| 牛忠荣,葛大丽,程长征,叶建乔.插值矩阵法分析双材料平面V形切口奇异阶[J].计算力学学报,2009,26(6):893~899 |
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| 插值矩阵法分析双材料平面V形切口奇异阶 |
| Analysis of the stress singularity of plane bimaterial V-notcheswith interpolating matrix method |
| 投稿时间：2007-12-06 |
| DOI：10.7511/jslx20096022 |
| 中文关键词: 应力奇异阶 插值矩阵法 V形切口 粘结材料 |
| 英文关键词:stress singularity orders the interpolating matrix method V-notch biomaterial |
| 基金项目:教育部博士点基金(20050359009)资助项目. |
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| 摘要点击次数: 1466 |
| 全文下载次数: 1097 |
| 中文摘要: |
| 对二维V形切口问题提出奇异阶分析的一个新方法。首先,以V形切口尖端附近位移场沿其径向渐近展开为基础,将其线弹性理论控制方程转换成切口尖端附近关于周向变量的常微分方程组特征值问题,然后将数值求解两点边值问题的插值矩阵法进一步拓展为求解一般常微分方程组特征值问题,插值矩阵法是在离散节点上采用微分方程中待求函数的最高阶导数作为基本未知量。由此,V形切口的应力奇性阶问题通过插值矩阵法获得,同时相应的切口附近位移场和应力场特征向量一并求出。 |
| 英文摘要: |
| In this paper, a new way was proposed to evaluate the orders of singularity for plane V-notch problems. Based on an asymptotic displacement field in terms of radial coordinates at the V-notch tip, the governing equations of the elastic theory were transformed into an eigenvalue problem of ordinary differential equations (ODEs). Then the interpolating matrix method which was a numerical method of solving two-point boundary valve problems was further developed to solve the general ODEs eigenvalue problem. Thus the singularity orders of the V-notch problem are determined through solving the corresponding ODEs by means of the interpolating matrix method. In addition, the associated eigenvectors of the displacement and stress fields near the V-notches are also obtained. |
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