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Singular element construction using a mapping technique
Author(s) -
Tsamasphyros George
Publication year - 1987
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.1620240707
Subject(s) - conformal map , plane (geometry) , finite element method , mathematics , geometry , mathematical analysis , element (criminal law) , infinity , structural engineering , engineering , political science , law
Conformal mapping regularizes (in the new plane) the singular stress field around the crack tip. So, conventional finite elements can be used in the transformed plane. The inverse mapping of the above elements gives another class of ‘mapped elements’. The crack‐tip mapped element is a singular element. Thus, using various elements (the ‘parent elements’) in the mapped plane we obtain an infinity of singular elements, the ‘product elements’. These singular elements are introduced naturally and have no defect, as many other singular elements have.