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Topology optimization: perimeter restriction using total variation

Fredriksson, Jonas LU (2022) In ISRN LUTFD2/TFHF-21/5245-SE(1-49) FHLM01 20211
Solid 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 2-dimensional 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 PDE-filter, 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:
author
Fredriksson, Jonas LU
supervisor
organization
alternative title
Topologioptimering: användning av totalvariation för omkretsbegränsning
course
FHLM01 20211
year
type
H3 - Professional qualifications (4 Years - )
subject
keywords
Topology optimization, structural optimization, solid mechanics, total variation
publication/series
ISRN LUTFD2/TFHF-21/5245-SE(1-49)
report number
TFHF-5245
language
English
id
9075524
date added to LUP
2022-03-03 14:14:27
date last changed
2022-03-10 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 2-dimensional 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 PDE-filter, 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/TFHF-21/5245-SE(1-49)}},
  title        = {{Topology optimization: perimeter restriction using total variation}},
  year         = {{2022}},
}