Eigenfunction expansion variational method for the solution of a cusp crack problem in a finite plate

In this paper, the EEF (eigenfunction expansion form) for the cusp crack in a finite plate is obtained, and the EEVM (eigenfunction expansion variational method) is used to solve the cusp crack problem in a finite plate. Each term in the EEF satisfies the governing equation of elasticity and the traction free condition along the cusp crack. As a result of using EEVM, the final solution for complex potentials is obtainable. It is found that the slenderness of the cusp crack has a significant influence to the SIF (stress intensity factor) at the crack tip. Particular attention is paid to a compression loading applied in the direction of the cusp crack axis. This can make an explanation for the rupture of rock with cusp crack under compression. Finally, numerical examples with the calculated results are presented.