CAJ | 학술논문

提出了双周期平行四边形排列裂纹反平面问题的有限元方法,通过对单位胞元引入周期边界条件,在裂纹尖端采用奇异单元,解决了有限元分析这类问题的效率和精度问题.利用Ansys软件计算,在各种有解析解对照的情形下,应力强度因子的相对误差都在0.2%以内.与现有通常限于对称阵列的双周期裂纹的研究相比,本文发展的方法适用于一般的非对称平行四边形裂纹阵列.算例揭示了行向裂纹间的相互干涉放大应力强度因子,而叠向裂纹间的作用相互屏蔽.对于平行四边形阵列的情形,这两种相反的干涉效应使应力强度因子与裂纹错动参数间呈现非单调依赖关系.
제출료쌍주기평행사변형배렬렬문반평면문제적유한원방법,통과대단위포원인입주기변계조건,재렬문첨단채용기이단원,해결료유한원분석저류문제적효솔화정도문제.이용Ansys연건계산,재각충유해석해대조적정형하,응력강도인자적상대오차도재0.2%이내.여현유통상한우대칭진렬적쌍주기렬문적연구상비,본문발전적방법괄용우일반적비대칭평행사변형렬문진렬.산례게시료행향렬문간적상호간섭방대응력강도인자,이첩향렬문간적작용상호병폐.대우평행사변형진렬적정형,저량충상반적간섭효응사응력강도인자여렬문착동삼수간정현비단조의뢰관계.
A finite element scheme is developed to analyze an elastic solid weakened by a doubly periodic parallelogramic array of cracks under antiplane shear. With periodic boundary condition of the unit cell and a singular element at the crack tips, the computational efficiency and accuracy are greatly improved. A comparison with the available exact solution in the case of a rectangular array of cracks shows that the relative errors for the stress intensity factor get less than 0.2%. It differs from the available researches confined to the case of a symmetric array of cracks, the present method can be applied to the case of non-symmetric general parallelogramic array of cracks. The numerical results reveal that the interaction of row-directional cracks shows an amplifying effect on the stress intensity factors, but the interaction of stack- directional cracks shows a shielding effect. In the case of a parallelogramic array of cracks, the two opposite effects result in nonmonotonic relations between the stress intensity factors and the staggered parameters.