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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 crack effect, the bending deformation of the Euler-Bernoulli beam with open and close crack is studied. First, the crack is equivalent to an internal rotating spring, and the equivalent of the Euler-Bernoulli beam considering the influence of crack is given by using the generalized function Bending stiffness, the explicit general solutions of bending deformation with any number of open and close cracked beams are deduced.On the basis of this, we study the effect of uniform load and concentrated force on the simple cracked upper beam under the uniform loading The effects of the beam slenderness ratio, the depth and location of the crack and the load on the crack opening and closing state and the beam bending deformation were analyzed. The results show that the deflection distribution of the beam has sharp points at the crack tip, and the angular distribution has a jump. The response of the beam deflection to the load is generally in the form of a double-fold line corresponding to the open and closed states of the crack respectively. When the crack is open, Flexibility decreases with increasing slenderness ratio and decreasing crack depth. These results are instructive for nondestructive testing of beam cracks.