scholarly journals Investigation of the interaction of two parallel shifted cracks in plate bending adjusted for their closure

2019 ◽  
Vol 46 (2) ◽  
pp. 147-155
Author(s):  
Taras Dalyak
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Relative Position ◽  
Singular Integral Equations ◽  
Plate Bending ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Smooth Contact ◽  
Dimensional Statement

The problem of interaction of two parallel shifted cracks in plate bending is considered. The cracks closure has been investigated in the classical two-dimensional statement, using the model of smooth contact along a line. The influence of the relative position of cracks and of the contact of their edges on the forces and moment intensity factors has been studied by the singular integral equations method.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials

1984 ◽  
Vol 51 (4) ◽  
pp. 780-786 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Mathematical Problem ◽  
Stress Singularity ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Intensity Factors

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.

Stress Analysis for a Double Lap Joint

1975 ◽  
Vol 42 (2) ◽  
pp. 353-357 ◽  
Author(s):  
L. M. Keer ◽  
K. Chantaramungkorn
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Lap Joint ◽  
Intensity Factors

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.

scholarly journals POLYNOMIAL SPLINE COLLOCATION METHOD FOR NONLINEAR TWO‐DIMENSIONAL WEAKLY SINGULAR INTEGRAL EQUATIONS

1997 ◽  
Vol 2 (1) ◽  
pp. 122-129 ◽  
Author(s):  
Arvet Pedas
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Polynomial Spline ◽  
Two Dimensional ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

„Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations" Mathematical Modelling Analysis, 2(1), p. 122-129

scholarly journals ON SOLUTION OF AMPLITUDE-PHASE PROBLEM

2018 ◽  
pp. 64-68 ◽  
Author(s):  
I. V. Boykov ◽  
Ya V. Zelina
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integrals ◽  
Singular Integral Equations ◽  
Quadrature Formulas ◽  
Two Dimensional ◽  
Phase Problem ◽  
The Fourier Transform ◽  
The Hilbert Transform ◽  
Unconventional Method

The paper describes an unconventional method of solving the amplitude-phase problem. The main properties of the Hilbert transform in the discrete and continual cases for one-dimensional and two-dimensional mappings are considered. These transformations are widely used to solve amplitude-phase problem. A numerical method for solving of two-dimensional amplitudephase problem is proposed. Preliminary information about the zeros of the Fourier transform of the initial signal is not required for this method. The method is based on the apparatus of nonlinear singular integral equations. Computational schemes for solving the corresponding nonlinear singular integral equations are developed. An algorithm for finding initial values for realization of iterative methods is proposed. Quadrature formulas of the calculation of singular integrals are proposed.

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