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Singular Integral Equations: Applications to Elasticity and Numerical Solution

Englund, Jonas LU (2006)
Abstract
The purpose of this thesis is to develop stable, accurate, and efficient numerical algorithms for the solution of certain problems in materials science using integral equations. All the appearing integral equations are of the second kind. Such equations are typically well suited for numerical solution. The second kind equations are obtained from first kind equations through analytical regularizations. Several modifications and generalizations of earlier numerical schemes for the solution of the



appearing equations are presented. The obtained integral equations and numerical schemes are applied to the solution of problems from, for instance,



linear elastic fracture mechanics. Using an ordinary... (More)
The purpose of this thesis is to develop stable, accurate, and efficient numerical algorithms for the solution of certain problems in materials science using integral equations. All the appearing integral equations are of the second kind. Such equations are typically well suited for numerical solution. The second kind equations are obtained from first kind equations through analytical regularizations. Several modifications and generalizations of earlier numerical schemes for the solution of the



appearing equations are presented. The obtained integral equations and numerical schemes are applied to the solution of problems from, for instance,



linear elastic fracture mechanics. Using an ordinary workstation, fairly complex setups can be simulated accurately. As a final application, quasi-static crack growth is simulated in a linearly elastic material. The growing crack is approximated by a piecewise smooth curve in such a way that the computed crack path converges quadratically to the true path. (Less)
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author
supervisor
opponent
  • Assistant Professor Martinsson, Per-Gunnar, Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado, USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Datalogi, numerisk analys, system, kontroll, fracture mechanics, second kind integral equation, Nyström scheme, Computer science, control, systems, numerical analysis
pages
210 pages
publisher
Numerical Analysis, Lund University
defense location
Room M:E, M-building, Ole Römers väg 1, Faculty of Engineering, Lund University
defense date
2006-06-16 10:15:00
ISBN
978-91-628-6846-8
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
2223ddef-3f86-45a4-8901-86b1420bbafa (old id 546980)
date added to LUP
2016-04-01 15:42:32
date last changed
2018-11-21 20:35:54
@phdthesis{2223ddef-3f86-45a4-8901-86b1420bbafa,
  abstract     = {The purpose of this thesis is to develop stable, accurate, and efficient numerical algorithms for the solution of certain problems in materials science using integral equations. All the appearing integral equations are of the second kind. Such equations are typically well suited for numerical solution. The second kind equations are obtained from first kind equations through analytical regularizations. Several modifications and generalizations of earlier numerical schemes for the solution of the<br/><br>
<br/><br>
appearing equations are presented. The obtained integral equations and numerical schemes are applied to the solution of problems from, for instance,<br/><br>
<br/><br>
linear elastic fracture mechanics. Using an ordinary workstation, fairly complex setups can be simulated accurately. As a final application, quasi-static crack growth is simulated in a linearly elastic material. The growing crack is approximated by a piecewise smooth curve in such a way that the computed crack path converges quadratically to the true path.},
  author       = {Englund, Jonas},
  isbn         = {978-91-628-6846-8},
  language     = {eng},
  publisher    = {Numerical Analysis, Lund University},
  school       = {Lund University},
  title        = {Singular Integral Equations: Applications to Elasticity and Numerical Solution},
  year         = {2006},
}