考虑前屈曲耦合变形时功能梯度简支梁的稳定性分析

在某些边界条件下，功能梯度材料（FGM）梁会由于拉弯耦合产生前屈曲耦合变形，而该变形对FGM梁的稳定性有影响。本文假设FGM梁的材料性质只沿厚度方向进行变化，基于经典非线性梁理论和物理中面概念，推导出FGM梁的平衡方程以及包含前屈曲耦合变形影响的屈曲控制方程，并用打靶法进行数值求解。讨论了前屈曲耦合变形、梯度指数以及材料性质的温度依赖等因素对FGM梁非线性变形和稳定性的影响。

Stability Analysis of Functionally Graded Simply Supported Beams Considering Pre-buckling Coupling Deformation

The pre-buckling coupling deformation of functionally graded material (FGM) beams will be caused by stretching-bending coupling effect under some boundary conditions, and this deformation has an effect on the stability of FGM beams. It is assumed that the material properties of FGM beams only change along the thickness direction, the equilibrium equation and the buckling governing equation including the effect of the pre-buckling coupling deformation, of FGM beams are derived based on the classical nonlinear beam theory and the concept of physical neutral surface in this paper, which are solved numerically by the shooting method. The effects of pre-buckling coupling deformation, gradient index and temperature dependence of material properties on the nonlinear deformation and stability of FGM beams are discussed.