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: 10.18698/2309-3684-2017-3-3848

The study introduces a method for calculating the load-bearing capacity of a smooth cylindrical shell, which has been under the action of axial and transverse loads for a long time. We assume that with prolonged loading, the shell material is subject to the phenomenon of creep, which in turn affects the load-bearing capacity of the shell. As a result, we obtained relations that made it possible to estimate this influence.

Dubrovin V.M., Semenov K.S. Modeling of load-bearing capacity of a smooth cylindrical shell under conditions of material creep .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 38-48

doi: 10.18698/2309-3684-2019-1-2742

A method for calculating the loads on a composite cylindrical shell, consisting of external and internal shells connected by a system of elastic transverse supports, is proposed. Between the shells is an elastic filler. The method takes into account the geometry and mechanical characteristics of the shells, the elastic characteristics of the transverse supports and the physico-mechanical properties of the material of the elastic aggregate. In solving the problem, it is assumed that the material of the elastic aggregate satisfies the basic relations of the theory of elasticity, and the elastic characteristics of the aggregate under dynamic loading correspond to the characteristics under static loading. This allows you to use the results to solve problems in both static and dynamic formulations. By choosing a different combination of characteristics of the shells and the elastic filler, it is possible to provide the most favorable loading conditions for both the inner and outer shells, depending on the statement of the problem. As an example, the loads on the inner shell were studied depending on the characteristics of the outer shell and the specific stiffness of the elastic filler. Similarly, estimates of the loads acting on the outer shell can be obtained.

Дубровин В.М., Семёнов К.С. Моделирование нагрузок на составную цилин-дрическую оболочку с упругим заполнителем. Математическое моделирование и численные методы, 2019, № 1, с. 27–42.

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: 10.18698/2309-3684-2018-3-3848

We consider the technical system, comprising a plurality of structural elements operating under the influence of a complex external loads. For such a system, we proposed a method for calculating the reliability criterion for the occurrence of one or more of the limit states design elements.

Дубровин В.М., Семёнов К.С. Моделирование квазистатической надежности конструкции технической системы. Математическое моделирование и численные методы, 2018, № 3, с. 38–48.

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

doi: 10.18698/2309-3684-2018-2-3246

Cylindrical shell, which is under the influence of considerable loads for a long time, can lose the ability to withstand the level of these loads, as its carrying capacity decreases. This is due to the fact that the shell material is subject to the creep phenomenon. As studies [1-3] show, creep is noticeably manifested even at normal temperature and stresses, much lower than the yield point of the shell material. Experimental and theoretical work on the stability of shells show [4-5] that the main reason for reducing the critical load for real shells in comparison with ideal shells is the initial design imperfections. Therefore, it is to be expected that additional deflections that arise as a result of creep deformation have a significant effect on the critical load (bearing capacity) of the shell. A method is proposed for calculating the load-bearing capacity of a cylindrical shell reinforced by a longitudinal (stringers) and a final (frame) power set under the action of axial and transverse loads, as well as internal excess pressure. As an example, a shell is considered, the material of which is an aluminum-magnesium alloy AMg6-M and AMg6-H. The dependence of the bearing capacity on the operating time is obtained.

Дубровин В.М., Семенов К.С. Моделирование несущей способности подкрепленной силовым набором цилиндрической оболочки в условиях ползучести материала. Математическое моделирование и численные методы, 2018, № 2, с. 32–46.