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.

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.

scholarly journals FAST SOLVERS OF WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND

2018 ◽  
Vol 23 (4) ◽  
pp. 639-664 ◽  
Author(s):  
Sumaira Rehman ◽  
Arvet Pedas ◽  
Gennadi Vainikko
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Fredholm Integral Equations ◽  
Free Term ◽  
Fast Solvers ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
Derivatives Of ◽  
Smooth Data

We discuss the bounds of fast solving weakly singular Fredholm integral equations of the second kind with a possible diagonal singularity of the kernel and certain boundary singularities of the derivatives of the free term when the information about the smooth coefficient functions in the kernel and about the free term is restricted to a given number of sample values. In this situation, a fast/quasifast solver is constructed. Thus the complexity of weakly singular integral equations occurs to be close to that of equations with smooth data without singularities. Our construction of fast/quasifast solvers is based on the periodization of the problem.

scholarly journals STABILITY OF SYSTEMS OF SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNEL

T-Comm ◽  
2020 ◽  
Vol 14 (9) ◽  
pp. 48-55
Author(s):  
Aleksey V. Yudenkov ◽  
◽  
Aleksandr M. Volodchenkov ◽  
Liliya P. Rimskaya ◽  
◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
System Stability ◽  
Strength Analysis ◽  
Fredholm Integral Equations ◽  
Cauchy Integral ◽  
Mean Square Stability ◽  
The Absolute

Singular Cauchy integral equations have been widely used for mathematical simulation of the actual physical and technical systems. They are considered universal at every level of simulation beginning with quantum field theory and up to strength analysis of the underground constructions. Therefore investigating system stability of such models under perturbation of their absolute terms and coefficients appears an urgent scientific task. The aim of the study is to show various aspects of stability of singular Cauchy integral sets of equations which are generalizing simulation models of the primal problems of the elasticity theory for homogeneous isotropic bodies. The methods of study are based on the properties of the Cauchy singular integral, on the general theory of Fredholm operators. When in use, systems of the singular integral equations are reduced to a set of Fredholm integral equations of the second kind and a set of the boundary value problems for analytic functions. The key results of the study are the following: development of the general determination method of the system index for singular integral equations, proof of the system stability against perturbations of the absolute terms of the set. Against perturbations of the boundary coefficients, the singular integral system is unstable. Demonstration of the stability of the singular integral Cauchy sets generalizing primal problems of the elasticity theory appears a significantly new result. The research of singular integral equations sets has been performed conducted on the space of functions satisfying the Holder condition. However the main research results prove to be true if we operate random functions converting in mean square. Stability of singular integral equations sets against perturbations of the absolute terms lays a foundation for calculus of approximations in real world tasks of defining the built-in stress of an elastic complex body.

scholarly journals Toeplitz operators and Wiener-Hopf factorisation: an introduction

2017 ◽  
Vol 4 (1) ◽  
pp. 130-145 ◽  
Author(s):  
M. Cristina Câmara
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Toeplitz Operators ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Necessary And Sufficient Conditions ◽  
Upper Half Plane ◽  
Necessary And Sufficient

Abstract Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)

The Singularity at the Apex of a Bonded Wedge-Shaped Stamp

1979 ◽  
Vol 46 (3) ◽  
pp. 577-580 ◽  
Author(s):  
K. S. Parihar ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Singular Integral Equations ◽  
Elastic Half Space

The problem of determining the singularity at the apex of a rigid wedge bonded to an elastic half space is formulated by considerations of Green’s functions for the loaded half space. The eigenvalue problem is reduced to finding the solution of a coupled pair of singular integral equations. A numerical solution for small wedge angles is given.

scholarly journals Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

2020 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Youn-Sha Chan ◽  
Edward Athaide ◽  
Kathryn Belcher ◽  
Ryan Kelly
Keyword(s):  
Integral Equations ◽  
Functionally Graded Materials ◽  
Singular Integral ◽  
Mixed Mode ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Mixed Mode Fracture ◽  
Graded Materials

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

scholarly journals PRODUCT QUASI-INTERPOLATION IN LOGARITHMICALLY SINGULAR INTEGRAL EQUATIONS

2012 ◽  
Vol 17 (5) ◽  
pp. 696-714 ◽  
Author(s):  
Eero Vainikko ◽  
Gennadi Vainikko
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Numerical Experiments ◽  
Singular Integral Equations ◽  
Fredholm Integral Equations ◽  
Order Method ◽  
Boundary Behaviour ◽  
Product Integration ◽  
High Order Method ◽  
Change Of Variables

A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna
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