含高温度梯度及接触热阻非线性热力耦合问题的谱元法  

SPECTRAL ELEMENT METHOD FOR NONLINEAR THERMOMECHANICAL COUPLING PROBLEMS WITH HIGH TEMPERATURE GRADIENT AND THERMAL CONTACT RESISTANCE

作　　者：史鑫 赵建宁 杨苗苗 张家雷[3] 刘冬欢 Shi Xin;Zhao Jianning;Yang Miaomiao;Zhang Jialei;Liu Donghuan(Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science,School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China;School of Energy and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China;Institute of Fluid Physics,China Academy of Engineering Physics,Mianyang 621900,Sichuan,China)

机构地区：[1]北京科技大学数理学院,磁光电复合材料与界面科学北京市重点实验室,北京100083 [2]北京科技大学能源与环境工程学院,北京100083 [3]中国工程物理研究院流体物理研究所,四川绵阳621900

出　　处：《力学学报》2022年第7期1960-1969,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(11772045)。

摘　　要：建立了含高温度梯度及接触热阻的非线性热力耦合问题的谱元法格式,考虑了温度相关的热导率、弹性模量、泊松比和热膨胀系数,以及界面应力相关的接触热阻的影响.谱元法的插值函数基于非等距分布的Lobatto结点集或第二类Chebyshev结点集,兼具谱方法的高精度和有限元法的灵活性.数值算例表明,建立的谱元法计算格式可以高效高精度地求解域内高温度梯度以及含接触热阻的非线性热力耦合问题,不仅收敛速度快于传统有限元法,而且用较少的自由度和较短的计算时间即可得到比传统有限元法更高精度的计算结果,在工程实际热力耦合问题中具有广阔的应用前景.The spectral element method for nonlinear thermomechanical coupling problems with high temperature gradient and thermal contact resistance is proposed here,and temperature-dependent thermal conductivity,elasticity modulus,Poisson’s ratio and thermal expansion coefficient,as well as the interface stress related thermal contact resistance are considered.The interpolation function of spectral element method is based on the unevenly spaced Lobatto points or Chebyshev points of the second kind.The spectral element method keeps both the high accuracy of spectral method and the flexibility of finite element method.Numerical results show that,the present spectral element method could solve the nonlinear thermomechanical coupling problems with high temperature gradient and thermal contact resistance with high accuracy and efficiency.Not only the convergency rate is larger than traditional finite element method,but also employ less degree of freedom and computational time to obtain results with higher accuracy,and has broad application potential in practical engineering thermomechanical coupling problems.

关 键 词：热力耦合 谱元法 接触热阻 高温度梯度 

分 类 号：O343.6[理学—固体力学]