热传导问题有限元线法平面高精度曲线曲边单元研究  

The Study of High Precision Plane FEMOL Element with Curved Line and Curved Boundary in Heat Conduction

作　　者：张俊哲[1] 徐冰[1] 高建岭[1] 

机构地区：[1]北方工业大学土木工程学院,北京100144

出　　处：《北方工业大学学报》2016年第3期85-88,29,共5页Journal of North China University of Technology

摘　　要：本文首次将3次B样条插值基函数引入到平面温度场的单元映射中,建立了有限元线法平面高精度曲线曲边单元;以平面高精度曲线曲边单元的单元映射及泛函变分为理论基础,运用FORTRAN语言进行相关程序TFEMOL3.0的开发;将程序计算得到的数值解与解析解进行对比.结果表明:有限元线法平面高精度曲线曲边单元适用性良好,在解决不规则平面热传导问题上,单元划分较简单,具有较高的计算精度.This paper,for the first time,utilized cubic spline interpolation to expand the FEMOL into the irregular plane precision regional and established the high precision plane curved line with curved boundary element.Based on the discretization of the plane high precision curved line with curved boundary element,the heat conduction program TFEMOL3.0is developed with FORTRAN language.The examples were constructed by comparing the numerical results with analytical solutions.The comparison showed that the finite element method of lines of the plane high precision curved and curved-side element has a good applicability in solving the problem of irregular plane heat conduction,and this method has some advantages in element discretization and high precision.

关 键 词：热传导问题 有限元线法 平面高精度曲线曲边单元 三次样条 

分 类 号：O242.21[理学—计算数学]