Mathematic modeling of nonlinear deformation elastomeric layer
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2011), pp. 56-63
Nonlinear theory of an elastomeric layer for Saint-Venant–Kirchhoff material is constructed. Creation of such theory essentially simplifies the solution of nonlinear boundary problems of a layer and multilayered structures in comparison with those of the equations of the three-dimensional nonlinear theory of elasticity. It is necessary to solve only one equation of the second order for one required function under the theory of a layer. Numerous calculations for a layer of the ring form on the equations of the nonlinear theory of a layer and on the equations of the nonlinear theory of elasticity have been executed. These calculations enabled to establish a number of important laws. The rigidity characteristic of a layer at compression is essentially nonlinear already at enough small compression of 3% order. Limits of applicability of the material model considered depending on a degree of compression of a layer are established. These limits are approximately equal 5–10%. The equations of the layer theory are applicable at relative thickness $h/R<0.2$. The equations of the linear theory of a layer can be used only at relative compression of order 0.005 and less.
Keywords:
nonlinear problems elasticity, nonlinear theory of elastomeric layer, material Saint-Venant–Kirchhoff, semi-linear material.
@article{VSPUI_2011_3_a6,
author = {V. M. Mal{\textquoteright}kov and S. A. Kabrits and S. E. Mansurova},
title = {Mathematic modeling of nonlinear deformation elastomeric layer},
journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
pages = {56--63},
year = {2011},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a6/}
}
TY - JOUR AU - V. M. Mal’kov AU - S. A. Kabrits AU - S. E. Mansurova TI - Mathematic modeling of nonlinear deformation elastomeric layer JO - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ PY - 2011 SP - 56 EP - 63 IS - 3 UR - http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a6/ LA - ru ID - VSPUI_2011_3_a6 ER -
%0 Journal Article %A V. M. Mal’kov %A S. A. Kabrits %A S. E. Mansurova %T Mathematic modeling of nonlinear deformation elastomeric layer %J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ %D 2011 %P 56-63 %N 3 %U http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a6/ %G ru %F VSPUI_2011_3_a6
V. M. Mal’kov; S. A. Kabrits; S. E. Mansurova. Mathematic modeling of nonlinear deformation elastomeric layer. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2011), pp. 56-63. http://geodesic.mathdoc.fr/item/VSPUI_2011_3_a6/
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