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Kinematic (or hour‐glass) mode control for a uniform strain quadrilateral by an assumed strain technique
Author(s) -
Last N. C.,
Harkness R. M.
Publication year - 1989
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610130404
Subject(s) - finite element method , context (archaeology) , degrees of freedom (physics and chemistry) , structural engineering , stiffness , spurious relationship , kinematics , quadrilateral , bending , polygon mesh , mathematics , engineering , geometry , geology , physics , classical mechanics , paleontology , statistics , quantum mechanics
Finite element and finite difference solid mechanics computer programs have often been observed to overestimate the stiffness of an elastic beam or the collapse load in elasto‐plastic problems. There are a number of ways of overcoming these difficulties but many lead to unwanted degrees of freedom in the mesh which continuously degrade the solution if the errors are allowed to accumulate. These unwanted distortions are referred to as spurious or hour‐glass modes, and special measures have to be taken if accurate predictions are to be achieved without their appearance. In this paper a new scheme based on assumed strains at the element level is described in the context of a two‐dimensional, explicit, finite difference program. The scheme is compared with an earlier solution to this problem and is shown to have some advantages, particularly when irregular meshes and/or large deformations are encountered. Thorough testing indicates that the new formulation passes the patch test and leads to accurate predictions of bending stiffnesses and plastic collapse loads. An underlying consideration of the development was that the new scheme should be applicable to three‐dimensional calculations. Although this has not been tested numerically, the extension to three dimensions is discussed.