复杂边界条件功能梯度板三维分析的半解析方法

推导出适应功能梯度材料构件分析的半解析方法基本算式,并针对功能梯度构件的材料参数随空间坐标变化的特点,将材料参数纳入到力学方程中进行整体积分计算,从而编制统一程序计算不同边界条件下的板件问题.该法适应性强而又简洁高效,且不同于一般的半解析法,可采用一维离散,给出三维分析结果,是一种解决功能梯度构件力学性能分析的有效数值方法.文中用半解析法分析几种具有不同复杂边界条件的功能梯度板,给出了板件的力学量三维分布形态.

Semi-analytical method for 3-D analysis of functionally graded material plates with complex boundary conditions

The basic formulas of semi-analytical method applied to the analyses of functionally graded structures were derived,and according to the characteristics of functionally graded material parameters varying with the space coordinates,the material parameters were entered into mechanical equations for the whole integral calculation,then the unified program was formed for calculating plate problems under different boundary conditions.The method,which has strong adaptability,brevity and high efficiency,is different from general semi-analytical method,can use 1-D discretization,obtain 3-D analytical results.It's an effective numerical method to solve mechanical analysis of functionally graded material structures.In the paper the semi-analytical method was used to analyse several different functionally graded material plates with complex boundary conditions,and the 3-D distributions of mechanical quantities were given.