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Bending of inflated curved hyperelastic tubes
Author(s) -
Kolesnikov Alexey M.,
Popov Alexander V.,
Shubchinskaya Nataliya Yu.
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800093
Subject(s) - hyperelastic material , curvature , tube (container) , bending , materials science , mechanics , bending moment , strain energy density function , deformation (meteorology) , compressibility , pure bending , nonlinear system , structural engineering , composite material , physics , geometry , finite element method , engineering , mathematics , quantum mechanics
Abstract We discuss large flexure of an inflated curved thin‐walled tube within the framework of the nonlinear theory of elastic membranes. Wrinkling of the membrane is taken into account by using a relaxed strain energy density derived from a strain energy function of incompressible hyperelastic material. We consider curved tubes with elliptical cross‐section and analyze the influence of a cross‐section shape and initial curvature of the tube at its deformation. Dependence of the bending moment on the tube curvature is obtained and discussed. In particular, the comparison with the pure bending of a cylindrical tube same material is made. We study the fact that the curving of the curved tube under in‐plane bending might be realized in two directions. Depending on the flexure direction the behavior of a curved tube can be similar or significantly different from the behavior of a cylindrical tube.