Crack can significantly affect the performance of structures and is one of the crucial indicators of damage in structural health monitoring. In this paper, the deflection behaviors of Euler–Bernoulli beams with arbitrary open edge cracks under arbitrary elastic boundary conditions are investigated. A continuous diffused stiffness reduction crack model is implemented to simulate the cracks in beams, which can incorporate multiple cracks and consider the stiffness reduction effect in the vicinity of a crack. With the proposed diffused stiffness reduction model, the fourth-order differential equation governing the deflection behavior of the multi-cracked Euler–Bernoulli beam is constructed. The powerful variational iteration method is applied to obtain the analytical solution of the multi-cracked beams on elastic foundations. Five shape functions are introduced, based on which the deflection of the multi-cracked beam is proposed. Both the solutions corresponding to the general elastic boundary conditions and the conventional boundary conditions are presented explicitly. The deflection solution is benchmarked and verified against the literature, and encouraging agreements are obtained. Parametric studies are carried out to investigate the influences of crack position, crack ratio, stiffness of the elastic foundation, and boundary conditions on the deflection of the cracked beams. The proposed crack model and the deflection solution overcome some of the limitations in the literature.

裂纹会严重影响结构的性能，并且是结构健康监测中损坏的关键指标之一。本文研究了在任意弹性边界条件下具有任意开口边缘裂纹的Euler-Bernoulli梁的挠度行为。实现了连续扩散的降低刚度的裂缝模型来模拟梁中的裂缝，该模型可以包含多个裂缝并考虑裂缝附近的刚度降低效果。利用所提出的扩散刚度减小模型，构造了控制多裂纹欧拉-伯努利梁的挠曲特性的四阶微分方程。运用强大的变分迭代法获得了弹性地基上多裂纹梁的解析解。介绍了五个形状函数，在此基础上提出了多裂纹梁的挠度。明确给出了对应于一般弹性边界条件和常规边界条件的两种解。根据文献对挠度解决方案进行了基准测试和验证，并获得了令人鼓舞的协议。进行了参数研究，以研究裂纹位置，裂纹比率，弹性基础的刚度和边界条件对裂纹梁挠度的影响。所提出的裂缝模型和挠度解决方案克服了文献中的某些限制。分别给出了与一般弹性边界条件和常规边界条件相对应的解。根据文献对挠度解决方案进行了基准测试和验证，并获得了令人鼓舞的协议。进行了参数研究，以研究裂纹位置，裂纹比率，弹性基础的刚度和边界条件对裂纹梁挠度的影响。所提出的裂缝模型和挠度解决方案克服了文献中的某些限制。分别给出了与一般弹性边界条件和常规边界条件相对应的解。根据文献对挠度解决方案进行了基准测试和验证，并获得了令人鼓舞的协议。进行了参数研究，以研究裂纹位置，裂纹比率，弹性基础的刚度和边界条件对裂纹梁挠度的影响。所提出的裂缝模型和挠度解决方案克服了文献中的某些限制。以及裂纹梁挠度的边界条件。所提出的裂缝模型和挠度解决方案克服了文献中的某些限制。以及裂纹梁挠度的边界条件。所提出的裂缝模型和挠度解决方案克服了文献中的某些限制。