Kushnir Roman, Yasinskyy Anatoliy, Tokovyy Yuriy, Hart Eteri
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060 Lviv, Ukraine.
Department of Applied Mathematics, Institute of Applied Mathematics and Fundamental Sciences, National University Lviv Polytechnic, 79013 Lviv, Ukraine.
Materials (Basel). 2021 May 19;14(10):2657. doi: 10.3390/ma14102657.
Within the framework of the one-dimensional model for a tribo-couple consisting of two elastic cylinders accounting for the frictional heat generation on the interface due to the roughness of the contacting dissimilar materials, a problem on the identification of the unknown temperature on one of the limiting surfaces of either inner or outer cylindrical layers is formulated and reduced to an inverse thermoelasticity problem via the use of the circumferential strain given on the other surface. To solve the latter problem, a semi-analytical algorithm is suggested, and its stability with respect to the small errors in the input data is analyzed. The efficiency of the proposed solution algorithm is validated numerically by comparing its results with the solution of a corresponding direct problem. The temperature and thermal stresses in the tribo-couple are analyzed.
在由两个弹性圆柱体组成的摩擦副的一维模型框架内，考虑到由于接触的异种材料粗糙度导致界面上产生摩擦热，提出了一个关于确定内圆柱层或外圆柱层任一极限表面上未知温度的问题，并通过使用另一表面上给出的周向应变将其归结为一个逆热弹性问题。为解决后一个问题，提出了一种半解析算法，并分析了其对输入数据中小误差的稳定性。通过将其结果与相应直接问题的解进行比较，对所提出的求解算法的效率进行了数值验证。分析了摩擦副中的温度和热应力。
