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A non‐hypersingular time‐domain BIEM for 3‐D transient elastodynamic crack analysis
Author(s) -
Zhang Ch.,
Gross D.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361709
Subject(s) - mathematics , traction (geology) , transient (computer programming) , mathematical analysis , time domain , square root , collocation method , collocation (remote sensing) , function (biology) , geometry , wedge (geometry) , boundary element method , domain (mathematical analysis) , boundary (topology) , structural engineering , finite element method , differential equation , geology , engineering , computer science , ordinary differential equation , remote sensing , geomorphology , evolutionary biology , computer vision , biology , operating system
A three‐dimensional (3‐D) time‐domain boundary integral equation method (BIEM) is presented for transient elastodynamic crack analysis. A non‐hypersingular traction BIE formulation is used with the crack opening displacements and their derivatives as unknown quantities. A collocation method in conjunction with a time‐stepping scheme is developed to solve the non‐hypersingular time‐domain BIEs. To simplify the analysis and to describe the proper behaviour of the unknown quantities at the crack front, a constant spatial shape function is applied for elements away from the crack front, while a spatial ‘square‐root’ crack‐tip shape function is adopted for elements near the crack front. A linear temporal shape function is used in the time‐stepping scheme. Numerical calculations, have been carried out for penny‐shaped and square cracks. Results for the elastodynamic stress intensity factors are presented as functions of the temporal and the spatial variables. For the test examples considered, good agreement between the present results and those of other authors is obtained.