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Improved hybrid solid element with a traction‐free cylindrical surface
Author(s) -
Tian Zongshu,
Tian Zheng
Publication year - 1990
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.1620290409
Subject(s) - traction (geology) , perpendicular , stress field , plane stress , finite element method , stress (linguistics) , free surface , mathematical analysis , geometry , mathematics , compatibility (geochemistry) , mechanics , structural engineering , materials science , engineering , physics , mechanical engineering , composite material , linguistics , philosophy
New 8‐node solid elements with two parallel faces and one traction‐free cylindrical surface are derived using the assumed stress hybrid model. Six new expressions of stress components are developed by using four stress functions and cylindrical co‐ordinates, so that the normal stress σ z on the plane perpendicular to the two parallel faces varies as a parabola, and the assumed stress field satisfies the equilibrium equations as well as the traction‐free conditions over the cylindrical boundary. The assumed stress field also satisfies the compatibility conditions when the new element is degenerated into the 2‐dimensional case. Examples have clearly demonstrated that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress σ z .