Finite Element Analysis of Wave Diffraction by a Crack

The time history of mode III stress intensity factor K₃ is calculated, and compared with exact solutions. It is found that crack-tip elements with a singular strain field are much less effective in elastodynamics than elastostatics. The nonsingular (ordinary) crack tip element whose crack-opening displacement is calibrated against the exact value of k₃ by means of a static finite element solution for load applied at remote boundaries was found to be most effective. Detailed studies have also been carried out for implicit and explicit time-step algorithms; proper sizes of elements; methods for solving equation systems; the questions of nonreflecting boundary; lumping of mass matrix; and elimination of spurious oscillations superimposed on the correct solution. The convergence and accuracy of various singular crack-tip elements have been examined. Finally, application of the technique for in-plane motions is also presented.