The Plane Solution for the Elastic Contact Problem of a Semi-Infinite Strip and Half Plane

1976 ◽  
Vol 43 (4) ◽  
pp. 603-607 ◽  
Author(s):  
G. G. Adams ◽  
D. B. Bogy
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Numerical Solutions ◽  
Stress Singularity ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Elastic Contact ◽  
Shearing Stress ◽  
Elastic Materials ◽  
Plane Solution

The solution is obtained for both smooth and bonded contact between the strip and half plane of different elastic materials. First, the problems are reduced to singular integral equations of the second kind. Then the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are obtained. Interface normal and shearing stress are exhibited graphically for several material combinations.

The Plane Symmetric Contact Problem for Dissimilar Elastic Semi-Infinite Strips of Different Widths

1977 ◽  
Vol 44 (4) ◽  
pp. 604-610 ◽  
Author(s):  
G. G. Adams ◽  
D. B. Bogy
Keyword(s):  
Boundary Condition ◽  
Integral Equations ◽  
Numerical Solutions ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Stress Singularity ◽  
Singular Integral Equations ◽  
Width Ratio ◽  
Elastic Materials ◽  
Plane Symmetric

The solution is obtained for both smooth and bonded contact between strips of different elastic materials and widths. First, the problems are reduced to singular integral equations which are unusual because of the mixed boundary condition on the end of the wider strip. With minor extensions of the usual methods the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are then obtained for various material combinations and width ratios. The results are compared to previous solutions in which the width ratio is either one or infinity.

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

Interaction of Three Interfacial Cracks between an Orthotropic Half-Plane Bonded to a Dissimilar Orthotropic Layer with Punch

2017 ◽  
Vol 72 (11) ◽  
pp. 1021-1029
Author(s):  
P.K. Mishra ◽  
P. Singh ◽  
S. Das
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Singular Integral Equations ◽  
Orthotropic Layer ◽  
Central Crack ◽  
Interfacial Cracks ◽  
Crack Shielding

AbstractThis article deals with the interactions between a central crack and a pair of outer cracks situated at the interface of an orthotropic elastic half-plane bonded to a dissimilar orthotropic layer with a punch. The problem is reduced to the solution of three simultaneous singular integral equations that are finally solved using Jacobi polynomials. The phenomena of crack shielding and crack amplification have been depicted through graphs for different particular cases.

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE FLAT PUNCH PROBLEM FOR AN ELASTIC HALF-PLANE

2009 ◽  
Vol 06 (04) ◽  
pp. 605-614
Author(s):  
Y. Z. CHEN ◽  
Z. X. WANG ◽  
X. Y. LIN
Keyword(s):  
Stress Distribution ◽  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Integral Equation Method ◽  
Angle Distribution ◽  
Flat Punch ◽  
Singular Stress ◽  
Punch Problem

When a flat punch is indented on elastic half-plane, the singular stress distribution at the vicinity of the punch corners is studied. The angle distribution for the stress components is also achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor is defined. The multiple punch problem can be considered as a superposition of many single punch problems. Taking the stress distribution under the punch base as the unknown function and the deformation under punch as the right-hand term, a set of the singular integral equations for the multiple punch problem can be achieved. After the singular integral equations are solved, the stress distributions under punches can be obtained. In addition, the exerting locations of the resultant forces under punches can also be determined. Two numerical examples with the calculated results are presented.

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.

Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space

1972 ◽  
Vol 39 (2) ◽  
pp. 527-534 ◽  
Author(s):  
J. E. Luco ◽  
R. A. Westmann
Keyword(s):  
Dynamic Response ◽  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Elastic Half Space ◽  
Vertical Shear ◽  
Fredholm Integral Equations ◽  
Interface Conditions ◽  
Rigid Footing

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.

Fractional calculus and Sinc methods

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Gerd Baumann ◽  
Frank Stenger
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Integral Equations ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Fractional Integrals ◽  
Sinc Methods ◽  
Weakly Singular Integral Equations ◽  
Fractional Differential

AbstractFractional integrals, fractional derivatives, fractional integral equations, and fractional differential equations are numerically solved by Sinc methods. Sinc methods are able to deal with singularities of the weakly singular integral equations of Riemann-Liouville and Caputo type. The convergence of the numerical method is numerically examined and shows exponential behavior. Different examples are used to demonstrate the effective derivation of numerical solutions for different types of fractional differential and integral equations, linear and non-linear ones. Equations of mixed ordinary and fractional derivatives, integro-differential equations are solved using Sinc methods. We demonstrate that the numerical calculation needed in fractional calculus can be gained with high accuracy using Sinc methods.

Singular Integral Equation Method for Interaction Between Elliptical Inclusions

1998 ◽  
Vol 65 (2) ◽  
pp. 310-319 ◽  
Author(s):  
Nao-Aki Noda ◽  
Tadatoshi Matsuo
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Singular Integral ◽  
Body Force ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Integral Equation Method ◽  
The Body ◽  
Force Density ◽  
Cauchy Type

This paper deals with numerical solutions of singular integral equations in interaction problems of elliptical inclusions under general loading conditions. The stress and displacement fields due to a point force in infinite plates are used as fundamental solutions. Then, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknowns are the body force densities distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. To determine the unknown body force densities to satisfy the boundary conditions, four auxiliary unknown functions are derived from each body force density. It is found that determining these four auxiliary functions in the range 0≦φk≦π/2 is equivalent to determining an original unknown density in the range 0≦φk≦2π. Then, these auxiliary unknowns are approximated by using fundamental densities and polynomials. Initially, the convergence of the results such as unknown densities and interface stresses are confirmed with increasing collocation points. Also, the accuracy is verified by examining the boundary conditions and relations between interface stresses and displacements. Randomly or regularly distributed elliptical inclusions can be treated by combining both solutions for remote tension and shear shown in this study.

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