and Computational Methods

doi: 10.18698/2309-3684-2017-2-2838

The article presents a method for computing loads (such as strain or torque) on a compound shell consisting of elastically linked external and internal shells for the case when the external shell is subjected to transverse loading (bending moment, shear forces and distributed inertial loads). To demonstrate the application of our method, we investigated the effect the rigidity properties of the external shell have on the internal shell loading.

Dubrovin V.M., Butina T.A. Modeling loads on compound elastic shells by means of the initial approximation method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 28-38

doi: 10.18698/2309-3684-2019-2-314

One of the main properties of structural materials is creep. The prob-lem of determining the stress-strain state of axisymmetrically loaded shells of rotation at creep is considered

Бутина Т.А., Дубровин В.М. Моделирование напряженно-деформированного состояния оболочек вращения в условиях ползучести материала. Математическое моделирование и численные методы, 2019, № 2, с. 3–14.

doi: 10.18698/2309-3684-2015-2-4657

The article describes a method for calculating the dynamic stability of cylindrical shell under axial compressive time-varying load. The case of linearly varying load was con-sidered as an example.

Dubrovin V., Butina T. Modeling of the dynamic stability of a cylindrical shell under the axial compressive load. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 46-57

doi: 10.18698/2309-3684-2015-4-3852

The objective of this research is to examine the shock wave with cylindrical shell and to propose a method for calculating its dynamic stability under axial compressive timevarying load. For weak shock waves we conducted comparative analysis of the exact solution and the existing approximate solutions. We evaluated the wave radiation effect after the shell deformation. The case of linearly varying load was considered as an example.

Dubrovin V., Butina T., Polyakova N. Modeling of the process of interaction of the shock wave with cylindrical shell considering wave radiation effect. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 38-52

doi: 10.18698/2309-3684-2015-3-316

The article describes the method for calculating the stability of a rod under simultaneous action of axial force and torque, considering changing the torsion of the rod when it’s bent. The method is based on the use of the complete system of equations. The following cases are considered: end clamped rod, rod with a hinged support, the rod in the form of compressed and twisted console. Diagrams of dependence of the critical axial force versus the critical torque are obtained, i.e., the range of rod stability for the case of loading is determined.

Dubrovin V., Butina T. Modeling the stability of compressed and twisted rods in precise problem statement. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 3-16

doi: 10.18698/2309-3684-2022-1-97108

Under prolonged loading during operation, structures are subject to the phenomenon of creep, which can affect its performance. This influence depends on the load level, loading duration, operating conditions, design features, and type of material. All of these factors are taken into account in testing to obtain creep curves for a specific material and various environmental conditions corresponding to the operating conditions of the structure. The paper considers the problem of calculating the creep deformations of thin-walled cylindrical shells under the combined action of internal pressure and axial force. A model of the theory of flow with hardening under variable loading is considered. A numerical example of calculating the creep deformations of a cylindrical shell for an aluminum alloy is given

Бутина Т.А., Дубровин В.М. Моделирования ползучести тонкостенных оболочек при переменных нагружениях. Математическое моделирование и численные методы, 2022, № 1, с. 97–108.

doi: 10.18698/2309-3684-2016-3-2432

In this article we suggest a method for calculating the dynamic stability of a cylindrical shell with its axial compressive time-varying load, and cyclic axial load, which varies according to a certain law. As an example, we consider the axial load, changing linearly and the cyclic load, which varies according to the harmonic law. To show the cyclic load, we use Ince — Strutt diagram, defining the stable and unstable regions of the shell fluctuations.

Dubrovin V., Butina T. Simulation of dynamic stability of a cylindrical shell under cyclic axial impact. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 24-32