| 陈梦成.横观各向同性材料三维裂纹问题的数值分析[J].计算力学学报,2009,26(1):109~113 |
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| 横观各向同性材料三维裂纹问题的数值分析 |
| Three-dimensional numerical analysis of cracks in transversely isotropic materials |
| 投稿时间：2006-10-30 |
| DOI：10.7511/jslx20091017 |
| 中文关键词: 横观各向同性 弹性体 三维片状裂纹 超奇异积分方程 边界元 |
| 英文关键词:transversely isotropic material elasticity three-
dimensional crack problem hypersingular integral equation boundary element met
hod |
| 基金项目:国家自然科学基金(10132020,10302022)资助项目. |
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| 中文摘要: |
| 严格从三维横观各向同性材料弹性空间问题的Green函数出发,采用Hadamard有限部积分概念,导出了三维状态下单位位移间断(位错)集度的基本解。在此基础上,将三维任意形状的片状裂纹问题归结为求解一组以未知位移间断表示的超奇异积分方程;并给出了边界元离散形式。对方程中出现的超奇异积分,采用了Hadamard定义的有限部积分来处理。论文最后给出了若干典型片状裂纹问题的数值算例,数值结果表明了本文方法是非常有效的。 |
| 英文摘要: |
| In this paper,started rigorously from Green functions for
elastic spac
e problems of transversely isotropic materials,the fundamental solutions for a
displacement-jump (dislocation) were derived by Hadamard’s finite-part integr
a
l concepts.Subsequently,the problem of a three-dimensional planar crack with a
r
bitrary shape in an infinite transversely isotropic solid was reduced to the sol
ution of a set of hyper-singular integral equations with unknown displacement j
umps.Discretization of the boundary element method on the crack surfaces was dis
cussed.The hyper-singular integrals in the equations were numerically treated b
y
the use of Hadamard’s finite-part integral concepts.Finally,some numerical ex
amples of typical-shaped planar crack problems were given and the effeetiveness
of the analysis was validated. |
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