Skip to main content
SpringerLink
Log in

Topology optimization of flexible micro-fluidic devices

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A multi-objective topology optimization formulation for the design of dynamically tunable fluidic devices is presented. The flow is manipulated via external and internal mechanical actuation, leading to elastic deformations of flow channels. The design objectives characterize the performance in the undeformed and deformed configurations. The layout of fluid channels is determined by material topology optimization. In addition, the thickness distribution, the distribution of active material for internal actuation, and the support conditions are optimized. The coupled fluid-structure response is predicted by a non-linear finite element model and a hydrodynamic lattice Boltzmann method. Focusing on applications with low flow velocities and pressures, structural deformations due to fluid-forces are neglected. A mapping scheme is presented that couples the material distributions in the structural and fluid mesh. The governing and the adjoint equations of the resulting fluid-structure interaction problem are derived. The proposed method is illustrated with the design of tunable manifolds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

References

  • Aage N, Poulsen TH, Gersborg-Hansen A, Sigmund O (2008) Topology optimization of large scale Stokes flow problems. Struct Multidiscipl Optim 35(2):175–180. doi:10.1007/s00158-007-0128-0

    Article  MathSciNet  Google Scholar 

  • Andreasen SC, Gersborg AR, Sigmund O (2009) Topology optimization of microfluidic mixers. Int J Numer Methods Fluids 61(5):498–513. doi:10.1002/fld.1964

    Article  MATH  MathSciNet  Google Scholar 

  • Babuška I (1973) The finite element method with penalty (variational principle with penalty for finite element solution of model Poisson equation with homogeneous Dirichlet boundary conditions, noting convergence). Math Comput 27:221–228

    MATH  Google Scholar 

  • Bar-Cohen Y (2004) Electroactive polymer (EAP) actuators as artificial muscles—reality, potential, and challenges. Bellingham SPIE—The International Society for Optical Engineering

  • Belytschko T, Liu WK, Moran B (2005) Nonlinear finite elements for continua and structures. Wiley, New York

    Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Heidelberg

    Google Scholar 

  • Borrvall T, Petersson J (2003) Topology optimization of fluids in Stokes flow. Int J Numer Methods Fluids 41(1):77–107. doi:10.1002/fld.426

    Article  MATH  MathSciNet  Google Scholar 

  • Buhl T (2002) Simultaneous topology optimization of structure and supports. Struct Multidiscipl Optim 23(5):336–346. doi:10.1007/s00158-002-0194-2

    Article  Google Scholar 

  • Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329–364

    Article  MathSciNet  Google Scholar 

  • Dimitrov D, Schreve K, de Beer N (2006) Advances in three dimensional printing–state of the art and future perspectives. Rapid Prototyping J 12(3):136–147

    Article  Google Scholar 

  • Evgrafov A (2006) Topology optimization of slightly compressible fluids. ZAMM 86(1):46–62. doi:10.1002/zamm.200410223

    Article  MATH  MathSciNet  Google Scholar 

  • Evgrafov A, Pingen G, Maute K (2008) Topology optimization of fluid domains: kinetic theory approach. ZAMM 88(2):129–141. doi:10.1002/zamm.200700122

    Article  MATH  MathSciNet  Google Scholar 

  • Gersborg-Hansen A, Sigmund O, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidiscipl Optim 30(3):181–192. doi:10.1007/s00158-004-0508-7

    Article  MathSciNet  Google Scholar 

  • Guest JK, Prévost JH (2006) Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. Int J Solids Struct 43(22–23):7028–7047. doi:10.1016/j.ijsolstr.2006.03.001

    Article  MATH  Google Scholar 

  • Kim H, Lee HBR, Maeng WJ (2009) Applications of atomic layer deposition to nanofabrication and emerging nanodevices. Thin Solid Films 517(8):2563–2580

    Article  Google Scholar 

  • Klimetzek FR, Paterson J, Moos O (2006) Autoduct: topology optimization for fluid flow. In: Proceedings of Konferenz für angewandte Optimierung. Karlsruhe, Germany

    Google Scholar 

  • Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidiscipl Optim 27:27–42

    Article  Google Scholar 

  • Maute K, Reich GW (2006) Integrated multidisciplinary topology optimization approach to adaptive wing design. AIAA J Aircr 43(1):253–263

    Google Scholar 

  • Moos O, Klimetzek FR, Rossmann R (2004) Bionic optimization of air-guiding systems. In: Proceedings of SAE 2004 world congress & exhibition. Detroit, MI

  • Niklaus F, Stemme G, Lu J-Q, Gutmann RJ (2006) Adhesive wafer bonding. J Appl Phys 99(3):031101

    Article  Google Scholar 

  • Othmer C (2008) A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. Int J Numer Methods Fluids 58(8):861–877. doi:10.1002/fld.1770

    Article  MATH  MathSciNet  Google Scholar 

  • Othmer C, Klimetzek T, Giering R (2006) Computation of topological sensitivities in fluid dynamics: cost function versatility. In: Proceedings of ECCOMAS CFD. Delft, Netherlands

    Google Scholar 

  • Pingen G (2008) Optimal design for fluidic systems: topology and shape optimization with the lattice Boltzmann method. PhD thesis, University Of Colorado at Boulder

  • Pingen G, Evgrafov A, Maute K (2006) Towards the topology optimization of fluid-structure interaction problems with immersed boundary techniques. In: NSF design, service, and manufacturing grantees and research conference, St. Louis, Missouri

  • Pingen G, Evgrafov A, Maute K (2007a) Topology optimization of flow domains using the lattice Boltzmann method. Struct Multidiscipl Optim 36(6):507–524. doi:10.1007/s00158-007-0105-7

    Article  MathSciNet  Google Scholar 

  • Pingen G, Waidmann M, Evgrafov A, Maute K (2007b) Application of a parametric level-set approach to topology optimization fluid with the Navier–Stokes and lattice Boltzmann equations. In: Proceedings of the 7th world congress of structural and multidisciplinary optimization, 21–25 May 2007, Seoul, Korea, ISSMO

  • Pingen G, Evgrafov A, Maute K (2009a) Adjoint parameter sensitivity analysis for the hydrodynamic lattice Boltzmann method with applications to design optimization. Comput Fluids 38(4):910–923. doi:10.1016/j.compfluid.2008.10.002

    Article  Google Scholar 

  • Pingen G, Waidmann M, Evgrafov A, Maute K (2009b) A parametric level-set approach for topology optimization of flow domains. Struct Multidiscipl Optim. doi:10.1007/s00158-009-0405-1

    Google Scholar 

  • Ramm E, Maute K, Schwarz S (1998a) Adaptive topology and shape optimization. In: Proceedings of 4th world congress on computational mechanics, 29 June–2 July. Mendoza, Argentina, pp 19–38

  • Ramm E, Maute K, Schwarz S (1998b) Conceptual design by structural optimization. In: Proceedings of EURO-C, 31 March–3 April. Badgastein, Austria, pp 879–896

  • Spaid MAA, Phelan FR (1997) Lattice Boltzmann methods for modeling microscale flow in fibrous porous media. Phys Fluids 9(9):2468–2474

    Article  MATH  MathSciNet  Google Scholar 

  • Stadler W (1988) Multicriteria optimization in engineering and in the sciences. Springer, Heidelberg

    MATH  Google Scholar 

  • Succi S (2001) The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Proceedings of the first world congress of structural and multidisciplinary optimization, 28 May–2 June 1995, pp 9–16, Goslar, Germany

  • Yoon GH (2009) Topology optimization for stationary fluid-structure interaction problems using a new monolithic formulation. In: Proceedings of 8th world congress on structural and multidisciplinary optimization, Lisbon, Portugal

  • Yu D, Mei R, Luo LS, Shyy W (2003) Viscous flow computations with the method of lattice Boltzmann equation. Prog Aerosp Sci 39(5):329–367. doi:10.1016/S0376-0421(03)00003-4

    Article  Google Scholar 

  • Zhang XQ, Lowe C, Wissler M, Jahne B, Kovacs G (2005) Dielectric elastomers in actuator technology. Adv Eng Mater 7(5):361–367

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support of the National Science Foundation under grant DMI-0348759. The opinions and conclusions presented in this chapter are those of the authors and do not necessarily reflect the views of the sponsoring organization.

Author information

Authors and Affiliations

  1. Center for Aerospace Structures, University of Colorado at Boulder, Boulder, CO, USA

    Sebastian Kreissl & Kurt Maute

  2. Department of Mechanical and Aerospace Engineering, University of Colorado at Colorado Springs, Colorado Springs, CO, USA

    Georg Pingen

  3. Department of Mathematics, Technical University of Denmark, Lyngby, Denmark

    Anton Evgrafov

Authors
  1. Sebastian Kreissl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georg Pingen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anton Evgrafov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kurt Maute
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kurt Maute.

Additional information

Preliminary results of the work presented in this paper have been published in the proceedings of WCSMO-8, Lisbon, Portugal, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kreissl, S., Pingen, G., Evgrafov, A. et al. Topology optimization of flexible micro-fluidic devices. Struct Multidisc Optim 42, 495–516 (2010). https://doi.org/10.1007/s00158-010-0526-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-010-0526-6

Keywords

Search

Navigation