Singular Integral Equations: Applications to Elasticity and Numerical Solution
(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, quasistatic 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/546980
 author
 Englund, Jonas ^{LU}
 supervisor

 Johan Helsing ^{LU}
 opponent

 Assistant Professor Martinsson, PerGunnar, Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado, USA
 organization
 publishing date
 2006
 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, Mbuilding, Ole Römers väg 1, Faculty of Engineering, Lund University
 defense date
 20060616 10:15:00
 ISBN
 9789162868468
 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
 2223ddef3f8645a4890186b1420bbafa (old id 546980)
 date added to LUP
 20160401 15:42:32
 date last changed
 20181121 20:35:54
@phdthesis{2223ddef3f8645a4890186b1420bbafa, 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, quasistatic 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 = {9789162868468}, language = {eng}, publisher = {Numerical Analysis, Lund University}, school = {Lund University}, title = {Singular Integral Equations: Applications to Elasticity and Numerical Solution}, year = {2006}, }