基于直线积分边界元法的温度应力研究  

Thermal stress analysis based on line integration boundary element method

作　　者：刘彪 高宇 李通盛 程勇刚 王桥 周伟[1] LIU Biao;GAO Yu;LI Tongsheng;WANG Qiao;ZHOU Wei(School of Water Resources and Hydropower Engineering,Wuhan University,Wuhan 430072,China;Datang Xuanwei Hydropower Development Co.,Ltd.,Qujing 655400,China)

机构地区：[1]武汉大学水利水电学院,湖北武汉430072 [2]大唐宣威水电开发有限公司,云南宣威655400

出　　处：《人民长江》2022年第3期169-174,共6页Yangtze River

基　　金：国家自然科学基金资助项目(51979207)。

摘　　要：边界元法作为一种半解析解的数值计算方法,除了在同自由度下能够获得相对更高的精度以外,更为突出的优点是降维,只需要对研究域的边界进行离散。但是在进行温度应力问题求解时,积分方程中会出现域积分。为了保证边界元法降维的优点,基于散度定理提出将直线积分法的域积分转化为边界积分。边界积分可以用带积分点的边界单元来计算。每个积分点可以构造一条积分线,由积分线上的线积分计算域积分。同时为了获得更高的精度,可以利用背景单元网格将积分线切割成更多的子线进行计算。最后通过一个矩形梁的热弹性分析和一个重力坝的温度应力分析验证了所提方法的有效性和精度。As a semi-analytical method,boundary element method(BEM)has the advantage of dimension reduction,which means this method only need to disperse the boundary for the research field.However,when it comes to solving the thermo-elastic problems,the domain integral will appear in the boundary integral equations.In order to ensure the advantage of BEM,the line integration method(LIM)is used to transform the domain integral into the boundary integral based on the divergence theorem.The boundary integral can be calculated by the boundary element with integral points.An integral line can be constructed for each integral point,and the domain integral can be calculated by the line integral on the integral line.In order to obtain higher accuracy,the integral line can be cut into sub-lines by using the background cell.This method feasibility and accuracy is proved by a thermal-elastic analysis of a rectangular beam and thermal stress analysis of a gravity dam.

关 键 词：直线积分边界元法 降维 域积分 热应力 

分 类 号：TV311[水利工程—水工结构工程]