径向压力作用下功能梯度圆板的过屈曲

Post-buckling of a functionally graded circular plate subjected to radial compression

基于经典非线性板理论,研究了功能梯度圆板在均匀的径向压力作用下的轴对称过屈曲问题.假设功能梯度材料性质只沿板厚度方向,并呈成分含量的幂指数函数形式变化.推导了问题的控制方程,并用打靶法对其进行数值求解.利用数值结果考察了梯度材料性质以及边界条件对板过屈曲行为的影响.结果表明,功能梯度板的过屈曲行为与各向同性均匀板有很大区别,材料的梯度性质和边界条件都对其有重要影响.

Based on the classical nonlinear plate theory, axisymmetric post-buckling behavior of a functionally graded circular plate under radial compression was investigated. It was assumed that the thermal and mechanical 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 were derived, and then a shooting method was employed to numerically solve the resulted differential equations. Furthermore, the effects of gradients of material properties and boundary conditions on the critical buckling load and post-buckling behavior of the functionally graded plates were discussed. Numerical results showed that the post-buckling behavior of a functionally graded plate was different from that of homogenous plate, the gradients of material properties and the boundary conditions played an important role in analyzing post-buckling behavior of the functionally graded materials plates.