Postbuckling Behavior of Compressed Rods in an Elastic Medium

Kayumov, R. A.

doi:10.3103/s0025654417050120

Cited by 19 publications

(7 citation statements)

References 6 publications

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“…The expressions of the functions w1, w2 from ( 6) are introduced into (3). Taking into account the ratios: 1(t) defined in (5). Through Sd[1] + (t) they denote the limit of the function Sd[1](z) at z → t  Г from inside the region .…”

Section: Definitionmentioning

confidence: 99%

“…Currently, there are a large number of works devoted to the strength of thin-walled shell structures, taking into account the geometric and/or physical nonlinearity [1][2][3][4][5][6][7][8][9]. This is due to the widespread use of elastic thin-walled shell structures in aviation, space technology, shipbuilding, mechanical engineering and construction.…”

Section: Introductionmentioning

confidence: 99%

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Stress state of hinged supported thin-wall elastic structures

Kharasova

Timergaliev

2021

E3S Web Conf.

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The paper studies the stress-strain state of flat elastic isotropic thin-walled shell structures in the framework of the S. P. Timoshenko shear model with pivotally supported edges. The stress-strain state of shell structures is described by a system of five second-order nonlinear partial differential equations under given static boundary conditions with respect to generalized displacements. The system of equations under study is linear in terms of tangential displacements, rotation angles, and nonlinear in terms of normal displacement. To find a solution to the system that satisfies the given static boundary conditions, integral representations for generalized displacements containing arbitrary holomorphic functions are used. Finding holomorphic functions is one of the main and difficult points in the proposed study. The integral representations constructed in this way allow us to reduce the original problem to a single nonlinear operator equation with respect to the deflection, the solvability of which is established using the principle of compressed maps.

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Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stress state of hinged supported thin-wall elastic structures

Kharasova

Timergaliev

2021

E3S Web Conf.

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“…Therefore, a rigorous study of boundary value problem solvability, the proof of existence theorems and the development of the methods for finding solutions are very urgent problems in the mathematical theory of elasticity. Currently, there is a large number of works devoted to the strength of thin-walled shell structures, taking into account the geometric and/or physical nonlinearity [1][2][3][4][5][6][7][8][9]. This is due to the widespread use of elastic thin-walled shell structures in aviation, space technology, shipbuilding, mechanical engineering and construction.…”

Section: Introductionmentioning

confidence: 99%

Strength of thin-walled elastic building structures

Kharasova

2021

E3S Web Conf.

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The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.

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“…Such systems and objects include irrigation, watering, drainage and drainage systems, tanks, bunkers, storage, silos and other structures, the need for which will only grow At the same time, considerations of material and resource conservation necessitate the development of modern computing technologies to determine the strength parameters of the aforementioned systems and AIC facilities. Such technologies include numerical methods for determining the stress-strain state (SSS) of systems and objects [1][2][3][4][5][6][7][8][9], in particular, the finite element method (FEM) [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Application of finite elements of various dimensions in strength calculations of thin-wall constructions of agro-industrial complex

et al. 2020

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The article presents a comparative analysis of the effectiveness of the use of finite elements of various dimensions in the study of the stress-strain state (SSS) of objects of the agro-industrial complex (AIC). To determine the strength parameters of the AIC objects, which can be attributed to the class of thinwalled, it is proposed to use a two-dimensional finite element in the form of a fragment of the middle surface of a triangular shape with nodes at its vertices. To improve the compatibility of a two-dimensional finite element at the boundaries of adjacent elements, it is proposed to use the Lagrange multipliers introduced in additional nodes located in the middle of the sides of the triangular fragment as additional unknowns. It is proposed to use a three-dimensional finite element in the form of a prism with triangular bases to study the SSS of agricultural objects of medium thickness and thick-walled. To improve the compatibility of the prismatic element, Lagrange multipliers in the middle of the sides of the upper and lower bases are also used. On the example of calculating a fragment of a cylindrical pipeline rigidly clamped at the ends loaded with internal pressure, the effectiveness of the developed two-dimensional and three-dimensional finite elements with Lagrange multipliers was proved. The validity of the use of a twodimensional element for researching the SSS of agricultural objects belonging to the class of thin-walled was proved.

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Postbuckling Behavior of Compressed Rods in an Elastic Medium

Cited by 19 publications

References 6 publications

Stress state of hinged supported thin-wall elastic structures

Stress state of hinged supported thin-wall elastic structures

Strength of thin-walled elastic building structures

Application of finite elements of various dimensions in strength calculations of thin-wall constructions of agro-industrial complex

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