热-机械载荷下梯度材料圆筒的应力分析

对梯度材料圆筒在内外压及非均布温度载荷作用下的应力状态进行理论分析.通过引入弹性梯度因子和温度梯度因子获得热-机械载荷下梯度材料圆筒的应力解析解,进而探讨弹性梯度因子和温度梯度因子对径向、周向和轴向应力分布的影响,为梯度材料圆筒的结构设计提供可靠的理论依据.计算结果表明,应力分量沿壁厚的分布随内外压比值的不同而不同,其中径向应力与坐标位置密切相关,与梯度因子关系不大.对于不同的梯度因子比,存在一最优值使得梯度圆筒内外壁面周向应力差值最小.与内壁处轴向应力相比,外壁处轴向应力对内外压比值的变化更为敏感,并且当弹性梯度因子与温度梯度因子比小于1时,轴向应力几乎不受梯度因子比值变化的影响;而当梯度因子比大于1时,轴向应力迅速减小,且外壁处的减小速度远大于内壁处的减小速度.

STRESS ANALYSIS ON FUNCTIONALLY GRADED MATERIAL CYLINDER UNDER THERMAL-MECHANICAL LOAD

The stress state of a functionally graded material cylinder is theoretically analyzed under the internal/external pressure and non-uniform distributed temperature along the wall thickness. With the use of elastic grade factor and temperature grade factor the stress components can be analytically expressed by solving a nonhomogeneous second order differential equation. The numerical example is conducted to examine the effects of elastic grade factor and temperature grade factor on the distribution of radial, circumferential and axial stress in the cylinder, which can be further used to guide the structural design of functionally graded material cylinder. The numerical results show that the values of each stress component vary along the cylinder wall according to the different internal/external pressure ratio. The radial stress depends on the radial coordinate and is hardly relevant to the elastic grade factor and the temperature grade factor. There is an optimum grade factor ratio to minimize the difference of circumferential stress between the inner surface and the outer surface of the cylinder. The axial stress at outer surface is more sensitive to the changing of pressure ratio than that at inner surface. When the grade factor ratio is less than 1, the axial stress is nearly unaffected to the changing of the grade factor ratio. However, when the grade ratio is larger than 1, the axial stress reduces quickly and the decay speed at the outer surface is larger than that at the inner surface.