Fan Jian Ling, Ma Lian Sheng, Zhang Lu, De Su Hou
Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou - China.
College of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou - China.
J Appl Biomater Funct Mater. 2016 Jul 4;14 Suppl 1:e15-9. doi: 10.5301/jabfm.5000300.
This paper establishes a density gradient model along the thickness direction of a circular plate made of foamed material. Based on the first shear deformation plate theory, the result is deduced that the foamed metal circular plate with graded density along thickness direction yields axisymmetric bending problem under the action of uniformly distributed load, and the analytical solution is obtained by solving the governing equation directly. The analyses on two constraint conditions of edge radial clamping and simply supported show that the density gradient index and external load may affect the axisymmetric bending behavior of the plate. Then, based on the classical plate theory, the paper analyzes the behavior of axisymmetric buckling under radial pressure applied on the circular plate. Shooting method is used to obtain the critical load, and the effects of gradient nature of material properties and boundary conditions on the critical load of the plate are analyzed.
本文建立了沿泡沫材料制成的圆形板厚度方向的密度梯度模型。基于一阶剪切变形板理论，推导得出沿厚度方向具有密度梯度的泡沫金属圆形板在均布载荷作用下产生轴对称弯曲问题，并通过直接求解控制方程得到了解析解。对边缘径向夹紧和简支两种约束条件的分析表明，密度梯度指数和外载荷可能会影响板的轴对称弯曲行为。然后，基于经典板理论，分析了圆形板在径向压力作用下的轴对称屈曲行为。采用打靶法获得临界载荷，并分析了材料性能的梯度性质和边界条件对板临界载荷的影响。
