摘要
严格地求出了当泊松比不为零时对数梯度材料的裂纹尖端场．虽然在本构方程中对数项为exp(ax),但严格地证明了在最后应力的表达式中,它却变为exp(ax/2+ak_1^(1/2)y/2-kr/2)与exp(ax/2-ak_1^(1/2)y/2-kr/2)．对于数值解法,若考虑了此种严格关系,将会很容易地解释其结果．
The present paper derives the solution of the crack tip field in functional gradient materials with exponential variation of elastic constants for the case v ≠0. In the constitutive equations, only the exponential term exp（αx） is considered. On the basis of the exact mathematical theory, it is found that although the exponential term is exp（αx） in the constitutive equations, it becomes exp（αx/2 ＋ ακ1^1/2y/2- kr/2） and exp（αx/2 - ακ1^1/2y/2 - kr/2） in the exact relation. With the exact relation, some numerical solutions can be explained more easily. Further study must be focused on the influence of the large deformation.
出处
《力学学报》
EI
CSCD
北大核心
2006年第5期688-691,共4页
Chinese Journal of Theoretical and Applied Mechanics
关键词
裂纹
平面问题
梯度材料
对数型
crack, plane case, functional gradient material, exponential variation
