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A three‐dimensional stress field solution for pointed and sharply radiused V‐notches in plates of finite thickness
Author(s) -
LAZZARIN P.,
ZAPPALORTO M.
Publication year - 2012
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/j.1460-2695.2012.01698.x
Subject(s) - plane (geometry) , stress field , radius , mathematical analysis , plane stress , field (mathematics) , stress (linguistics) , harmonic , mathematics , shear (geology) , shear stress , geometry , finite element method , physics , structural engineering , mechanics , materials science , engineering , computer science , composite material , acoustics , pure mathematics , linguistics , philosophy , computer security
By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three‐dimensional governing equations lead to a system where a bi‐harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out‐of‐plane shear notch problem. The system can be applied not only to pointed three‐dimensional V‐notches but also to sharply radiused V‐notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models.