Existence, uniqueness, and numerical simulations of Föppl‐von Kármán equations for simply supported plate | Zendy

Alkhayal Jana | Zendy; Chehab JeanPaul | Zendy; Jazar Mustapha | Zendy

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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.

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