Editing Topology optimization (section)

=== Multiphysics problems ===

==== 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.]]

==== Thermoelectric energy conversion ====

[[File:Design-sketch.png|thumb|A sketch of the design problem. The aim of the design problem is to spatially distribute two materials, Material A and Material B, to maximise a performance measure such as cooling power or electric power output]]

[[File:Topology-optimization-off-diagonal-design-evolution.gif|thumb|Design evolution for an off-diagonal thermoelectric generator. The design solution of an optimisation problem solved for electric power output. The performance of the device has been optimised by distributing [[Skutterudite]] (yellow) and [[bismuth telluride]] (blue) with a density-based topology optimisation methodology. The aim of the optimisation problem is to maximise the electric power output of the thermoelectric generator.]]

[[File:Evolution-design solution.gif|thumb|Design evolution for a thermoelectric cooler. The aim of the design problem is to maximise the cooling power of the thermoelectric cooler.]]

[[Thermoelectric effect|Thermoelectricity]] is a multi-physic problem which concerns the interaction and coupling between electric and thermal energy in semi conducting materials. Thermoelectric energy conversion can be described by two separately identified effects: The Seebeck effect and the Peltier effect. The Seebeck effect concerns the conversion of thermal energy into electric energy and the Peltier effect concerns the conversion of electric energy into thermal energy.<ref>Rowe, David Michael. [https://books.google.com/books?id=VvCb_deT4kIC&q=Seebeck Thermoelectrics handbook: macro to nano]. CRC press, 2005.</ref> By spatially distributing two thermoelectric materials in a two dimensional design space with a topology optimisation methodology,<ref>{{Cite journal | doi=10.1007/s00158-018-1919-1| title=A density-based topology optimization methodology for thermoelectric energy conversion problems| journal=Structural and Multidisciplinary Optimization| volume=57| issue=4| pages=1427–1442| year=2018| last1=Lundgaard| first1=Christian| last2=Sigmund| first2=Ole| s2cid=126031362| url=https://backend.orbit.dtu.dk/ws/files/163153924/grayscale_Lundgaard_C._Sigmund_O_2018_.pdf}}</ref> it is possible to exceed performance of the constitutive thermoelectric materials for [[Thermoelectric cooling|thermoelectric coolers]] and [[thermoelectric generator]]s.<ref>{{Cite journal |doi = 10.1007/s11664-018-6606-x|title = Topology Optimization of Segmented Thermoelectric Generators|journal = Journal of Electronic Materials|volume = 47|issue = 12|pages = 6959–6971|year = 2018|last1 = Lundgaard|first1 = Christian|last2 = Sigmund|first2 = Ole|last3 = Bjørk|first3 = Rasmus|bibcode = 2018JEMat..47.6959L |s2cid = 105113187|url=https://www.researchgate.net/publication/323143969}}</ref>