含高温度梯度及接触热阻非线性热力耦合问题的谱元法

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. 

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

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.