Study of a spherical shell with a surface crack by the line-spring model

The Sih and Hagendorf shell theory and the line-spring model are used to derive the governing equations of the spherical shell with a semi-elliptical internal or external surface crack. By assuming the functions of the displacement and the rotation as u=Ci(1−η2)1/2 and β=Di(1−η2)1/2, the computation of governing equations is simplified into linear algebraic equations through the proper treatment of singular equations. Displacement and stress fields for the spherical shell with a surface crack are calculated and the stress intensity factor at every point of the surface crack front is given in the paper. By comparison with the modified existing results, which are obtained by multiplying the finite element solutions for a surface crack in a finite plate with a modified factor, the line-spring model gives the expected results.