We considered compression of a strip made of an inhomogeneous material and having an uneven surface on the sides. The forces applied on the upper and lower sides and on the lateral edges of the cross section are considered independent. As a necessary condition for disruption of the normal functioning of the band, it is proposed to use the criterion of continuous dependence of the function characterizing the behavior of the studied object on the initial data. A violation of this continuity can cause loss of stability (the first group of limiting states) or excessive deformations, deviations from the projected design values (the second group of limiting states). Mathematical models for studying continuous dependence with boundary conditions in a deformed state are considered, as well as a model in which rotation angles in equilibrium equations were taken into account (according to the works of Novozhilov and Ivlev). A condition we obtained that makes it possible to determine the area at the boundary of which the state of the strip will become marginal (loss of stability of the equilibrium shape). The reliability of the obtained results is confirmed by the coincidence with the known results of other authors. For different values of the cross-section parameters, regions we constructed within which the stress-strain state of the strip is close to homogeneous.

Alexey V. Kovalev, Doctor of Physico-Mathematical Sciences, Professor; e-mail: kovalev@amm.vsu.ru ; https://orcid.org/0000-0002-3730-9621; AuthorID: 11051

Mikhail M. Korotkov, Scientific Researcher; e-mail: mihailkorotkov97@rambler.ru

Nadezhda V. Minaeva, Doctor of Physico-Mathematical Sciences, Associate Professor; e-mail: minaeva@yandex.ru ; https://orcid.org/0000-0002-9366-5575; AuthorID: 11715

Alexander I. Shashkin, Doctor of Physico-Mathematical Sciences, Professor; e-mail: shashkin@amm.vsu.ru ; https://orcid.org/0000-0001-9925-5019; AuthorID: 156046