Editing Topology optimization (section)

==== Fluid-structure-interaction ====
[[Fluid–structure interaction|Fluid-structure-interaction]] is a strongly coupled phenomenon and concerns the interaction between a stationary or moving fluid and an elastic structure. Many engineering applications and natural phenomena are subject to fluid-structure-interaction and to take such effects into consideration is therefore critical in the design of many engineering applications. Topology optimisation for fluid structure interaction problems has been studied in e.g. references<ref>{{Cite journal |doi = 10.1002/nme.2777|title = Topology optimization for stationary fluid-structure interaction problems using a new monolithic formulation|journal = International Journal for Numerical Methods in Engineering|volume = 82|issue = 5|pages = 591–616|year = 2010|last1 = Yoon|first1 = Gil Ho|bibcode = 2010IJNME..82..591Y| s2cid=122993997 }}</ref><ref>{{Cite journal |doi = 10.1016/j.finel.2017.07.005|title = Evolutionary topology optimization for structural compliance minimization considering design-dependent FSI loads|journal = Finite Elements in Analysis and Design|volume = 135|pages = 44–55|year = 2017|last1 = Picelli|first1 = R.|last2 = Vicente|first2 = W.M.|last3 = Pavanello|first3 = R.}}</ref><ref>{{Cite journal |doi = 10.1007/s00158-016-1467-5|title = An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems|journal = Structural and Multidisciplinary Optimization|volume = 54|issue = 5|pages = 1191–1208|year = 2016|last1 = Jenkins|first1 = Nicholas|last2 = Maute|first2 = Kurt|s2cid = 124632210}}</ref> and.<ref name=Lundgaard_FSI>{{Cite journal | doi=10.1007/s00158-018-1940-4| title=Revisiting density-based topology optimization for fluid-structure-interaction problems| journal=Structural and Multidisciplinary Optimization| volume=58| issue=3| pages=969–995| year=2018| last1=Lundgaard| first1=Christian| last2=Alexandersen| first2=Joe| last3=Zhou| first3=Mingdong| last4=Andreasen| first4=Casper Schousboe| last5=Sigmund| first5=Ole| s2cid=125798826| url=https://backend.orbit.dtu.dk/ws/files/163153999/grayscale_Lundgaard_C._Alexandersen_J._Zhou_M._Andreasen_C._S._Sigmund_O_2018_.pdf}}</ref> Design solutions solved for different Reynolds numbers are shown below. The design solutions depend on the fluid flow with indicate that the coupling between the fluid and the structure is resolved in the design problems.

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 | caption1 = Design solution and velocity field for Re=1

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 | caption2  = Design solution and velocity field for Re=5

 | image3 = Fluid-structure-interaction-pressure-field-topology-optimization.png
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 | caption3  = Design solution and pressure field for Re=10

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 | caption4  = Design solution and pressure field for Re=40

 | footer = Design solutions for different Reynolds number for a wall inserted in a channel with a moving fluid.
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[[File:Wall-flow-problem-topology-optimization-for-fluid-structure-interaction-problems.png|thumb|Sketch of the well-known wall problem. The objective of the design problem is to minimize the structural compliance.]]

[[File:Fluid-structure-interaction-design-evolution.gif|thumb|Design evolution for a fluid-structure-interaction problem from reference.<ref name=Lundgaard_FSI /> The objective of the design problem is to minimize the structural compliance. The fluid-structure-interaction problem is modelled with Navier-Cauchy and Navier-Stokes equations.]]