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Reduced minimization of product and non‐product type in Mindlin plate elements
Author(s) -
YongWoo Kim
Publication year - 1997
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(19970915)40:17<3117::aid-nme202>3.0.co;2-2
Subject(s) - minification , energy minimization , mathematics , dimension (graph theory) , serendipity , type (biology) , product (mathematics) , finite element method , element (criminal law) , shear (geology) , plate theory , structural engineering , geometry , mathematical optimization , engineering , physics , materials science , combinatorics , geology , law , paleontology , quantum mechanics , astronomy , political science , composite material
This paper presents concepts of two‐dimensional reduced minimization of product type and non‐product type: the analytical reduced minimization theory in one dimension when extended to that of Mindlin plate elements reveals that the two‐dimensional reduced minimization for Lagrangian plate elements can be obtained by the successive use of the one‐dimensional reduced minimization. But this relation does not hold for serendipity elements due to an incompleteness of displacement functions. This paper examines effects of various integrations of shear strain energy by applying the one‐dimensional successive reduced minimization to Lagrangian and serendipity plate elements. The results show why the selective 2×3 and 3×2 rule for the transverse shear strain energies of an 8‐noded plate element cannot eliminate locking and why a conventional 12‐noded plate element of serendipity family does not have one‐order‐lower, optimal Gauss strain locations. © 1997 John Wiley & Sons, Ltd.