Cracking in a circular disk under mixed boundary conditions

Мирсалимов, В. М.; Kalantarly, Nailya

doi:10.1007/s00707-014-1292-0

Cited by 8 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By means of change of a variable, we reduce all integration intervals to one segment [21,1]. For that we put t = l n t, x = l n h, t j j\l n , x j j\l n :…”

Section: Algebraization Of Main Resolving Equationsmentioning

confidence: 99%

“…Here, the functions u n (t) are Holder continuous on the segment [21,1] and the functions u n (t) are replaced by an interpolational polynomial constructed by Chebyshev nodes. By means of Gauss-Chebyshev-type quadrature formulas [32][33][34], the system of integral equations (34) under conditions ( 35) is reduced to the system of N × M algebraic equations with respect to the unknowns…”

Section: Algebraization Of Main Resolving Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Crack nucleation in rod-type nuclear fuel pellet

Мирсалимов

2018

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

A plane problem of fracture mechanics on crack nucleation in a rod-type nuclear fuel pellet is considered. Nuclear reactor fuel pellets in operation may be damaged in various ways; in particular, crack nucleation. We consider a problem for the case of a heat-releasing fuel pellet with cladding: as the heat release intensity increases, zones of heightened stress are formed in the nuclear fuel pellet. The heightened stress will promote the appearance of prefracture bands that are simulated as zones of weakened interparticle bonds of the material. Interaction of prefracture zone faces is simulated by placing bonds between faces that have a specified deformation pattern. The problem of equilibrium of a fuel pellet with prefracture zones is reduced to the solution of a system of singular integral equations. An analysis of the ultimate state of the zone of weakened interparticle bonds of the material is realized on the basis of the criterion of critical opening of prefracture zone faces.

show abstract

“…By means of change of a variable, we reduce all integration intervals to one segment [21,1]. For that we put t = l n t, x = l n h, t j j\l n , x j j\l n :…”

Section: Algebraization Of Main Resolving Equationsmentioning

confidence: 99%

Section: Algebraization Of Main Resolving Equationsmentioning

confidence: 99%

Crack nucleation in rod-type nuclear fuel pellet

Мирсалимов

2018

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…Compared to the Airy stress function, the complex variable method [7,8] turns to a pair of complex potentials, which are related to the displacement and stress components in close form. By combining with conformal mapping and analytic continuation principle, the complex variable method exhibits powerful ability and flexibility to solve mixed boundary value problems in elastic regions of complicated shapes, especially for simply-connected regions [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus

Lin

Chen

Xian-hai

2023

Preprint

View full text Add to dashboard Cite

This paper provides two parallel generalized solutions on a fundamental mixed boundary value problem that a unit annulus is subjected to a partially fixed outer periphery and an arbitrary traction acting along the inner periphery by using the complex variable method. The mixed problem is transformed into two parallel Riemann-Hilbert problems with respective sets of different mathematically rigorous boundary conditions, which are solved by successive approximation method with the Lanczos filtering technique to obtain numerically equivalent stress and displacement results. Four typical numerical cases coded by FORTRAN are carried out and compared to the same cases performed on ABAQUS to validate these two parallel solutions. Based on the case results, the detailed reasons of numerically equivalence between these two parallel solutions are analytically elaborated and several insights of the application of the complex variable method are revealed.

show abstract

Cracking in heat-releasing perforated material

Мирсалимов

2016

Acta Mech

View full text Add to dashboard Cite

Cracking in a circular disk under mixed boundary conditions

Cited by 8 publications

References 10 publications

Crack nucleation in rod-type nuclear fuel pellet

Crack nucleation in rod-type nuclear fuel pellet

On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus

Cracking in heat-releasing perforated material

Contact Info

Product

Resources

About