Rectangular shell finite element with an open crack

Abstract The paper presents a method for the formulation of a thin, rectangular, shell finite element with a transverse, internal, open crack. The element is a compound of a rectangular, cracked plate finite element subjected to “in-plane forces” and a rectangular, cracked plate finite element subjected to “bending forces”. The crack is modelled by additional flexibility matrices, the terms of which are calculated on the basis of laws of fracture mechanics. The influence of a single crack on static deflections and natural frequencies of a cantilever beam with a hollow cross-section, simply supported square plate and simply supported cylindrical shell is analyzed. This method of stiffness martrix formulation may be used to determine the stiffness matrix for shell finite elements with other types of cracks (one-edge, double-edge, skew, etc.) if their stress intensity factors are known.

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