Boundary integral equation for notch problems in an elastic half-plane based on Green’s function method

Normal incidence of the plane time-harmonic longitudinal wave on double-periodic array of coplanar elliptical cracks, which are located in 3D infinite elastic space is considered. Corresponding symmetric wave scattering problem is reduced to a boundary integral equation for the displacement jump across the crack surfaces in a unit cell by means of periodic Green’s function, which is presented in the form of Fourier integrals. A regularization technique for this Green’s function involving special lattice sums in closed forms is adopted, which allows its effective calculation in a wide range of wave numbers. The boundary integral equation is correctly solved by using the mapping method. The frequency dependencies of mode-I stress intensity factor in the vicinity of the crack front points for periodic distances in the system of elliptical cracks are revealed.

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Computer programmes for the numerical Green’s function boundary integral equation method

Hypersingular Integral Equations in Fracture Analysis ◽

10.1533/9780857094803.173 ◽

2013 ◽

pp. 173-184

Keyword(s):

Integral Equation ◽

Green’S Function ◽

Boundary Integral Equation ◽

Green's Function ◽

Integral Equation Method ◽

Boundary Integral ◽

Boundary Integral Equation Method ◽

Equation Method

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A recursive Green's function method for boundary integral analysis of inhomogeneous domains

IEEE Transactions on Antennas and Propagation ◽

10.1109/8.743817 ◽

1998 ◽

Vol 46 (12) ◽

pp. 1810-1816 ◽

Cited By ~ 9

Author(s):

M.A. Jensen ◽

J.D. Freeze

Keyword(s):

Green’S Function ◽

Green's Function ◽

Function Method ◽

Boundary Integral ◽

Green’S Function Method ◽

Integral Analysis

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Punch Problem for Planar Anisotropic Elastic Half-Plane

Journal of Mechanics ◽

10.1017/jmech.2011.26 ◽

2011 ◽

Vol 27 (2) ◽

pp. 215-226 ◽

Cited By ~ 3

Author(s):

R.-L. Lin

Keyword(s):

Integral Equation ◽

Green’S Function ◽

Half Plane ◽

Green's Function ◽

Boundary Integral ◽

Fredholm Integral Equations ◽

Surface Traction ◽

Rigid Punch ◽

Anisotropic Elastic ◽

Punch Problem

ABSTRACTThe two dimensional punch problem for planar anisotropic elastic half-plane is revisited using the Lekhnitskii's formulation with aid of the Fourier transform and boundary integral equation. Four different conditions of contact problem for the rigid punch are analyzed in this study. From the combination of surface Green's function of half-plane and Hooke's law of anisotropic material, a set of Fredholm integral equations are obtained for mixed boundary value problems. After solving the integral equation according to specified contact condition, the explicit distributions of surface traction under the punch are obtained in closed-form. From the surface traction and Green's function of anisotropic half-plane, the full-field solutions of stresses are constructed. Numerical calculations of surface traction under the rigid punch are presented base on the analysis and are discussed in detail.

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