Solutions of multiple crack problems of a circular region with free or fixed boundary condition in antiplane elasticity

1986 ◽  
Vol 30 (4) ◽  
pp. 287-293 ◽  
Author(s):  
Y. Z. Chen ◽  
Z. X. Wang
Keyword(s):  
Boundary Condition ◽  
Circular Region ◽  
Multiple Crack ◽  
Fixed Boundary ◽  
Antiplane Elasticity ◽  
Crack Problems ◽  
Fixed Boundary Condition

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.

scholarly journals Bosonization of Quantum Sine–Gordon Field with Boundary

1997 ◽  
Vol 12 (09) ◽  
pp. 1711-1741 ◽  
Author(s):  
Bo-Yu Hou ◽  
Kang-Jie Shi ◽  
Yan-Shen Wang ◽  
Wen-Li Yang
Keyword(s):  
Boundary Condition ◽  
Ground States ◽  
Form Factors ◽  
Fixed Boundary ◽  
Boundary Operators ◽  
Sine Gordon Model ◽  
Fixed Boundary Condition

Boundary operators and boundary ground states in sine–Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also obtain the form-factors of this model.

Low Frequency Study of Te2 Cluster and CdSeTe Nanoparticles Embedded in Borosilicate Glass

2016 ◽  
Vol 28 ◽  
pp. 120-124
Author(s):  
Venu Mankad ◽  
Vaishali Sharma ◽  
Prafulla K. Jha
Keyword(s):  
Boundary Condition ◽  
Borosilicate Glass ◽  
Glass Matrix ◽  
Continuum Model ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Elastic Continuum ◽  
Fixed Boundary ◽  
Fixed Boundary Condition

The objective of this paper is to study the low frequency acoustic vibration of Te2 cluster and CdSeTe nanoparticle embedded in borosilicate glass matrix. Lamb’s model is used to predict the occurrence of various mode to support the experimental observations by considering the elastic continuum model and fixed boundary condition. The presence of medium significantly affects the phonon peaks and results into the broadening of the modes. The linewidth is found to depend inversely on the size, similar to that reported experimentally.

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