摘要
采用新的方法研究非局部理论中Ⅰ_型裂纹的断裂问题,进而确定裂纹尖端的应力状态,这种方法就是Schmidt方法· 所得结果比艾林根研究同样问题的结果准确和更加合理,克服了艾林根研究同样问题时遇到的数学困难· 与经典弹性解相比,裂纹尖端不再出现物理意义上不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题·
Field equations of the non_local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual_integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's one for solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present at the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.
出处
《应用数学和力学》
EI
CSCD
北大核心
1999年第10期1025-1032,共8页
Applied Mathematics and Mechanics
基金
国家优秀青年研究基金!资助项目 ( 1972 5 2 0 9)
