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A comparison of the plate theories in the sense of Kirchhoff–Love and Reissner–Mindlin
Author(s) -
Ebenfeld Stefan
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19991125)22:17<1505::aid-mma90>3.0.co;2-k
Subject(s) - mathematics , uniqueness , limit (mathematics) , mathematical analysis , sense (electronics) , boundary value problem , plate theory , boundary (topology) , calculus (dental) , medicine , electrical engineering , dentistry , engineering
In this article we compare the two plate theories in the sense of Kirchhoff–Love and Reissner–Mindlin for several different settings of the physical system. We establish existence, uniqueness and regularity of solutions to the respective boundary and initial boundary value problems. Moreover, we give asymptotic expansions of the solutions in the limit of a vanishing plate thickness, ϵ →0, whenever this is possible. Finally, we compare the solutions in the sense of Kirchhoff–Love and Reissner–Mindlin in that very limit. Copyright © 1999 John Wiley & Sons, Ltd.