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A novel four‐node quadrilateral smoothing element for stress enhancement and error estimation
Author(s) -
Tessler A.,
Riggs H. R.,
Dambach M.
Publication year - 1999
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/(sici)1097-0207(19990410)44:10<1527::aid-nme497>3.0.co;2-1
Subject(s) - quadrilateral , smoothing , finite element method , mathematical optimization , algorithm , robustness (evolution) , quadratic equation , mathematics , computer science , geometry , engineering , structural engineering , biochemistry , statistics , chemistry , gene
A four‐node, quadrilateral smoothing element is developed based upon a penalized‐discrete‐least‐squares variational formulation. The smoothing methodology recovers C 1 ‐continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five‐node macro‐element configuration consisting of four triangular anisoparametric smoothing elements in a cross‐diagonal pattern. This element pattern enables a convenient closed‐form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge‐wise penalty constraints. The degree‐of‐freedom reduction scheme leads to a very efficient formulation of a four‐node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component. Copyright © 1999 John Wiley & Sons, Ltd.