Solvability of One Nonlinear Boundary-value Problem for a System of Differential Equations of the Theory of Shallow Timoshenko-type Shells

Ahmadiev, Marat G.; Timergaliev, S. N.; Kharasovay, Lilya S.

doi:10.17516/1997-1397-2016-9-2-131-143

Cited by 4 publications

(10 citation statements)

References 7 publications

(17 reference statements)

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“…Let us calculate all the integrals on the right-hand side of the representation (19). Taking into account the operator T representation (6) and changing the variable t → φ(t), we obtain:…”

Section: Definitionmentioning

confidence: 99%

“…Then the first integral in the formula (19), taking into account (20) and the representation Tf from (6), is transformed to the form:…”

Section: Definitionmentioning

confidence: 99%

“…Let us transform the second integral in representation (19). First, for this we use (20), then we apply the formula (4.9) to the integral over the domain T [10, p. 29], and then -the last formula in (21), and calculate the integral:…”

Section: Definitionmentioning

confidence: 99%

“…Vorovich [10] and remained open until recently. To date, there are a number of works [18][19][20][21][22][23][24] devoted to the study of the stress-strain state in the framework of the Timoshenko shear model. The research in [18][19][20][21][22][23][24] is based on integral representations for generalized displacements containing arbitrary holomorphic functions that are found in such a way that the generalized displacements satisfy the given boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The first approach is based on the application of explicit representations of solutions to Riemann -Hilbert problems for holomorphic functions in the unit circle. Therefore, a flat region homeomorphic to the median surface of the shell is either assumed to be a unit circle from the very beginning [18][19][20], or conformally mapped to a unit circle [22], [24]. In the second approach, the theory of onedimensional singular integral equations is used to determine holomorphic functions [21], [23].…”

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%

“…Then the first integral in the formula (19), taking into account (20) and the representation Tf from (6), is transformed to the form:…”

Section: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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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On the question of the existence of solutions of one nonlinear boundary-value problem for the system of differential equations of the theory of shallow shells of Timoshenko type

Kharasova

2019

J. Phys.: Conf. Ser.

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Solvability of One Nonlinear Boundary-value Problem for a System of Differential Equations of the Theory of Shallow Timoshenko-type Shells

Cited by 4 publications

References 7 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

On the question of the existence of solutions of one nonlinear boundary-value problem for the system of differential equations of the theory of shallow shells of Timoshenko type

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