摘要
文章基于在切口尖端附近区域温度场的渐近展开表达式,提出了计算切口/裂纹尖端奇异点处热流密度奇异性特征指数的新方法;将温度场的表达式引入稳态齐次热传导微分方程,得到关于各向同性材料切口/裂纹奇异点处的一组非线性常微分方程的特征值问题,采用变量代换法,将该非线性常微分方程组转化为一组线性常微分方程组;用插值矩阵法求解,获得各向同性材料切口/裂纹奇异点处热流密度特征解的特征根,同时获得其相应的特征角函数;与解析解对照,证实了文中算法的有效性。
Based on the asymptotic expression of the temperature field near the notch tip ,a characteris-tic analysis method for calculating the singularity orders of heat flux density at the V-notch/crack tip is proposed .By introducing the generalized expression of steady-state temperature field into the homo-geneous differential equation of heat conduction ,the equilibrium equations are transformed into a set of non-linear characteristic ordinary differential equations with respect to the singularity orders .By a-dopting the variable substitution technique , the established non-linear characteristic equations are transformed into a set of linear ones .T he interpolation matrix method is introduced to solve the estab-lished equations for getting the characteristic root of heat flux density characteristics of the solution at the singular point and its corresponding characteristic angle function .The validity of the presented method is confirmed by comparing with the analytical solution .
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第3期281-285,共5页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(11102056
11272111
11372094)
关键词
各向同性材料
温度场
热流密度
插值矩阵法
isotropic material
temperature field
heat flux density
interpolation matrix method
