复杂边界条件功能梯度板三维分析的细观元法

发展一种细观分析和宏观计算相结合的计算方法—细观元法。细观元法是使功能梯度构件宏观响应和材料组分的几何、物理、构造参数直接发生关联的分析方法,实现材料细观结构到构件宏观响应的直接过度分析,为解决功能梯度构件宏、细观跨尺度分析提供了一种有力工具。细观元方法不增加结点自由度,却使得功能梯度板件的任意功能梯度变化、各种复杂边界条件得到反映。用细观元法得到了几种具有不同复杂边界条件的功能梯度板件的力学量三维分布形态。

MICROELEMENT METHOD FOR 3-D ANALYSIS OF FUNCTIONALLY GRADED PLATES WITH COMPLEX BOUNDARY CONDITIONS

A microelement computational method was proposed to establish the relationship between micro-analysis and macro-calculation. The method can provide the immediate relations between macro-response of functionally graded structures and the geometric, physical and structural parameters of material components. Therefore, it is an effective numerical method for the analyses of functionally graded materials and a practical means for scale-span analyses of functionally graded structures. In this method, functionally graded change, arbitrary form of plate and complex boundary conditions can be reflected without increasing the degrees of freedom. The applicability and accuracy of the microelement method to analyze functionally graded structures under different conditions were demonstrated by examples, in which the three-dimensional distributions of mechanical quantities of functionally graded plates with several complex (including point supported) boundary conditions were given by the microelement method.