Evaluation of the degenerate scale for BIE in plane elasticity and antiplane elasticity by using conformal mapping

2009 ◽  
Vol 33 (2) ◽  
pp. 147-158 ◽  
Author(s):  
Y.Z. Chen ◽  
X.Y. Lin ◽  
Z.X. Wang
Keyword(s):  
Conformal Mapping ◽  
Plane Elasticity ◽  
Degenerate Scale ◽  
Antiplane Elasticity

Degenerate Scale Problem for a Hypocycloid Hole in an Infinite Plate in Plane Elasticity

2016 ◽  
Vol 32 (4) ◽  
pp. N7-N10
Author(s):  
Y.-Z. Chen
Keyword(s):  
Boundary Condition ◽  
Conformal Mapping ◽  
Closed Form ◽  
Infinite Plate ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Scale Problem ◽  
Exterior Region ◽  
Degenerate Scale

AbstractBased on the conformal mapping, this paper provides a closed form solution for the degenerate scale of the hypocycloid hole in plane elasticity. In the derivation, we assume the vanishing displacements along the boundary in the degenerate scale problem. Some functions in the boundary condition are decomposed into three parts with particular behavior. Even the displacements are vanishing along the boundary of an exterior region, the displacements and stresses are not equal to zero in the exterior region. This is a particular feature in the degenerate scale problem.

Closed form Solution for Degenerate Scale Problem of Joukowcki Airfoil Configuration in Antiplane Elasticity

2013 ◽  
Vol 29 (4) ◽  
pp. N21-N23 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Conformal Mapping ◽  
Closed Form ◽  
Closed Form Solution ◽  
Mapping Function ◽  
Form Solution ◽  
Scale Problem ◽  
Thin Airfoil ◽  
Degenerate Scale ◽  
Antiplane Elasticity

ABSTRACTThis paper provides a closed form solution for degenerate scale problem of the Joukowcki thin airfoil configuration in antiplane elasticity. The solution depends on a conformal mapping function for the Joukowcki thin airfoil configuration.

Mechanisms of Synchronous Belt Tooth Failure due to Fatigue Shear Fracture

2011 ◽  
Vol 86 ◽  
pp. 566-569
Author(s):  
Jian Hua Guo ◽  
Hong Yuan Jiang ◽  
Dong Sheng Li
Keyword(s):  
Conformal Mapping ◽  
Compressive Stress ◽  
Shear Fracture ◽  
Complex Function ◽  
Fatigue Cracking ◽  
Plane Elasticity ◽  
Mapping Method ◽  
Tooth Surface ◽  
Tooth Root ◽  
Shear Cracking

Conformal mapping with complex function based on plane elasticity mechanics is an analytical method for resolving stress and displacement at any point of a half-plane domain. Using complex function conformal mapping method in this article we investigated the relationship between load on tooth surface and maximum stress at tooth root for calculating the maximum compressive stress on the opposite side of working flank and maximum tensile stress on working flank side when loads are applied to tooth top and root of working flank side, respectively. The maximum tensile and compressive stress at the tooth root are the main forces that cause fatigue cracking of the tooth root, which may extend along the elastomer compound-cord interface resulting in shear cracking of the belt tooth. The results of our calculation reveal the mechanisms whereby tooth shear cracking causes fatigue failure of synchronic belt, which are consistent with the experimental research results of Lizuka.

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.

Sign in / Sign up

Export Citation Format

Share Document