Crack problem in plane elasticity under antisymmetric loading

1989 ◽  
Vol 41 (2) ◽  
pp. R29-R34 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Crack Problem ◽  
Plane Elasticity ◽  
Antisymmetric Loading

Integral Equation Methods for Multiple Crack Problems and Related Topics

2007 ◽  
Vol 60 (4) ◽  
pp. 172-194 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Point Sources ◽  
Fredholm Integral Equations ◽  
Hypersingular Integral Equation ◽  
Multiple Crack ◽  
Antiplane Elasticity ◽  
Crack Problems

The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

A generalized crack problem in plane elasticity

1980 ◽  
Vol 18 (3) ◽  
pp. 491-499
Author(s):  
P.S. Theocaris ◽  
N.I. Ioakimidis
Keyword(s):  
Crack Problem ◽  
Plane Elasticity

T-stress in the Zener–Stroh arc crack problem in plane elasticity

2008 ◽  
Vol 75 (16) ◽  
pp. 4721-4726 ◽  
Author(s):  
Y.Z. Chen ◽  
Z.X. Wang ◽  
X.Y. Lin
Keyword(s):  
Crack Problem ◽  
Plane Elasticity ◽  
T Stress ◽  
Arc Crack

scholarly journals Analytical Solution of a Crack Problem in a Radially Graded FGM

2009 ◽  
Vol 631-632 ◽  
pp. 115-120
Author(s):  
Suat Çetin ◽  
Suat Kadıoğlu
Keyword(s):  
Stress Intensity ◽  
Plane Strain ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Approximate Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Homogeneous Layer ◽  
Intensity Factors ◽  
Functionally Graded Layer

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a functionally graded layer bonded to a homogeneous substrate. Functionally graded coating contains an edge crack perpendicular to the interface. It is assumed that plane strain conditions prevail and the crack is subjected to mode I loading. By introducing an elastic foundation underneath the homogeneous layer, the plane strain problem under consideration is used as an approximate model for an FGM coating with radial grading on a thin walled cylinder. The plane elasticity problem is reduced to the solution of a singular integral equation. Constant strain loading is considered. Stress intensity factors are obtained as a function of crack length, strip thicknesses, foundation modulus, and inhomogeneity parameter.

An Analysis of Cracking in a Layered Medium With a Functionally Graded Nonhomogeneous Interface

1996 ◽  
Vol 63 (2) ◽  
pp. 479-486 ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Layered Medium ◽  
Crack Problem ◽  
Crack Size ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Interfacial Region ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Transitional Layer ◽  
Homogeneous Surface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method of formulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.

STUDY ON ELASTIC ANALYSIS OF CRACK PROBLEM OF TWO-DIMENSIONAL DECAGONAL QUASICRYSTALS OF POINT GROUP 10, $\overline {10}$

2009 ◽  
Vol 23 (16) ◽  
pp. 1989-1999 ◽  
Author(s):  
WU LI ◽  
TIAN YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Two Dimensional ◽  
Partial Differential ◽  
Decagonal Quasicrystal ◽  
Complex Variable Function ◽  
Variable Function ◽  
Group 10

By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, [Formula: see text] to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.

The Surface Crack Problem for a Plate With Functionally Graded Properties

1997 ◽  
Vol 64 (3) ◽  
pp. 449-456 ◽  
Author(s):  
F. Erdogan ◽  
B. H. Wu
Keyword(s):  
Crack Opening ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Opening Displacement ◽  
Nonhomogeneous Layer ◽  
Edge Cracks ◽  
Graded Properties ◽  
Plane Elasticity Problem

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.

Solution of Zener–Stroh arc crack problem in plane elasticity

2005 ◽  
Vol 32 (3) ◽  
pp. 300-305 ◽  
Author(s):  
Y.Z. Chen ◽  
X.Y. Lin ◽  
Z.X. Wang
Keyword(s):  
Crack Problem ◽  
Plane Elasticity ◽  
Arc Crack

Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem

2001 ◽  
Vol 10 (8) ◽  
pp. 743-747 ◽  
Author(s):  
Zhou Wang-min ◽  
Fan Tian-you
Keyword(s):  
Crack Problem ◽  
Plane Elasticity ◽  
Elasticity Problem ◽  
Two Dimensional ◽  
Plane Elasticity Problem
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