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

Vaysfeld, Natalya; Kryvyi, О. F.; Zhuravlova, Zinaida

doi:10.3221/igf-esis.38.01

Cited by 4 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution of the vector boundary problem was obtained in the form [27,28] A Green's matrix function [29]. The expression (10) can be rewritten in scalar form …”

Section: General Solving Scheme For the Semi-strip Stress State Estimmentioning

confidence: 99%

“…In this article the misprint in [28] for the coefficients , 1,2,3 The generalized method developed in [28] was applied to solve the SSIE (13). According to it the function      is searched in the form…”

Section: Solving Of the Sie System For The Two Casesmentioning

confidence: 99%

“…In the first case, the first equation in (13) has only one fixed singularity. Similarly to the previous case the unknown function      is searched in the form [28].…”

Section: Solving Of the Sie System For The Two Casesmentioning

confidence: 99%

“…Thus it was possible to find directly the real mechanical characteristics without using any auxiliary functions. This approach was shown first in [28] to solve the problem of the semi-strip without the existence of a crack.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Elastic crack-tip stress field in a semi-strip

Reut

Vaysfeld

Zhuravlova

2018

Frattura Ed Integrità Strutturale

View full text Add to dashboard Cite

ABSTRACT. In this article the plain elasticity problem for a semi-strip with a transverse crack is investigated in different cases of boundary conditions at the semi-strip's end. Unlike many works dedicated to this subject, the fixed singularities in the singular integral equation's kernel are considered. The integral transformations' method is applied by a generalized scheme to reduce the initial problem to a one-dimensional problem. The one-dimensional problem is formulated as a vector boundary value problem which is solved with the help of matrix differential calculations and Green's matrix apparatus. The problem is reduced to solve the system of three singular integral equations. Depending on the conditions given on the short edge of the semistrip, the obtained singular integral equation can have one or two fixed singularities. A special method is applied to solve this equation in regard to the singularities existence. Hence, the system of the singular integral equations (SSIE) is solved with the help of the generalized method. The stress intensity factors (SIF) are investigated for different lengths of crack. The novelty of this work is the application of a new approach allowing the consideration of fixed singularities in the problem of a transverse crack in the elastic semi-strip. The comparison of the accuracy of numerical results during the use of different approaches to solve the SSIE is calculated.

show abstract

“…The solution of the vector boundary problem was obtained in the form [27,28] A Green's matrix function [29]. The expression (10) can be rewritten in scalar form …”

Section: General Solving Scheme For the Semi-strip Stress State Estimmentioning

confidence: 99%

Section: Solving Of the Sie System For The Two Casesmentioning

confidence: 99%

“…In the first case, the first equation in (13) has only one fixed singularity. Similarly to the previous case the unknown function      is searched in the form [28].…”

Section: Solving Of the Sie System For The Two Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Elastic crack-tip stress field in a semi-strip

Reut

Vaysfeld

Zhuravlova

2018

Frattura Ed Integrità Strutturale

View full text Add to dashboard Cite

show abstract

“…The generalized method of SIE solving [46], [52] was applied for the solving of the equation (15). According to it the unknown functionχ(ξ) is searched in the following form [53]…”

mentioning

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

View full text Add to dashboard Cite

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

show abstract