一类带单位圆洞的无限平面焊接问题的稳定性(英文)  

STABILITY OF A KIND OF WELDING PROBLEMS OF INFINITE PLANE WITH A UNIT CIRCULAR HOLE

作　　者：林娟[1,2] 段萍[2] 谢碧华[3] 

机构地区：[1]福建商业高等专科学校基础部,福建福州350012 [2]武汉大学数学与统计学院,湖北武汉430072 [3]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《数学杂志》2013年第6期969-976,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11171260);Science and Technology Foundation of Education Department of Fujian Province,China(JA11341)

摘　　要：本文研究了在带一个单位圆洞的无限平面中焊入相同材料圆盘的焊接问题的稳定性,借助于复应力函数,把焊接问题转化为黎曼边值问题.利用解析函数边值理论和柯西型积分在积分曲线发生光滑摄动且核密度发生索波列夫型摄动下的稳定性,获得了复应力函数的表达式及其相应的误差估计,从而获得了应力和位移的误差估计.In this paper, we study the stability of the welding problems of an infinite plane with a unit circular hole and a circular plate which are welded together by using the same materials. By complex stress functions, the welding problems are transformed into Riemann boundary value problems. Using boundary value theory for analytic function and the result of the stability of Cauchy type integral under the smooth perturbation for the integral curve and Sobolev perturbation for the kernel density, expressions of complex stress functions are shown and their error estimates are obtained, thus error estimates of stresses and displacement are obtained respectively.

关 键 词：弹性体 复应力函数 柯西型积分 跳跃问题 摄动 

分 类 号：O175.8[理学—数学]