Journal of Nonlinear Mathematical Physics

Volume 6, Issue 1, February 1999, Pages 35 - 50

Variational Methods for Solving Nonlinear Boundary Problems of Statics of Hyper-Elastic Membranes

Authors
V.A. TROTSENKO
Corresponding Author
V.A. TROTSENKO
Received 10 June 1998, Accepted 13 July 1998, Available Online 1 February 1999.
DOI
https://doi.org/10.2991/jnmp.1999.6.1.4How to use a DOI?
Abstract
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics [1]­[6]. In the present paper, using the variational method for solving nonlinear boundary problems of statics of hyper-elastic membranes under the regular hydrostatic load, we investigate peculiarities of deformation of a circular membrane whose mechanical characteristics are described by the Bidermann-type elastic potential. We develop an algorithm for solving a singular perturbation of nonlinear problem for the case of membrane loaded by heavy liquid. This algorithm enables us to obtain approximate solutions both in the presence of boundary layer and without it. The class of admissible functions, on which the variational method is realized, is chosen with account of the structure of formal asymptotic expansion of solutions of the corresponding linearized equations that have singularities in a small parameter at higher derivatives and in the independent variable. We give examples of calculations that illustrate possibilities of the method suggested for solving the problem under consideration.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 1
Pages
35 - 50
Publication Date
1999/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.1.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - V.A. TROTSENKO
PY  - 1999
DA  - 1999/02
TI  - Variational Methods for Solving Nonlinear Boundary Problems of Statics of Hyper-Elastic Membranes
JO  - Journal of Nonlinear Mathematical Physics
SP  - 35
EP  - 50
VL  - 6
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.1.4
DO  - https://doi.org/10.2991/jnmp.1999.6.1.4
ID  - TROTSENKO1999
ER  -