双周期裂纹场平面弹性焊接的数学问题
On the Mathematical Problems of Composite Materials with a Doubly Periodic Set of Cracks
-
摘要: 本文讨论双周期胞腔中含任意形状裂纹的不同材料的弹性平面焊接(焊线为任意形状的封闭光滑曲线)的第二基本问题.运用Мусхелишвили复变函数方法,对这类弹性平面问题建立起了数学模型,将求解弹性平衡问题化归为寻求复应力函数满足一定边界条件的边值问题,然后构造其解的形式,再将其转化为正则型的奇异积分方程,数学上严格证明其解的存在与唯一.Abstract: In this paper, the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution, then, under some general restrictions it is reduced to normal type singular integral equation, the unique solvability is proved mathematically.
-
Key words:
- double period /
- crack /
- welding
-
[1] Muskhelishvili,N.I.,Some Basic Problems of the Mathematical Theory of Elasticity,Noordhoff,Groningen(1963). [2] Muskhelishvili,N.I.,Singular Integral Equations,3rd.Ed.Nauka,Moscow(1968). [3] Koiter W.T.,Some general theorems on doubly-periodic and quasi-periodic functions,Proc.Kon.Ned AK WT Amseerdam,A,157,2(1959),120--128. [4] Koiter,W.T.,Stress distribution in an infinite elastic sheet with a doubly periodic set ofholes,Boundary Problems in Differential Equations,The Univ.of Wisconsin Press,Madison(1960),191-213. [5] Ланасюк В.В.,Распредление напряжения окол трещин в пластинах и оболочках,киее《Наукова Пумка》,Акад.Наук.УССР,Хиз-махан ИН-У,(443)(1976),149-162 [6] Филъшитинский л.А.,К теовии упругих ндоднородиых срсД с регулярной струкгурой,ПММ,37(1973)263-273 [7] 曾祥勇, 朱爱军, 邓安福. Winkler地基上厚板分析的自然单元法[J]. 固体力学学报, 2008,29(2): 163-169.(ZENG Xiang-yong, ZHU Ai-jun, DENG An-fu. Natural element method for analysis of thick plates lying over Winkler foundations[J]. Chinese Journal of Solid Mechanics,2008,29(2): 163-169.(in Chinese)) [8] 刘土强,弹性长条的周期基本问题,数学杂志,(2)(1984), [9] 路见可,《解析函数边值问题》,上海科技出版社,上海(1986), [10] 郭建林,双周期解析函数的Poincaré问题,科学通报,14(13)(1987). [11] 黄烈德,Riemann-Hilberé问题的一些新发展,数学进展,(3)(1990), [12] Li Xing,On the doubly periodic and quasi-periodic Riemann boundary value problems,Acta Ningxia Univ.,1(1988).(in Chinese) [13] 李星.具有间断系数的双周期和双准周期Ricmann边值问题,宁夏大学学报(自然科学版)(1)(1988). [14] Zhang Xiao-si,General solutions of double periodic cracks in an anisotropic infinite plate,Scientia Sinica(Series A),28(1985). [15] 郑可,双周期平面弹性基术问题,数学物理学报,8(1)(1988). [16] 李星,带双周期裂缝与孔洞的弹性平面基本问题,宁夏大学学报,(2)(1990),71-24
点击查看大图
计量
- 文章访问数: 1736
- HTML全文浏览量: 83
- PDF下载量: 442
- 被引次数: 0