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C 0 finite element discretization of Kirchhoff's equations of thin plate bending
Author(s) -
Ortiz M.,
Morris G. R.
Publication year - 1988
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.1620260707
Subject(s) - discretization , finite element method , quadrilateral , bending of plates , mathematics , interpolation (computer graphics) , mathematical analysis , bending , geometry , mixed finite element method , physics , structural engineering , classical mechanics , engineering , motion (physics)
An alternative formulation of Kirchhoff's equations is given which is amenable to a standard C 0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C 0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three‐dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.