一种特殊梯度分布的功能梯度矩形板弯曲问题解析解

Analytical Solutions for Bending Problems of Functionally Graded Rectangular Plates With Specific Material Gradient

研究了一种特殊梯度分布功能梯度材料矩形板弯曲问题。假设材料的弹性模量在板厚度方向上呈幂函数分布,泊松比为常数,引入PLEVAKO解,利用分离变量法,导出四边简支功能梯度材料矩形板弯曲问题的解析解。通过算例分析了材料组分变化时,功能梯度板应力和位移的变化规律。结果显示不同梯度分布板结构中的应力、位移的变化规律是不同的,有时甚至差别很大。该方法为发展针对功能梯度材料特点的数值算法和简化理论提供依据。

Bending problems of functionally graded rectangular plates were analyzed. In terms of Plevako function,assuming that the Yang＇s modulus of the material was distributed through a power function in the thickness direction,an exact solution of bending problem of simply supported functionally graded rectangular plates was obtained by variable separation method. Through numerical examples,the variations of displacement and stress components with different graded material distributions were analyzed and different graded parameters were found to have significant effects on the structural behavior. The research serves as theoretical basis for the development of numerical methods and simplified theories of functionally graded material structure.