基于等几何-边界元法的热弹性力学问题分析  

Thermoelastic Mechanics Analysis Based on Isogeometric Boundary Element Method

作　　者：张伟 姚玲 赵帆 尹晓萌 ZHANG Wei;YAO Ling;ZHAO Fan;YIN Xiaomeng(College of Architecture and Civil Engineering,Xinyang Normal University,Xinyang 464000,China;Shanxi Zhongji Geotechnical Engineering Co.,Ltd.,Xi’an 710043,China)

机构地区：[1]信阳师范学院建筑与土木工程学院,河南信阳464000 [2]陕西中机岩土工程有限责任公司,陕西西安710043

出　　处：《信阳师范学院学报（自然科学版）》2021年第4期661-666,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(41807240);信阳师范学院青年基金项目(2020-QN-046)。

摘　　要：温度变化引起的固体热应力问题一直是影响固体材料寿命的重要因素之一.边界元方法利用边界积分代替域积分,对复杂问题的降维处理大大降低了计算复杂度.利用非均匀有理B样条曲线(NURBS)构建计算模型边界,采用等几何思想进行单元划分,从而克服了单元离散造成的几何误差.由于热应力的存在,导致构造的等几何边界积分方程里含有域积分项,采用径向基函数法将该域积分转化成边界积分,以充分发挥等几何边界元法的降维计算优势.模型验算表明,该计算方法比传统边界元方法更加可靠.Solid thermal stress caused by temperature has always been one of the important factors affecting the life of solid materials.The boundary element method,using boundary integrals instead of domain integrals,reduces the dimensionality of complex issue and the computational complexity.The non-uniform rational B-splines(NURBS)curve is used to construct the boundary of the calculation model,and the isogeometric idea is used to divide the unit,so as to overcome the geometric error caused by the unit discretization.Because of the existence of thermal stress,the constructed isogeometric boundary integral equation contains the domain integration term.The radial basis function method is used to convert the domain integration to the boundary integration.The advantage of the dimensionality reduction can be fully presented by using isogeometric boundary element method.The model calculation shows that the proposed calculation method is more reliable than the traditional boundary element method.

关 键 词：等几何 非均匀有理B样条 边界元法 弹性力学 热应力 

分 类 号：TU111.1[建筑科学—建筑理论]