剪切变形对FGM圆板轴对称屈曲的影响

Effect of Shear Deformation on Buckling Behavior of FGM Annular Plates

基于一阶剪切变形板理论 ,推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中 ,忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性 ,得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系 ,可以直接从已有的较为简单的经典理论的结果 ,获得一阶板理论下功能梯度材料板的临界屈曲载荷。

Based on the first-order shear deformation plate theory, axisymmetric governing buckling equations are derived for a functionally graded material circular plate subjected to in-plane pressure. The coupled deflections and rotations in the prebuckling state of the plates are not taken into account in the derivation. On the basis of the mathematic similarity of the governing equations to buckling problems between Kirchhoff and first-order shear deformation plate theories, exact relationship between buckling solution of the first-order theory for FGM circular plates and that of the classical theory for homogeneous circular plates has been derived. Then, exact solutions of FGM plates using first-order theory may be obtained from the solutions of the simpler classical plate theory for homogeneous circular plates. Effects of material properties, ratio of inter and outer radius and the boundary conditions on buckling behavior of FGM plates are discussed.