摘要
在线性非局部弹性理论中，具有均匀常应力边界的裂纹混合边界值问题的解是不存在的．本文从非局部场论的基本理论出发针对这一问题进行了研究．内容包括：对非局部能量守恒定律的客观性的考察，非局部热弹性体本构方程的推导，非局部体力的确定以及线性化理论，得到了一些新结果．其中，在线性化理论中所推出的应力边界条件不仅解决了本摘要开头所提到的问题，而且自然地包括了Barenblatt裂纹尖端的分子内聚力模型．
In this linear nonlocal elasticity theory, the solution to the boundary-valueproblem of the crack with a constant stress boundary condition does not exist.This problem has been studied in this paper. The contents studied contain examining objectivity of the energy balance, deducing the constitutive equations ofnonlocal thermoelastic bodies and determining nonlocal force and the linear nonlocal elasticity theory. Some new results are obtained. Among them, the stressboundary condition derived from the linear theory not only solves the problemmentioned at the beginning, but also contains the model of molecular cohesivestress on the sharp crack tip advanced by Barenblatt.
出处
《应用数学和力学》
CSCD
北大核心
1997年第1期45-54,共10页
Applied Mathematics and Mechanics
关键词
非局部场论
裂纹
混合边界值问题
断裂力学
nonlocal field theory
localization residuals
constitutive equations
stress boundary conditions
