热冲击下功能梯度圆板的动力屈曲

Dynamic buckling of functionally graded circular plate under thermal shock

基于von Kármán几何非线性板理论研究热冲击载荷作用下缺陷功能梯度圆板的动力屈曲及后屈曲。假设功能梯度材料的物理性能参数沿厚度方向按照幂函数形式连续变化。由Fourier热传导定律,采用Laplace变换法和微分方程幂级数解法求得热冲击载荷作用下功能梯度板内的动态温度场。利用幂级数展开圆板轴对称大变形的非线性动力学控制方程,并与Runge-Kutta法相结合进行数值求解,获得中心最大挠度的动力响应和屈曲临界温度。结果表明:随着材料参数和几何缺陷的增大,板发生屈曲的时间提前;临界升温载荷随径厚比和载荷参数的增大而降低。

Based on the von Kármán plate theory, dynamic buckling and post-buckling of an imperfect functionally graded circular plate subjected to thermal shock are investigated. The material properties of functionally graded plate are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on theory of Fourier heat conduction, the dynamic temperature fields of the functionally graded plate under thermal shock loading are obtained in combination of Laplace transform and power series method. The nonlinear dynamic equations governing a large axi-symmetric deformation are numerically solved by using series expansions and Runge-Kutta method. The buckling and post-buckling path is predicted by the dynamic response of the maximum deflection of the plate. It is found that the buckling time shorten as the material constitution and initial geometric imperfection increase. The buckling critical temperature decrease with the increasing ratio of radius and thickness or the load parameters.