A COMPARISON BETWEEN SERENDIPITY AND LAGRANGE PLATE ELEMENTS IN THE FINITE ELEMENT METHOD

✍ Scribed by DHAINAUT, MARC

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 163 KB
• Volume: 13
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199705)13:5<343::aid-cnm60>3.0.co;2-2

✦ Synopsis

The serendipity (eight nodes) and Lagrange (nine nodes) plate elements following the Reissner±Mindlin irreducible formulation for the bending of plates are among the most popular in the ®nite element method. However, reduced integration on the shearing part of the stiness matrix has to be performed in order to avoid locking of the mesh in the limit of thin plates, where numerical constraints are taking some degrees of freedom in order to be satis®ed. This paper explains the competition between those constraints and the degrees of freedom, giving a mean to predict whether a mesh will lock or not. It also shows why the Lagrange element performs better than the serendipity element. Numerical results con®rm this analysis.