A two-dimensional model of the dynamics of sharp bending of a non-linearly elastic plate

Dent patterns on the surface of a longitudinally compressed, non-linear elastic cylindrical shell

“…8 and have the meaning of effective moduli that characterize the "quasi-planar" non-linear elastic stress state of the shell:…”

“…It was shown in Ref. 8 in the case of an analytic description of two-dimensional multisolitons in a plate that hypotheses and formulations that are typical of the variational approach do not give a correct dispersion law of linear modes and lead to incorrect estimates and qualitative conclusions when the dynamics of non-linear elastic systems are analysed.…”

Transverse corrugation solitons in a three-layered non-linearly elastic medium

“…We define two parameters el = a/l and e2 = d/l which reflect the order of smallness of the amplitudes of the displacements and the thickness of the plate. In the dynamic equations of the plate, we change to the dimensionless variables The problem is simplified when there are no external loads of the order of e~ [5].1" We will describe the deformations of the supports with other dimensionless variables:…”

“…The domain of physical parameters of the problem, in which the non-linear dynamics of the plate can be studied within the framework of the simplified model, is separated out by the conditions which have been enumerated [5]. We next consider the case when the displacement fields of the three-layer medium are independent of the coordinate x2(22) and the components of the displacements u2 and a) 2 The superscripts indicate the general order of the terms with respect to the parameters el and E!…”

“…1 *t]~ n' ') = fi~ ~' ') (n = 1, 2; l = 0, 2, 3, ...). The coefficients ~" 1) (r/ = 1, 2) are expressed m terms of u~ °' ) -(2,1) Ul-(I' 1) -----_152ikq~t~o, 1) + ~{1, 1), fi(12, 1) = _ 151eiq~)Xfi~O, 1) + Ul is introduced which characterizes the stresses (in the linear approximation, see [5]) which arise in the middle layer when an element of its area is changed.…”