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断裂问题特征根的重根探讨
引用本文:徐永君,袁驷,柳春图.断裂问题特征根的重根探讨[J].力学学报,1999,31(5):618-624.
作者姓名:徐永君  袁驷  柳春图
作者单位:中国科学院力学研究所
基金项目:国家自然科学基金,中国博士后科学基金
摘    要:利用特征矩阵的秩与特征根所对应的子特征函数空间维数之间的关系。确定了反平面断裂问题和平面断裂问题的特征根可能出现的最大重根数.利用Reissner型板特征根与反平面和平面断裂问题特征根的关系确定其可能出现的最大重根数.得到了反平面断裂问题、平面断裂问题和Reissner板断裂问题可能出现的最大重根数分别为1,2,3.

关 键 词:特征根  重根  反平面  断裂问题  平面断裂

POSSIBLE MULTIPLE ROOTS FOR FRACTURE PROBLEMS
Xu Yongjun, Yuan Si, Liu Chuntu.POSSIBLE MULTIPLE ROOTS FOR FRACTURE PROBLEMS[J].chinese journal of theoretical and applied mechanics,1999,31(5):618-624.
Authors:Xu Yongjun  Yuan Si  Liu Chuntu
Abstract:In accordance with the relationship between the eigen-matrix rank and sub-eigenfunctiondimension of eigen-values, the maximum number of possible multiple roots for anti-plane problemand in-plane problem is determined. In view of the relationship with eigen-values of anti-plane andin--plane problem, the eigen-values for Reissuer plate consists of two parts. One part associateswith anti-plane problem, the other part pertains to in--plane problem. Therefore, the maximumnumber of multiple roots for anti--plane problem, in--plane problem and Reissuer plate are 1, 2and 3, respectively. The conclusion is demonstrated in a numerical example of single materialwith stress-free notch/crack. It is also found that multiple roots exist only in the case of crack.The present results offer significant insight into the study of notch/crack problem and the usefulguideline for program design.
Keywords:eigen-value  multiple roots  anti-plane problem  plane problem  Reissuer plate
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