功能梯度材料圆板在随从力作用下的稳定性

THE STABILITY OF FGM CIRCULAR PLATES SUBJECTED TO FOLLOWER FORCE

研究了由陶瓷和金属两种材料组成的功能梯度材料(FGM)圆板在非保守随从力作用下的稳定性问题。假设功能梯度材料性质只沿板厚度方向并按成分百分比的幂指数形式连续变化。推导了问题的控制微分方程,打靶法数值求解所得非线性边值问题,获得了两种边界下功能梯度圆板的变形与无量纲随从力之间的关系曲线。讨论了材料梯度指数以及两种边界条件对过屈曲和弯曲行为的影响。数值结果表明,两种边界条件下,各向同性均匀圆板都发生传统意义上的屈曲,而FGM圆板在随从载荷下,当梯度指标P<0.1时发生屈曲,当P>0.1时只发生弯曲。结果显示,材料的梯度性质和边界条件对弯曲和屈曲行为都有重要影响。

The stability of the functionally graded material circular plate made of ceramic and metal subjected to follower force were investigated. It is assumed that the properties of the functionally graded material vary continuously only with the thickness of the plate and their variation has a simple power law distribution with the volume fraction of the constituents. The governing equations are derived,and then the nonlinear governing equations with two kind boundary conditions are numerically solved by shooting method,respectively. The effects of power index and boundary condition on the behavior of buckling and bending were discussed. The numerical results indicated that homogenous circular plate occurred in the traditional sense of the buckling under two kinds of boundary conditions,and FGM circular plate under the follower load will be buckling when the gradient index p〈1,and plate only bending when p〉1. Results show that the gradient properties of the materials and the boundary conditions have important effects on the bending and buckling behavior.