Criteria for homothetic transformation and rotation for a hole in plane elasticity

In this paper, an arbitrary hole in infinite plane elasticity subjected to remote stresses is considered. We investigate the effect of the homothetic transformation and rotation to the considered hole using the governing equations for the displacement. The relation between stresses are obtained

General analytical solution for stress intensity factor of a hypocycloid hole with many cusps in an infinite plate.

In this article, the problem for the determination of the displacement functions and the stress intensity factors (SIFs) around a boundary of a hypocycloid hole with cusps in an infinite elastic plate subject to normal and shear stresses are presented. A hole with cusps (hypocycloid) is mapped onto a unit circle and the modified complex potential is used for solving the relevant boundary value problems. An analytical solution for the SIF of a hypocycloid hole is obtained. For a special case, our results agree with others

Analysis of stress in half plane elasticity with vibration load

In this paper, a vibration pressure is applied on the edge of half plane, and using the separation method the relevant boundary value problem is solved and the Airy’s function is obtained. Three kinds of stresses are obtained from the Airy’s function. These results are valid for the load functions in the class of piecewise functions

Approximating the singular integrals of Cauchy type with weight function on the interval.

It is known that the solutions of characteristic singular integral equations (SIEs) are expressed in terms of singular integrals of Cauchy type with weight functions w (x) = (1 + x)ν (1 - x)μ, where ν = ± frac(1, 2), μ = ± frac(1, 2). New quadrature formulas (QFs) are presented to approximate the singular integrals (SIs) of Cauchy type for all solutions of characteristic SIE on the interval [- 1, 1]. Linear spline interpolation, modified discrete vortex method and product quadrature rule are utilized to construct the QFs. Estimation of errors are obtained in the classes of functions Hα ([- 1, 1], A) and C1 ([- 1, 1]). It is found that the numerical results are very stable even for the cases of semi-bounded and unbounded solutions of singular integral equation of the first kind

Hypersingular integral equation for multiple curved cracks problem in plane elasticity.

The complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations. These hypersingular integral equations are solved numerically for the unknown function, which are later used to find the stress intensity factor, SIF, for the problem considered. Numerical examples for double circular arc cracks are presented

Interaction between inclined and curved cracks problem in plane elasticity

Interaction between inclined and curved cracks are studied and the hypersingular integral equations for the problem in plane elasticity are obtained using the complex variable functions method. The curved length coordinate technique and a suitable quadrature rule are used to solve the algebraic equations numerically for the unknown function, which are later used to find the stress intensity factor (SIF)

Formulation for multiple curved and kinked cracks problems in antiplane elasticity

Formulation in term of hypersingular integral equation for multiple curved and kinked cracks in antiplane elasticity are obtained using the complex variable function. The curved length coordinate technique and a suitable numerical scheme for such an integral are developed to solve numerically for the unknown function, which are later used to find the stress intensity factor, SIF

Effect of mechanical loadings on two unequal slanted cracks length in bi-materials plate

Although a lot of crack problems in bi-materials plate were previously treated, few solutions are available under mechanical loadings, arbitrary crack lengths and material combinations. In this paper the dimensionless stress intensity factors (SIFs) of two slanted cracks in the upper plate of bi-materials are considered under mechanical loadings with varying the crack length and material combinations systematically. In order to calculate the dimensionless SIFs accurately, the hypersingular integral equations (HSIEs) was formulated by using the modified complex potentials (MCP) function. The details numerical results of the dimensionless SIFs are given in tabular form and graphical presentations. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. Our results are described with clarifying the effect of the mechanical loadings, bi-elastic constant ratio and element size of cracks on the dimensionless SIFs

Analytical solutions of characteristic singular integral equations in the class of rational functions

We construct four kinds of solution of Cauchy type characteristic singular integral equations using four kinds of basis, when the known function is rational. We consider the denominator of this rational function has only simple roots. It is found that for this kinds of rational function, the solutions are irrational

Analytical-approximate solution of Abel integral equations

It is known that Abel integral equation has a solution in a closed form, with a removable singularity.The presence of Volterra integrals with weak singularity is not always integrable for continuous differentiable class of functions.In this work we propose an analytical approximate method for the solution of Abel integral equations. We showed that the proposed method is exact for the known function in the cases of polynomials and irrational function of the form f(t)tα+1(a0+a1t+···+antn),0<α<1.For the derivation of the proposed method we expand the known function to the Taylor series around a singular points. Substituting this expansion into the solution of Abel equation we could remove the singularity. All evaluations of the integrals are calculated analytically. The obtained solution is a series that is uniformly convergence to the exact solution