Mose Bruno R, Shin Dong-Kil, Nam Jeong Hwan, Alunda B O
School of Mechanical, Manufacturing and Materials Engineering, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya.
School of Mechanical Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan, 38541, Gyeongsangbuk-do, South Korea.
Sci Rep. 2025 May 4;15(1):15598. doi: 10.1038/s41598-025-88114-0.
In this paper, the mathematical theory of elasticity that enables the construction of representative stress functions for photoelastic experimental hybrid method (PEHM) is revisited and reviewed. PEHM has been shown as an important and powerful tool used by experimental stress analysts to predict the stress state in complex engineering structures. To demonstrate the utility of stress functions from the mathematical theory of elasticity in real engineering applications, the contact problem of a mechanical seal with a rectangular cross-section as well as a plate with a central hole are considered. It was found that when the stress functions are applied to the contact problem of a mechanical seal with rectangular cross section, the contact stresses on the upper side were larger compared to those on the front side. The highest stresses on the front side were concentrated in the region around the extrusion gap. When a comparison between theoretical and experimental stress concentration factors (SCF) was done, it was found that there was remarkable agreement between theoretical and experimental results. Therefore, the mathematical theory of elasticity from this study shows that it can provide stress functions that serve as an invaluable input tool to predict the SCF using the photoelastic experimental hybrid method.
本文重新审视并回顾了弹性力学数学理论，该理论能够构建用于光弹性实验混合法（PEHM）的代表性应力函数。PEHM已被证明是实验应力分析人员用于预测复杂工程结构应力状态的一种重要且强大的工具。为了证明弹性力学数学理论中的应力函数在实际工程应用中的效用，考虑了矩形截面机械密封以及带中心孔平板的接触问题。结果发现，当将应力函数应用于矩形截面机械密封的接触问题时，上侧的接触应力比前侧的接触应力大。前侧的最高应力集中在挤压间隙周围的区域。当对理论应力集中系数（SCF）和实验应力集中系数进行比较时，发现理论结果与实验结果之间存在显著的一致性。因此，本研究中的弹性力学数学理论表明，它可以提供应力函数，作为使用光弹性实验混合法预测SCF的宝贵输入工具。
