含裂纹功能梯度材料热接触的奇异积分方程方法

Singular Integral Equation Method for Thermal Contact Problem of FGM with Crack

摘要:

接触问题是我们生产、生活和实际工程中常见的物理现象，由于在接触过程中接触区内不可避免会产生应力集中现象，从而大大降低了机械结构部件的使用寿命。近些年来功能梯度材料的出现大大改善了这种缺陷，所以研究功能梯度材料的接触问题对于提高生产效率，增加经济效益和工程安全有着重要意义。本文讨论了带裂纹的半无限大功能梯度材料的热接触问题。利用叠加原理将所研究的问题转化为第一类带Cauchy核的奇异积分方程，并利用数值求积方法求解了奇异积分方程，得到了裂纹尖端的应力强度因子。通过程序画图分析了材料参数，摩擦系数及裂纹尺寸对裂纹尖端应力强度因子的影响。

Abstract:  Contact problems are common physical phenomena in the real life and engineering practices due to the inevitability of contact. At the end of the contact area, the phenomenon of stress concentration may happen, which can significantly reduce the service life of mechanical structural components. In recent years, functionally graded materials (FGMs) have been used in many important engineering practices to relieve stress concentration. The study of the contact problem of functionally graded materials can provide instruction to improve production efficiency and increase economic benefits with a great deal. The present paper discusses the thermal contact problem of a half-plane functionally graded material with a crack. By using the superposition principle, the stated problem is reduced to the Cauchy type singular integral equations of the first kind, which are solved via numerical quadrature method. Then, figures are plotted to reveal the influences of the parameters of the non-homogeneity, the friction coefficient, and the dimension of crack on the stress intensity factor.