功能梯度板动力分析的光滑有限元法研究

为提高功能梯度板动响应问题求解精度，基于一阶剪切变形板理论，提出了求解功能梯度板自由振动问题的Cell-Based 光滑有限元格式．功能梯度板材料属性沿厚度方向呈梯度连续变化，计算系统刚度矩阵时在光滑域内进行光滑梯度操作，可提高求解精度．采用Cell-Based 光滑有限元法，讨论了长厚比、形状因子和边界条件对两种典型功能梯度方板无量纲频率参数的影响，并与FEM法的解和文献中的解做了对比．数值算例的结果表明，光滑梯度操作可改善有限元系统的刚度，Cell-Based 光滑有限元法的计算结果更加逼近真实解，从而为功能梯度材料的进一步应用打下基础．

Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Plate

In order to improve the accuracy of resolution of the dynamic response of a functionally graded plate, based on the first-order shear deformation plate theory, the Cell-Based smoothed finite element method scheme for solving functionally graded plate free vibration problems was put forward. The material properties were assumed to be graded in the thickness direction, and the global stiffness matrix of the system was computed using smoothing operations over the smoothing domains, which can improve the accuracy of calculation. The influencies of plate length-to-thickness ratio, gradient index and boundary condition on the natural frequencies of the functionally graded plates were investigated in detail, and the result was compared with those of FEM and references. Numerical examples show that the smoothed gradient system can improve the calculation of rigidity by finite element method. Cell-Based smoothed finite element method is more close to the real solution, and thus lays the foundation for further application of functionally graded materials.