Stress in a Semi-infinite Strip under the Forces applied at Its End

Yamashida, Takashi

doi:10.1299/kikai1938.19.79_49

Cited by 3 publications

(3 citation statements)

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“…The superposition method of semi-plane and infinite strip was applied in [2] to achieve solution for the semi-strip. The approach based on the construction of the stress function as the combination of the Fouriers integrals and the series was used in [3], [4], [5]. The reducing of the problem to the Fredholm's integral equation of the first kind was applied in [6].…”

Section: Introductionmentioning

confidence: 99%

The plane mixed problem for an elastic semi-strip under different load types at its short edge

Menshykov¹,

Reut

et al. 2018

International Journal of Mechanical Sciences

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The mixed problem for the fixed semi-strip is investigated in this article for the three cases of the applied mechanical load. The solution of the boundary problem is reduced to the solution of the singular integral equation (SIE) with regard to the unknown displacements derivative. Three cases of SIE are investigated: when the mechanical load is applied on the center of the semi-strips edge, when the mechanical load is distributed near the left lateral side and when the mechanical load is distributed on the whole semi-strip's edge. In the first case SIE is solved by the using of the orthogonal polynomials method. In the second and third cases the characteristical equations to SIE are constructed, and the SIE are solved with the help of the generalized method. The stress state of the semi-strip is investigated for the three cases. Keywords semi-strip • singular integral equation • fixed singularity • orthogonal polynomials method • generalized method

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Section: Introductionmentioning

confidence: 99%

The plane mixed problem for an elastic semi-strip under different load types at its short edge

Menshykov¹,

Reut

et al. 2018

International Journal of Mechanical Sciences

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“…The reducing of the problem to the Fredholm's integral equation of the first kind was used in [1] for estimation of the symmetrically loaded semi-strip fixed by the short edge. Another approach based on the construction of the stress function as the combination of the Fourier's integrals and the series was used in [2,3]. The problems for a semi-strip considered in [4,5] were reduced to the singular integral equations which were solved numerically, it leaded to the solving T of an infinity system of the algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

On the stress investigation at the edges of the fixed elastic semi-strip

Vaysfeld¹,

Kryvyi²,

Zhuravlova³

2016

Frattura Ed Integrità Strutturale

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The stress state of the elastic fixed semi-strip with the regarding of the singularities at its edge is investigated in the article. The initial boundary problem is reduced to a vector boundary problem in the transformation's domain by the use of integral Fourier transformation. The one-dimensional vector boundary problem is solved exactly with the help of matrix differential calculations and Green's matrix apparatus. The problem's solving was focused at the solving of the singular integral equation (SIE) with the two fixed singularities at the ends of the integration's interval. The symbol of SIE was constructed and the generalized method of the SIE solving was applied. The stress' distributions of the semi-strip are investigated.

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“…Often, the stress function is performed as combination of Fourier integrals and series. An analogous approach is used in [12][13][14][15] for the problems on a semi-strip. As a result, the authors obtain an infinite system of algebraic equations (the question of its regularity they leave without research).…”

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confidence: 99%

On one new approach to the solving of an elasticity mixed plane problem for the semi-strip

Vaysfeld

Zhuravlova

2015

Acta Mech

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It is well known that the main approaches of the analytical solving of the elasticity mixed plane problems for a semi-strip are based on the different representations of the equilibrium equations' solutions: the representations through the harmonic and by harmonic functions, through the stress function, Fadle-Papkovich functions and so on. The main shortcoming of these approaches is connected with the fact that to obtain the expression for the real mechanical characteristics, one should execute additional operations, not always simple ones. The approach that is proposed in this paper allows the direct solution of the equilibrium equations. With the help of the matrix integral transformation method applied directly to the equilibrium equations, the initial boundary problem is reduced to a vector boundary problem in the transformation's domain. The use of matrix differential calculations and Green's matrix function leads to the exact vector solution of the problem. Green's matrix function is constructed in the form of a bilinear representation which simplifies the calculations. The method is demonstrated by the solving of the thermoelastic problem for the semi-strip. The zones and conditions of the strain stress occurrence on the semi-strip's lateral sides, important to engineering applications, are investigated.

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Stress in a Semi-infinite Strip under the Forces applied at Its End

Cited by 3 publications

References 0 publications

The plane mixed problem for an elastic semi-strip under different load types at its short edge

The plane mixed problem for an elastic semi-strip under different load types at its short edge

On the stress investigation at the edges of the fixed elastic semi-strip

On one new approach to the solving of an elasticity mixed plane problem for the semi-strip

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