Circumferential Crack Modeling of Thin Cylindrical Shells in Modal Deformation

TL;DR

This paper introduces a novel conversion technique for modeling circumferential cracks in thin cylindrical shells, enabling accurate analysis of modal deformation, buckling, and natural frequency changes through semi-analytical finite element methods.

Contribution

The paper presents a new conversion-based modeling approach for circumferential cracks in shells, integrating stiffness enrichment and validation with experiments and simulations.

Findings

Crack depth and length significantly affect buckling load.

The conversion technique accurately predicts natural frequency shifts.

Validation confirms the method's effectiveness against experimental and ABAQUS results.

Abstract

An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique.