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Topology optimization with optimal spatially varying length scale

Lopar, Stefan LU (2020) In ISRN LUTFD2/TFHF-20/5240-SE(1-63) MMKM10 20201
Product Development
Abstract
Density based topology optimization has become an efficient way to design optimal complex structures with different goals, constraints and boundary conditions. To regularize the solution, density filters are utilized and is controlled by the length scale. The length scale controls minimum feature sizes, as well as minimum curvatures in the structure. Usually a constant length scale is used throughout the design domain, but some recent articles have explored the possibility of varying the length scale spatially to control the peak stresses in a compliance minimization problem. The idea of a varying length scale and treating it as a design variable was then further explored in this thesis. The length scale was controlled by penalizing... (More)
Density based topology optimization has become an efficient way to design optimal complex structures with different goals, constraints and boundary conditions. To regularize the solution, density filters are utilized and is controlled by the length scale. The length scale controls minimum feature sizes, as well as minimum curvatures in the structure. Usually a constant length scale is used throughout the design domain, but some recent articles have explored the possibility of varying the length scale spatially to control the peak stresses in a compliance minimization problem. The idea of a varying length scale and treating it as a design variable was then further explored in this thesis. The length scale was controlled by penalizing variations from the initial length scale. The idea of penalizing variations can be tied into the cost of producing the structure, where the penalty parameter for the length scale can be seen as a tradeoff between optimal structure and manufacturing cost.

The concept of a varying length scale was then tested on a L-bracket with an objective function of minimizing the compliance of the structure with a volume constraint, and later on with a stress constraint as well. The optimization is solved using the Method of Moving Asymptotes. The final structures were quite similar to what was achieved with a constant length scale, but usually with 2-4\% increase in performance but at a cost at computation time.

Finally a variation in the filtering scheme is proposed to achieve consistent feature sizes without the need of padding the structure. (Less)
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author
Lopar, Stefan LU
supervisor
organization
course
MMKM10 20201
year
type
H3 - Professional qualifications (4 Years - )
subject
keywords
Topology optimization, Varying length scale
publication/series
ISRN LUTFD2/TFHF-20/5240-SE(1-63)
report number
TFHF-5240
language
English
id
9032576
date added to LUP
2020-12-07 08:27:31
date last changed
2020-12-07 08:27:31
@misc{9032576,
  abstract     = {Density based topology optimization has become an efficient way to design optimal complex structures with different goals, constraints and boundary conditions. To regularize the solution, density filters are utilized and is controlled by the length scale. The length scale controls minimum feature sizes, as well as minimum curvatures in the structure. Usually a constant length scale is used throughout the design domain, but some recent articles have explored the possibility of varying the length scale spatially to control the peak stresses in a compliance minimization problem. The idea of a varying length scale and treating it as a design variable was then further explored in this thesis. The length scale was controlled by penalizing variations from the initial length scale. The idea of penalizing variations can be tied into the cost of producing the structure, where the penalty parameter for the length scale can be seen as a tradeoff between optimal structure and manufacturing cost. 

The concept of a varying length scale was then tested on a L-bracket with an objective function of minimizing the compliance of the structure with a volume constraint, and later on with a stress constraint as well. The optimization is solved using the Method of Moving Asymptotes. The final structures were quite similar to what was achieved with a constant length scale, but usually with 2-4\% increase in performance but at a cost at computation time.

Finally a variation in the filtering scheme is proposed to achieve consistent feature sizes without the need of padding the structure.},
  author       = {Lopar, Stefan},
  keyword      = {Topology optimization,Varying length scale},
  language     = {eng},
  note         = {Student Paper},
  series       = {ISRN LUTFD2/TFHF-20/5240-SE(1-63)},
  title        = {Topology optimization with optimal spatially varying length scale},
  year         = {2020},
}