沿直线有多条裂纹的薄板弯曲问题  

ON THE BENDING OF AN ELASTIC PLATE CONTAINING MULTI-CRACKS

作　　者：段树金[1] 前田春和[2] 藤井康寿 中川建治 

机构地区：[1]石家庄铁道学院,石家庄050043 [2]岐阜大学工学院

出　　处：《工程力学》1999年第3期21-29,共9页Engineering Mechanics

摘　　要：本文首先用复变函数的虚部构成了一平面上沿y轴有矩形开口的位移函数，并用加权积分法将裂纹尖端交换为光滑接触的形状：然后由此函数构成的重调和函数，导出了沿不同弹性介质界面(y轴)有多条裂纹的薄板弯曲问题的应力函数。用加权积分法将裂纹尖端无穷大的应力集中有限化，并不意味着消除了复变函数中的奇异点。文中图示了将应力奇点移至其他分支，而在XY全平面应力呈有限连续的情形。本分析方法的成功之处在于在裂纹尖端附近构成了一开口位移和截面内力相并存的过渡区，同时消除了过去研究中呈现的界面裂纹尖端附近无穷大应力的剧烈振荡现象。In this paper,a crack opening function with rectangular shape along the y-axis isformed by the imagined part of complex function, and then the crack tip is transformed into asmoothed shape by the weight integral method; secondly, the saness functions of thin elastic platewith multi-cracks along the illterface(the y-hos) b^en tWO dissimilar mat6rials are deduced. Itis demonstrated in a diagram that the shes singular poied is removed into other branch, while thestress distribution is finite and continuous in the whole xy plane. An intermediate zone near thecrack tip is formed in which both the crack opening displacement and the cross-sechonal forceappear, removing the oscillating phenomenon of infinite stress near the crack tip.

关 键 词：薄板弯曲 裂纹 应力函数 过渡区 

分 类 号：O346.1[理学—固体力学]