Abstract A triangular cracked plane element is proposed for application in fracture mechanics’ problems. The new element is based on the strain formulation and the compliance concept. To formulate the non-cracked element, the assumed strain formulation is used. Due to strain formulation, the derived non-cracked element is free from shear parasitic error. Moreover, it demonstrates very low sensitivity to the mesh distortions. In comparison to the classical displacement-based elements, the proposed element leads to more accurate responses for the coarse meshes. To incorporate crack effects in the element, the additional flexibility caused by the crack is computed based on the principles of the linear elastic fracture mechanics. Because of acceptable accuracy of the proposed element in free-vibration analysis of structures with stable open cracks, it is applicable for vibration-based crack detection. Various numerical examples evaluate accuracy and efficiency of the cracked and non-cracked formulations.

中文翻译：

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用于断裂力学问题的基于应变的平面单元

摘要 针对断裂力学问题，提出了一种三角形裂纹平面单元。新元素基于应变公式和柔量概念。为了公式化非裂纹单元，使用了假定应变公式。由于应变公式，导出的非裂纹单元没有剪切寄生误差。此外，它对网格扭曲的敏感性非常低。与经典的基于位移的单元相比，所提出的单元对粗网格有更准确的响应。为了在单元中加入裂纹效应，基于线弹性断裂力学原理计算由裂纹引起的附加柔度。由于所提出的单元在具有稳定开裂结构的自由振动分析中的精度可以接受，适用于基于振动的裂纹检测。各种数值示例评估了裂纹和非裂纹配方的准确性和效率。