In the article provided the results of studies the optimization of energy-saving technologies in mechanical engineering using modern methods of simulation modeling is becoming an urgent area for the informatization of engineering production on the process of cold asymmetric rolling of metal sheets is accompanied by an inhomogeneous stress-strain state. The research considers the noncanonical areas of strain, an approach is proposed for determining the optimal technological parameters and studying the stress state of the cold rolling process using asymmetric rolling technology in the active zone of elastoplastic strains based on simulation using the application software LS-DYNA by LS-PrePost (R) version V4.6.1. To optimize energy-saving for rolling technologies, considered a stationary regime of symmetrical rolling, the kinetic energy does not change over time, and the potential energy in the active zone of elastic-plastic strains tends to increase. For the case of asymmetric rolling, a high level of kinetic energy is observed, and there is a fluctuation over time, explained by different coverage of asymmetric rollers in the zone of active elastic-plastic strains, as a result of which the stationary nature of the metal sheet rolling mode is violated.

The paper considers a circular cylindrical three-layer shell of arbitrary thickness from a viscoelastic material. It is believed that it consists of two outermost bearing layers and a middle layer between them, the materials of which are generally different. The problem of unsteady torsional vibrations of such a shell with rigid contact between the layers is formulated. Proceeding from the assumption that there is a rigid contact between the layers, the dynamic and kinematic contact conditions of the problem are formulated. On the basis of exact solutions in transformations of the three-dimensional problem of the linear theory of viscoelasticity for a circular cylindrical three-layer shell, a mathematical model of its unsteady torsional vibrations has been developed. The proposed model includes the derivation of the general equations of torsional vibrations of the shell with respect to two auxiliary functions, which are the main parts of the torsional displacement of the points of some intermediate surface of the middle layer of the shell. Along with the equations, an algorithm for calculating was created that allows, based on the results of solving the equations of vibration, to unambiguously determine the stress-strain state of the shell and its layers in their arbitrary sections.

The paper provides a detailed analysis of the methods for calculating the thin-walled structure stability under static and dynamic loads, and the results of well-known studies related to assessing the stability of thin-walled structures. The paper gives a methodology for assessing the thin-walled structure stability and the analysis of stability loss of rectangular plates beyond the elasticity of the material. The stability loss of rectangular plates beyond the elastic limit of the material is investigated in the paper. A formula is proposed for determining the longitudinal forces in a plate under a state of infinitely small bending. An analytical formula is given to assess stability for the case of a hinged supported rectangular plate compressed in two directions beyond the elastic limit at various widths (b)-thickness (h) ratios of the plate. The proposed diagram of the plate material strain is in good agreement with the Berlin – Dahlem experimental diagram. It was stated that under linear hardening of the material, a square plate of flexibility b/h ≥ 20, loses its stability within the yield strength. Beyond the yield strength, flexibility b/h < 5 corresponds to stability loss.