Defining Relations in Mechanics of Cross-Ply Fiber Reinforced Plastics Under Short-Term and Long-Term Monoaxial Load

Паймушин, В. Н.; Kayumov, R. A.; Kholmogorov, S. A.; Shishkin, V. M.

doi:10.3103/s1066369x18060087

Cited by 8 publications

(8 citation statements)

References 2 publications

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“…where d[g], Tf are defined in (6). The solution of the problem ( 8) is given by the formula [27, p. 253…”

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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“…where d[g], Tf are defined in (6). The solution of the problem ( 8) is given by the formula [27, p. 253…”

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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“…A generalized solution of the problem A is the vector of generalized displacements a = (w1, w2, w3, Ψ1, Ψ2) ∈ Wp (2) (Ω), p > 2, almost everywhere satisfying the system (6) and pointwise boundary conditions (2), ( 7)-( 9). Let's consider the system of the first two equations in (6), in which the deflection is assumed to be fixed temporarily. The general solution of the system (1) has the form [18]:…”

Section: Definitionmentioning

confidence: 99%

“…Taking into account the solution of the system (6) with respect to tangential displacements and angles of rotation, the conditions (2), ( 7), ( 8), integral representations ( 13), ( 14) are developed for wj, Ψj (j = 1.2). Now let us examine the third equation in (6). Before proceeding to it, we express the deflection w3, and its derivatives through υj (j = 1.2).…”

Section: Definitionmentioning

confidence: 99%

“…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%

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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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