Non-Linear Singular Integral Equations

Mathematics and Mechanics of Solids

Ахундова

2018

Methods of fracture mechanics enable a new approach to the design of structures, ensuring prevention of crack development. The plane problem of mechanics of contact fracture for the hub of a friction pair during operation is studied. It is accepted that near the rough friction surface, the hub has a rectilinear crack. A criterion and a method for solving the inverse problem of the mechanics of contact fracture on definition of the function of displacements of external contour points of the hub of a friction pair with regard to temperature drop and inequalities of the contact surface in friction pair components is given. The found function of displacements of the external contour points of the hub provides an increase of the load-bearing capacity of the hub of a friction pair. The problem of prevention of the fracture of the hub of a friction pair with allowance for the real friction surface was first posed and then solved.

Section: Methods Of Solutionmentioning

confidence: 99%

Inverse problem of contact fracture mechanics for a hub of friction pair taking into account thermal stresses

Mathematics and Mechanics of Solids

Ахундова

2018

“…For constructing the solution of a singular integral equation (29), we use the method of the direct solution of such equations (Ladopoulos, 2000; Mirsalimov, 1987; Panasyuk, 1976). The singular integral equation (29), except for singularity in the Cauchy kernel, has also a fixed singularity at the point of the crack outcome to the surface of the circular hole.…”

Section: Methods Of Numerical Solution and Analysismentioning

confidence: 99%

“…Furthermore, it should be noted that some gain in convergence by the refined method is lost because of awkwardness of formulas for the coefficients of the system matrix. We will use another simplified method for the numerical solution of integral equations of type (29), whose efficiency was verified on numerous problems (Ladopoulos, 2000; Mirsalimov, 1984, 1987; Panasyuk, 1976). As in the heat-releasing material, if the stresses are restricted, then the solution of each singular integral equations (24) and (25) should be sought in the class of everywhere bounded functions (stresses).…”

Section: Methods Of Numerical Solution and Analysismentioning

confidence: 99%

See 1 more Smart Citation

Cracks with interfacial bonds in perforated heat-releasing nuclear fuel

International Journal of Damage Mechanics

2017

We consider a fracture mechanics problem for heat-releasing isotropic material weakened by a doubly periodic system of identical cylindrical channels of circular cross section. It is considered that as the intensity of heat release increases in the material, its elastic properties become temperature dependent and failure of the material occurs. It is accepted that rectilinear cracks with bonds between the faces at the end zones originate from the surface of holes. The condition of limit equilibrium of a crack with end zone is formulated with regard to criterion of ultimate stretching of material’s bonds.

“…The obtained nonlinear integral equations may be solved only numerically. For solving them, we use the collocation scheme . In the case when the law of deformation of bonds is nonlinear, for determining

q_{y}^{0}

and

q_{x y}^{0}

in the bonds we use an iteration scheme similar to the method of elastic solutions .…”

Section: Problem Solutionmentioning

confidence: 99%

Influence of local temperature field on propagation of a curvilinear crack with interfacial bonds

Mustafayev

2016

Z Angew Math Mech

Key words Curvilinear crack, thermoelastic stress field, bonds between the faces at the end zone, cohesive forces.Influence of thermal source on growth of a curved crack in stretchable plane with regard to cohesive forces at the crack's end zone, is studied. It is assumed that the areas of action of tractions adjoin to the crack's tips. For inhibiting the growth of curvilinear crack, on the path of its extension in the vicinity of the crack's end, we form a zone of compressible stresses by heating the domain S by thermal source to temperature T 0 . The goal of local change of temperature is to delay or retardation of the crack growth. A boundary value problem on equilibrium of a bridged curvilinear crack with interfacial bonds under the action of external tensile loads, induced thermoelastic temperature field and tractions in the bonds preventing its opening is reduced to the system of nonlinear singular integral equations with a Cauchy-type integral. Normal and tangential tractions in the bonds are found from the solution of this system. The condition of limit equilibrium of a curvilinear crack with interfacial bonds is formed with regard to criterion of limit stretching of the bonds.