热应力边界元法中几乎超奇异积分的计算  

Evaluation of Nearly Hyper-singular Integrals in Thermal Stress Boundary Element Method

作　　者：程长征[1] 牛忠荣[1] 周焕林[1] 杨智勇[2] 

机构地区：[1]合肥工业大学土建学院,安徽合肥230009 [2]铜陵学院机械系,安徽铜陵244000

出　　处：《计算物理》2008年第1期113-118,共6页Chinese Journal of Computational Physics

基　　金：教育部博士学科点基金(20050359009);安徽省自然科学基金(050440503)资助项目

摘　　要：通过分部积分变换将热弹性力学应力边界积分方程中的超奇异积分转化为强奇异积分,然后与另一个强奇异积分求和,得到仅含几乎强奇异的热应力自然边界积分方程.再对其中的几乎强奇异积分施以正则化,消除了热弹性力学边界元法中的几乎奇异积分,可以准确计算出热弹性力学问题中近边界内点的热应力.算例证明了方法的有效性.An algorithm is developed to calculate stresses at the interior points near boundary in boundary element method of thermoelasticity. A series of transformations is manipulated on conventional derivative boundary integral equations （BIE）. It leads to a new natural BIE in thermoelasticity problem named thermal stress natural boundary integral equation （NBIE）. Hyper-singularity and strong-singularity in conventional BIE are converted into strong-singularity in NBIE. Nearly strong singular integrals are evaluated in NBIE by the regularization algorithm. Thermal stresses at points near boundary are calculated by NBIE. Numerical examples illustrate efficiency of the method.

关 键 词：边界元法 热弹性力学 热应力 几乎超奇异积分 

分 类 号：O343.6[理学—固体力学]