Finite Element Analysis of Wave Diffraction by a Crack

by Zdeněk P. Bažant, (M.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
Jan D. Achenbach, Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
John L. Glazik, Jr., Grad. Student; Northwestern Univ., Evanston, Ill.,

Serial Information: Journal of the Engineering Mechanics Division, 1976, Vol. 102, Issue 3, Pg. 479-496

Document Type: Journal Paper


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.

Subject Headings: Finite element method | Wave diffraction | Cracking | Domain boundary | History | Strain | Displacement (mechanics) | Calibration

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