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Numerical analysis of crack‐tip fields using the hodograph transformation
Author(s) -
Silling S. A.
Publication year - 1989
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.1620281103
Subject(s) - hodograph , discretization , transformation (genetics) , computation , numerical analysis , partial differential equation , mathematics , mathematical analysis , quadrilateral , geometry , finite element method , structural engineering , algorithm , engineering , biochemistry , chemistry , gene
A numerical method is discussed for analysis of anti‐plane shear crack‐tip fields in linear and non‐linear materials, including possible anisotropy. The method is based on the hodograph transformation. It allows efficient computation of singular stress fields because the transformed partial differential equation to be solved numerically is linear. The inversion of the transformation is also done numerically. The method is promising for the study of localizations, since regions with the largest stress gradients are automatically discretized with the finest mesh owing to the nature of the transformation.