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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.
In order to improve the accuracy of dynamic response of functional gradient plate, based on the first-order shear deformation plate theory, a Cell-Based smooth finite element method is proposed to solve the free-vibration problem of functional gradient plate.Functional gradient plate material properties change continuously along the thickness gradient , And calculating the stiffness matrix of the system in a smooth gradient domain can improve the accuracy of the solution.Using the Cell-Based smoothing finite element method, the effects of aspect ratio, shape factor and boundary conditions on the dimensionless frequency of two typical functionally graded square plates The results of the numerical examples show that the smooth gradient operation can improve the stiffness of the finite element system and the calculation result of the Cell-Based smoothing finite element method is more approximate to the real one So as to lay the foundation for the further application of FGM.