基于自然单元法的功能梯度中厚板自由振动分析

自然单元法是一种基于自然邻近插值的无网格数值方法．相对于移动最小二乘近似而言，自然邻近插值不涉及到复杂的矩阵求逆运算，也不需要任何人为的参数．基于一阶剪切变形板理论，利用自然单元法对功能梯度中厚板的自由振动进行了数值分析．功能梯度板材料属性沿厚度方向呈梯度连续变化．由于自然邻近插值函数具有Kronecker delta函数性质，可以直接施加本质边界条件．通过本文给出的方法，对不同梯度指数和不同边界条件的功能梯度中厚板的振动频率进行了计算．通过与文献结果的对比验证了自然单元法求解的有效性．

Free Vibration Analysis of Moderately Thick Functionally Graded Plates Using the Natural Element Method

The natural element method (NEM) is a kind of meshless method that is based on the natural neighbour interpolation. Compared with the moving least square (MLS) approximation, the natural neighbour interpolation does not involve the complex computation of matrix inversion and requires no artificial parameters. Based on the first order shear deformation plate theory, the NEM is used to numerically analyze the natural frequencies of moderately thick functionally graded plates. The material properties were assumed to vary in the thickness direction only. Because the natural neighbour interpolation function incorporates the Kronecker delta function properties, the essential boundary conditions can be enforced directly. Natural frequencies of the moderately thick functionally graded plates with various gradient indices and boundary conditions are computed by the present method. Correctness of the computational results is validated by comparison with those in the literature.