Topology optimization: perimeter restriction using total variation
(2022) In ISRN LUTFD2/TFHF21/5245SE(149) FHLM01 20211Solid Mechanics
Department of Construction Sciences
 Abstract
 Topology optimization is a method used to find optimal material distributions, within a specified domain, with respect to some performance measure. To avoid various artifacts to appear in the suggested design, the solution space is typically restricted,
where some restriction methods allow different length scales to be controlled in the design. The suggested material distribution may result in complex designs that are difficult and costly to manufacture. By controlling the perimeter of the design, solutions
with limited complexity can be found.
In this thesis, two different methods of controlling the perimeter of the solution in topology optimization are investigated. First, a method is presented where a constraint on the total... (More)  Topology optimization is a method used to find optimal material distributions, within a specified domain, with respect to some performance measure. To avoid various artifacts to appear in the suggested design, the solution space is typically restricted,
where some restriction methods allow different length scales to be controlled in the design. The suggested material distribution may result in complex designs that are difficult and costly to manufacture. By controlling the perimeter of the design, solutions
with limited complexity can be found.
In this thesis, two different methods of controlling the perimeter of the solution in topology optimization are investigated. First, a method is presented where a constraint on the total variation is added to the optimization problem. The method is evaluated by solving a 2dimensional heat flow topology optimization problem, where two different penalization strategies are used. With the total variation constraint
method, the perimeter cannot be fully controlled. However, some useful applications in engineering might still be found. For comparison, the topology optimization problem is also solved using a PDEfilter, which is modified for computational efficiency. Finally, a filter with total variation regularization is presented, without being successfully
implemented. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9075524
 author
 Fredriksson, Jonas ^{LU}
 supervisor

 Mathias Wallin ^{LU}
 organization
 alternative title
 Topologioptimering: användning av totalvariation för omkretsbegränsning
 course
 FHLM01 20211
 year
 2022
 type
 H3  Professional qualifications (4 Years  )
 subject
 keywords
 Topology optimization, structural optimization, solid mechanics, total variation
 publication/series
 ISRN LUTFD2/TFHF21/5245SE(149)
 report number
 TFHF5245
 language
 English
 id
 9075524
 date added to LUP
 20220303 14:14:27
 date last changed
 20220310 12:03:10
@misc{9075524, abstract = {{Topology optimization is a method used to find optimal material distributions, within a specified domain, with respect to some performance measure. To avoid various artifacts to appear in the suggested design, the solution space is typically restricted, where some restriction methods allow different length scales to be controlled in the design. The suggested material distribution may result in complex designs that are difficult and costly to manufacture. By controlling the perimeter of the design, solutions with limited complexity can be found. In this thesis, two different methods of controlling the perimeter of the solution in topology optimization are investigated. First, a method is presented where a constraint on the total variation is added to the optimization problem. The method is evaluated by solving a 2dimensional heat flow topology optimization problem, where two different penalization strategies are used. With the total variation constraint method, the perimeter cannot be fully controlled. However, some useful applications in engineering might still be found. For comparison, the topology optimization problem is also solved using a PDEfilter, which is modified for computational efficiency. Finally, a filter with total variation regularization is presented, without being successfully implemented.}}, author = {{Fredriksson, Jonas}}, language = {{eng}}, note = {{Student Paper}}, series = {{ISRN LUTFD2/TFHF21/5245SE(149)}}, title = {{Topology optimization: perimeter restriction using total variation}}, year = {{2022}}, }