基于物理中面FGM板屈曲的有限元分析

基于物理中面的概念，根据最小势能原理推导了功能梯度材料FGM薄板屈曲的有限元控制方程，求得临界荷载的有限元解。利用FGM板的屈曲方程与参考均匀板的屈曲方程之间的相似性，建立了FGM板的临界荷载与参考均匀板的临界荷载之间的相似转换关系式，从而将FGM板临界荷载的计算转变为参考均匀板的临界荷载和材料不均匀系数的计算，极大地提高了计算效率，为FGM的推广起积极的推动作用。通过数值算例，将由有限元法和转换关系式得到的临界荷载进行了比较，并讨论了边界条件、荷载工况、材料组成和几何尺寸等对FGM板临界荷载的影响。

Finite element analysis for the buckling of functionally graded material plates based on physical neutral surface

This paper presents the analysis of the buckling of the FGM(Functionally Graded Materials) thin plates based on the physical neutral surface.Based on the principle of minimum potential energy,the finite element forms of the governing equations are derived and then the critical buckling load is determined.Considering the similarity between the buckling equation of the FGM plate and that of the reference uniform plate,the relationship between the critical load of the FGM plate and that of the reference uniform plate is established.Then the calculation of the critical load of the FGM plate is transformed into the calculation of the critical load of the reference uniform plate and the inhomogeneity coefficient of the material.This work can greatly improve the computational efficiency and plays an active role in the promotion of the FGM.The results obtained by the finite element method and the transformation relation are compared.The effect of the boundary condition,load condition,material component and geometry on the critical load is also discussed.