A generic methodology to deal with the mechanics of beams and shafts with cracks is presented. The elastic energy of the system under static loading is written in a comprehensive manner to remarkably reduce the 3D computations indispensable to the identification of the crack breathing mechanism. With a new reformulation of the problem, the breathing mechanism identification is distilled down to the computation of a dimensionless function that gives a fine and precise description of the system flexibility evolution when the crack breathes. This breathing function is exclusively inherent to the crack geometry and completely independent of the 3D model parameters which makes the approach more universal and could be applied straightforward to similar problems. This standard and generic methodology is completed by a detailed description of the technique of construction of a Cracked Beam Finite Element. Moreover, we give a nonlinear fitting formula of the identified function that all the process of identification could be skipped when a cracked transverse section is to be inserted in a beam-like model of a cracked shaft. A validation of the approach under static loading is given for a cantilever beam with one, then two cracked transverse sections. We also show, for a simple cracked shaft, common features of its vibrational behavior.

提出了一种处理带有裂纹的梁和轴的力学的通用方法。全面记录了系统在静态载荷下的弹性能，从而显着减少了识别裂纹呼吸机制必不可少的3D计算。随着问题的新形式化，呼吸机理的识别被简化为无量纲函数的计算，该函数给出了裂缝呼吸时系统柔性演变的精细而精确的描述。这种呼吸功能完全是裂纹几何所固有的，并且完全独立于3D模型参数，这使得该方法更加通用，可以直接应用于类似问题。通过对裂纹梁有限元构造技术的详细描述，完成了该标准和通用方法。此外，我们给出了所识别函数的非线性拟合公式，当将裂纹横截面插入到裂纹轴的梁状模型中时，可以跳过所有识别过程。对于具有一个然后两个裂纹横截面的悬臂梁，该方法在静态载荷下得到了验证。对于简单的裂纹轴，我们还显示了其振动行为的共同特征。对于具有一个然后两个裂纹横截面的悬臂梁，在静态载荷下该方法进行了验证。对于简单的裂纹轴，我们还显示了其振动行为的共同特征。对于具有一个然后两个裂纹横截面的悬臂梁，在静态载荷下该方法进行了验证。对于简单的裂纹轴，我们还显示了其振动行为的共同特征。