功能梯度材料扁锥壳的热弹性大变形分析

LARGE THERMOELASTIC DEFORMATION ANALYSIS ON SHALLOW CONICAL SHELL OF FUNCTIONALLY GRADED MATERIALS

研究了功能梯度材料扁薄锥壳在横向非均匀升温场中的几何非线性大变形问题.基于von Kármán几何非线性理论推导出了以中面位移为基本未知量的功能梯度扁薄锥壳在横向非均匀热载荷作用下的轴对称大挠度控制方程.采用打靶法数值求解所得非线性常微分方程边值问题,得到了锥壳的大挠度弯曲变形数值解.给出了锥壳的变形与其形状参数、载荷和材料参数等变化的特征关系曲线,分析和讨论了温度参数和材料梯度变化参数对变形的影响.

Geometrically nonlinear large deformation of functionally graded material shallow conical shell under transversely nonuniform temperature rise field was investigated. On the basis of yon Kármán＇s geometrically nonlinear theory, equilibrium equations governing the axi-symmetrically large deformation of the FGM sallow conical shell under nonuniform thermal loadings are derived. By using the shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved and numerical solutions for the large deformation for the conical shell are obtained. Characteristic curves of the deformation versus the slope angle, temperature rising parameter and the volume fraction exponent are plotted. Especially, the effects of temperature rise and the parameter of gradient of the materials variation on the deflection of the shallow conical shell are examined and discussed.