基于最小二乘有限元的导热系数直接反算方法  

Inverse Estimation of Thermal Conductivity Based on Least Square Finite Element Method

作　　者：刘畅[1] 童富果[1] 李彪 LIU Chang;TONG Fu-guo;LI Biao(College of Hydraulic & Environmental Engineering,China Three Gorges University,Yichang 443002,China;College of Civil and Transportation Engineering,Hohai University,Nanjing 210098,China)

机构地区：[1]三峡大学水利与环境学院,湖北宜昌443002 [2]河海大学土木与交通学院,江苏南京210098

出　　处：《水电能源科学》2018年第12期113-116,128,共5页Water Resources and Power

基　　金：国家重点研发计划(2017YFC1501100);国家自然科学基金项目(51279090;51679129)

摘　　要：导热系数是温度场计算分析中的重要参数,针对基于优化方法反演导热系数计算量大、收敛慢、易陷入局部最优解等问题,提出了一种基于最小二乘有限元的直接反算方法,可快速得到材料导热系数。该方法是将有限单元法和最小二乘法引入热传导方程,直接求解材料导热系数时空分布,不需要进行大量的正算和迭代过程,大大提高了计算效率,且由于不需要事先假定导热系数分布函数形式,保证了计算精度。最后,以水泥砂浆导热系数测试试验为例,验证了最小二乘有限单元法在导热系数反算中的适用性和可靠性。Thermal conductivity is a key parameter in the calculation and analysis of temperature field.Aiming at the problems of large amount of calculation,slow convergence and easy to fall into local optimum solution for optimization method,a direct inverse calculation method based least square finite element method (LSFEM)was proposed,which can quickly obtain thermal conductivity.This method can directly solve the space-time distribution of the thermal conductivity by introducing the finite element method and least square method into the heat conduction equation.No iterations and forward calculations were required and no prior information on the functional form of thermal conductivity was needed,the calculation efficiency is greatly improved and the calculation accuracy is ensured.The applicability and reliability of the LSFEM in the back analysis of thermal conductivity were verified by taking the test of thermal conductivity of cement mortar as an example.

关 键 词：导热系数 最小二乘有限元 传热反问题 水泥砂浆 

分 类 号：TV31[水利工程—水工结构工程]