摘要
考虑裂纹的缝隙效应,研究了开闭裂纹Euler-Bernoulli梁的弯曲变形.首先,将裂纹等效为内部旋转弹簧,利用广义函数,给出了考虑裂纹缝隙影响的Euler-Bernoulli梁的等效抗弯刚度,推导了具有任意数目开闭裂纹梁弯曲变形的显式通解.在此基础上,研究了均布载荷作用下上侧单裂纹简支梁以及裂纹处承受集中力和集中力偶共同作用的固支梁的弯曲变形,分析了梁长细比、裂纹深度和位置以及载荷等对裂纹开闭状态和梁弯曲变形的影响。结果表明:梁挠度分布在裂纹处存在尖点,而转角分布存在跳跃;梁挠度与载荷的响应关系一般为双折线形式,分别对应于裂纹的张开和闭合状态;且裂纹张开时,裂纹梁的柔度随着梁长细比的增加和裂纹深度的减小而减小。这些结果对梁裂纹无损检测具有指导意义.
Considering the effect of crack gap,the equivalent flexural rigidity of the Euler-Bernoulli beam with switching cracks was presented by generalized functions,and an explicit general solution for the bending deformation of the Euler-Bernoulli beam having an arbitrary number of switching cracks with the crack gap effect was derived. Based on the these results the bending deformation of a simply-supported beam subjected to a uniform load with a crack at its top surface,together with the clamped beam subjected to concentrated force and couple at its crack location were investigated. Then,the influences of the beam＇s slenderness ratio,crack＇s depth and location and load on the crack state and bending performances were analyzed. It was revealed that there exists,at the crack location,a cusp on the deflection curve and a jump on the rotational angle curve; the relationship between the beam＇s deflection and load is bilinear,corresponding to open and closed crack states,respectively; and when the crack is open,the flexibility of the cracked beam decreases with the increase of the beam＇s slenderness ratio and the decrease of the crack depth. These results are helpful in guiding non-destructive identification of crack on beam.
出处
《力学季刊》
CSCD
北大核心
2015年第4期703-712,共10页
Chinese Quarterly of Mechanics
