热冲击下带裂纹功能梯度厚壁圆筒的分析

Numerical simulation for a functionally graded thick-walled cylinder with cracks under thermal shock

针对功能梯度材料热冲击下的断裂问题,对功能梯度材料的材料参数分类进行加权处理,建立带裂纹功能梯度厚壁圆筒的模型;给出热量平衡方程与边界条件,建立相关问题的有限元分析格式;改进Calahan算法以适用于带状稀疏矩阵的一阶非齐次常微分方程组,完善温度场的求解过程,计算了裂纹尖端的温度应力强度因子,并且分析功能梯度材料组分构成对温度应力强度因子的影响。以上研究为带裂纹功能梯度厚壁圆筒的可靠性分析及结构优化设计提供了参考。

Aiming at the fracture problem of functionally graded materials under thermal shock,physical parameters of functionally graded materials were classified and weighted to establish a model of a functionally graded thick-walled cylinder with cracks. Its heat balance equations and boundary conditions were deduced to build the relevant problem's finite element analysis procedure. Calahan algorithm was improved to solve the first order inhomogeneous ordinary differential equations of the corresponding banded sparse matrix and obtain the cylinder's temperature field and stress field. Then the thermal stress intensity factor of the crack tip was calculated,the effects of functionally graded material's components on the thermal stress intensity factor were analyzed. The results provided a reference for reliability analysis and structural optimal design of a functionally graded thick-walled cylinder with cracks under thermal shock.