Mathematic modeling of nonlinear deformation elastomeric layer

V. M. Mal’kov ; S. A. Kabrits ; S. E. Mansurova

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2011), pp. 56-63

Résumé

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 $h/R0.2$. The equations of the linear theory of a layer can be used only at relative compression of order 0.005 and less.

Détail

Keywords: nonlinear problems elasticity, nonlinear theory of elastomeric layer, material Saint-Venant–Kirchhoff, semi-linear material.