Abstract

The plane steady-state thermoelastic receding double contact problem between a rigid cylindrical punch and a homogenous layer lying on a half plane is investigated in this paper. The frictional rigid insulated punch slides over the layer with a constant velocity and heat flux is generated due to the friction. The speed of the punch is taken so small that the inertia effects may be neglected. The general stress and displacement expressions for the thermoelastic contact problem are derived using the theory of thermoelasticity and Fourier integral transform technique. Applying the boundary conditions, the contact problem is reduced to Cauchy-type singular integral equations of the second kind in which the contact stresses and contact widths are unknown. The singular integral equations are solved numerically using the Gauss-Jacobi integration formula. The effect of thermoelastic parameters, friction coefficient, external load, punch radius on the contact stress, and contact widths are discussed in detail. This is the first study to investigate the thermal effect on the receding contact problem.

摘要

本文研究了刚性圆柱冲头与位于半平面上的均质层之间的平面稳态热弹性后退双接触问题。摩擦刚性绝缘冲头以恒定的速度在层上滑动，并由于摩擦而产生热通量。冲头的速度是如此之小，以至于可以忽略惯性效应。利用热弹性理论和傅立叶积分变换技术推导了热弹性接触问题的一般应力和位移表达式。应用边界条件，将接触问题简化为第二类柯西型奇异积分方程，其中接触应力和接触宽度未知。使用Gauss-Jacobi积分公式对奇异积分方程进行数值求解。详细讨论了热弹性参数，摩擦系数，外部载荷，冲头半径对接触应力和接触宽度的影响。这是第一个研究热效应对后退接触问题的研究。