Abstract
We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates.
For the purpose of validation, the designs have been post processed using the image processing tools available in FEMLAB. In turn, this has enabled an evaluation of the design with a body fitted mesh in a standard analysis software relevant in engineering practice prior to design manufacturing.
This work investigates the proper choice of a maximum penalization value during the optimization process that ensures that the target outflow rates are met in the validation test.
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References
Bendsøe, M.P. and Sigmund, O., Topology Optimization — Theory, Methods, and Applications, Springer-Verlag, Berlin (2004).
Borrvall, T. and Petersson, J., Topology optimization of fluids in Stokes flow, Int. J. Num. Meth. Fluids, 41, 77–107, DOI:10.1002/fld.426 (2003).
See homepage of Tim Davis, http://www.cise.ufl.edu/research/sparse/umfpack/
Evgrafov, A., Topology optimization of slightly incompressible fluids, in Approximation of Topology Optimization Problems Using Sizing Optimization Problems, Ph.D. Thesis, Department of Mathematics, Chalmers University of Technology, Göteborg, Sweden, ISBN 91-7291-466-1, pp. 55–81 (2004).
Gersborg-Hansen, A., Sigmund, O. and Haber, R.B., Topology optimization of channel flow problems, Struct. Multidisc. Optim., 30(3), 181–192, DOI:10.1007/s00158-004-0508-7 (2005).
Glowinski, R., Finite element methods for the numerical simulation of incompressible viscous flow: Introduction to the control of the Navier-Stokes equations, in Vortex Dynamics and Vortex Methods, C.R. Anderson and C. Greengard (eds), Lectures in Applied Mathematics, Vol. 28, American Mathematical Society, pp. 219–301 (1991).
Guillaume, P. and Idris, K.S., Topological Sensitivity and Shape Optimization for the Stokes equations, Siam Journal on Control and Optimization, 43(1), 1–31, DOI:10.1137/S0363012902411210 (2005).
Klarbring, A., Petersson, J., Torstenfelt, B. and Karlsson, M., Topology optimization of flow networks, Computer Methods in Applied Mechanics and Engineering, 192(35–36), 3909–3932, DOI:10.1016/S0045-7825(03)00393-1 (2003)
Mohammadi, B. and Pironneau, O., Shape optimization in fluid mechanics, Annu. Rev. Fluid Mech., 36, 255–279, DOI:10.1146/annurev.fluid.36.050802.121926 (2004).
Olesen, L.O., Okkels, F. and Bruus, H., A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow, Int. J. Numer. Meth. Engng., in press, DOI:10.1002/nme.1468 (2005)
Sigmund, O., Gersborg-Hansen, A. and Haber, R.B., Topology optimization for multiphysics problems: A future femlab application?, in Nordic Matlab Conference (held in Copenhagen), L. Gregersen (ed.), Comsol, Søborg, Denmark, pp. 237–242 (2003).
Svanberg, K. The method of moving asymptotes — A new method for structural optimization, Int. J. Numer. Meth. Eng., 24, 359–373 (1987).
Svanberg, K., A class of globally convergent optimization methods based on conservative convex separable approximations, SIAM Journal on Optimization, 12(2), 555–573, DOI:10.1137/S1052623499362822 (2002).
Thellner, M., Topology optimization of convection-diffusion problems, in Multi-Parameter Topology Optimization in Continuum Mechanics, Ph.D. Thesis, Linköping Studies in Science and Technology Dissertations No. 934, ISBN 91-85297-71-2, pp. 71–87 (2005).
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Gersborg-Hansen, A., Berggren, M., Dammann, B. (2006). Topology Optimization of Mass Distribution Problems in Stokes Flow. In: Bendsøe, M.P., Olhoff, N., Sigmund, O. (eds) IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials. Solid Mechanics and Its Applications, vol 137. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4752-5_36
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DOI: https://doi.org/10.1007/1-4020-4752-5_36
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