Premium
Existence, uniqueness, and numerical simulations of Föppl‐von Kármán equations for simply supported plate
Author(s) -
Alkhayal Jana,
Chehab JeanPaul,
Jazar Mustapha
Publication year - 2019
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/mma.5872
Subject(s) - mathematics , uniqueness , constructive , constructive proof , gauss , nonlinear system , mathematical analysis , term (time) , numerical analysis , point (geometry) , combinatorics , geometry , physics , process (computing) , quantum mechanics , computer science , operating system
In this paper, we consider the Föppl‐von Kàrmàn equations in the case of a simply supported thin plate. We introduce a nonlinear Gauss‐Seidel fixed point scheme which allows to obtain a constructive proof of the existence and the uniqueness, when a small nonzero source term is considered. Numerical simulations are given using finite elements approximation. We point out the important role of a parameter which allows to select situations in which a buckling phenomena is observed numerically.