Abbas Ibrahim, Hobiny Aatef, Alshehri Hashim, Vlase Sorin, Marin Marin
Mathematics Department, Faculty of Science, Sohag University, Sohag 82725, Egypt.
Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 22233, Saudi Arabia.
Polymers (Basel). 2022 May 22;14(10):2112. doi: 10.3390/polym14102112.
In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of the Green and Lindsay model with two thermal relaxation times. The bounding surface of the half-space was subjected to a heat flux with an exponentially decaying pulse. Finite element techniques were used to solve the governing formulations, with eight-node isoparametric rectangular elements with three degrees of freedom (DOF) per node. The developed method was calculated using numerical results applied to the polymeric, orthotropic medium. The findings were implemented and visually shown. Finally, the results were displayed to demonstrate the differences between classical dynamic coupling (CT), the Lord-Shulman (LS) and the Green and Lindsay (GL) models.
在这项工作中，采用有限元技术来评估热松弛持续时间对二维聚合物正交各向异性弹性介质中的温度、位移和应力的影响。该问题是在具有两个热松弛时间的格林和林赛模型的背景下，在均匀的聚合物正交各向异性介质中进行考虑的。半空间的边界表面受到具有指数衰减脉冲的热通量作用。使用有限元技术来求解控制方程，采用每个节点具有三个自由度（DOF）的八节点等参矩形单元。所开发的方法是通过应用于聚合物正交各向异性介质的数值结果进行计算的。研究结果得到了实施并直观地展示出来。最后，展示结果以说明经典动态耦合（CT）、洛德 - 舒尔曼（LS）和格林与林赛（GL）模型之间的差异。
