On the solution of integral equations with strongly singular kernels
A. C. Kaya,Fazil Erdogan +1 more
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In this article, some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m,m greater than or equal 1.Abstract:
Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.read more
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Crack patterns in thin films
Z.Cedric Xia,John W. Hutchinson +1 more
TL;DR: In this article, a two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films and the existence of spiral paths is demonstrated.
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The Surface Crack Problem for a Plate With Functionally Graded Properties
Fazil Erdogan,B. H. Wu +1 more
TL;DR: In this article, the authors considered the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries and solved the problem under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region.
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Crack problems in fgm layers under thermal stresses
Fazil Erdogan,B. H. Wu +1 more
TL;DR: In this article, an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered, where the layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are continuous functions of the thickness coordinate.
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Numerical evaluation of hypersingular integrals
TL;DR: Boundary integral equations which employ integrals which exist only if defined in the Cauchy principal value sense or as the Hadamard finite part are currently used with success to solve many two-and three-dimensional problems of applied mechanics as mentioned in this paper.
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Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock
Zhi-He Jin,Romesh C. Batra +1 more
TL;DR: In this article, the authors analyzed thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface.
References
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Handbook of Mathematical Functions
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform