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.

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