the compatibility conditions,which were calculated by the computer.This micro-element method can fully reflect the functionally graded properties of the materials,realize the transition analysis from material micro-constitution to macro-response of structure,and its computational elements and freedom degrees are the same as the normal finite element method.Therefore,this method is an effective numerical method for the analyses of the functionally graded structures and a practical means for the scale-span analyses of FGM structures.The applicability and accuracy of the micro-element method to analyze functionally graded structures under different conditions can be demonstrated by the examples,the three-dimensional distributions of mechanical quantities of the functionally graded plates with different gradients or different composite materials and component constitutions are given in the paper.