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On the accuracy of polynomial finite elements for crack problems
Author(s) -
Johnson A. R.
Publication year - 1981
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.1620171208
Subject(s) - finite element method , stress intensity factor , mathematics , stiffness matrix , quadratic equation , interpolation (computer graphics) , mixed finite element method , mathematical analysis , matrix (chemical analysis) , square (algebra) , polynomial , geometry , polynomial interpolation , structural engineering , linear interpolation , materials science , engineering , composite material , telecommunications , frame (networking)
A square tensile sheet with symmetric edge cracks is analysed by the finite element method to demonstrate the accuracy obtained with polynomial elements when the mesh patterns are chosen on the basis of the element's interpolation functions. Numerical results are provided for the accuracy of the total strain energy, the stress intensity factor, and the numerical condition of the global stiffness matrix. The stress intensity factor is determined to within 1.0 per cent accuracy using quadratic (linear strain) triangular elements with only 138 degrees‐of‐freedom.