任意梯度分布功能梯度圆环的热弹性分析

Thermoelastic Analysis of a Functionally Graded Annulus With an Arbitrary Gradient

对沿径向任意变化的材料参数的功能梯度圆环进行了热弹性分析.与以前关于该问题的分析不同,既不需要预先给定具体的梯度变化形式,也不需要对结构进行细分.给出一种新的有效解法将问题转换为求解Fredholm积分方程,从而通过Fredholm积分方程的解给出热应力和位移的分布情况.最后通过算例分析了内外表面受不同温度作用时,材料参数呈现梯度变化对圆环的应力和位移变化的影响,计算结果表明某些特定的材料梯度可有效缓解圆环内的热应力分布.该文得到的结果对功能梯度圆环在结构安全设计方面有重要的理论指导意义.

A thermoelastic problem of a circular annulus made of functionally graded materials with an arbitrary gradient was investigated. Different from previous works, the analysis neither requires a special form of the gradient of material properties nor demands to partition the entire structure into a multflayered homogeneous structure. Instead, a new method for solving the thermoelastic problem of a functionally graded circular annulus by transforming it to a Fredholm integral equation was proposed. The distribution of thermal stresses and radial displacement could be obtained by the solution to the resulting equation. Finally, illustrative examples were given to show the effects of varying gradients on the thermal stresses and radial displacement for given temperature changes at the inner and outer surfaces. Obtained results indicate that the thermal stresses can be relaxed for specified gradients, which is of benefit to designing a non- homogeneous annulus to maintain structural integrity.