Abstract
This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systèmes. The considered physical problem of steady-state heat transfer under convection is simulated using SIMULIA-Abaqus. A corresponding topology optimization feature is provided by SIMULIA-Tosca. By following a standard workflow of design optimization, the proposed solution is able to accommodate practical design scenarios and results in efficient conceptual design proposals. Several design examples with verification results are presented to demonstrate the applicability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
1 For readers with a background in solid mechanics, the reaction flux is analogous to the reaction force when a prescribed displacement boundary condition is applied in a static mechanical problem.
2 The color bar shown in Fig. 1 applies to all the density-distribution plots in this paper.
3 Interested readers are referred to the monograph by Bendsøe and Sigmund (2003) for more technical discussions on the maximization of the fundamental structural frequency in topology optimization.
4 All the figures and the verification values provided in this section are the converged results based on a convergence study for the maximum temperature w.r.t. mesh size.
References
Ahn SH, Cho S (2010) Level set-based topological shape optimization of heat conduction problems considering design-dependent convection boundary. Numer Heat Transf Part B Fundam 58(5):304–322. doi:10.1080/10407790.2010.522869
Alexandersen J (2011a) Topology optimisation for axisymmetric convection problems. Tech. rep., Technical University of Denmark. http://orbit.dtu.dk/files/114889112/Alexandersen2011a.html
Alexandersen J (2011b) Topology optimisation for convection problems - B.Eng. Thesis. Master’s thesis, Technical University of Denmark. http://orbit.dtu.dk/en/publications/topology-optimization-for-convection-problems(2b27dfe6-a242-4849-8c8a-63d1e37792db).html http://orbit.dtu.dk/en/publications/topology-optimization-for-convection-problems(2b27dfe6-a242-4849-8c8a-63d1e37792db).html http://orbit.dtu.dk/en/publications/topology-optimization-for-convection-problems(2b27dfe6-a242-4849-8c8a-63d1e37792db).html
Alexandersen J, Aage N, Andreasen CS, Sigmund O (2014) Topology optimisation of natural convection problems. Int J Numer Methods Fluids 76(10):699–721. doi:10.1002/fld.3954
Bendsøe M, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Method Appl M 71:197–224
Bendsøe M, Sigmund O (2003) Topology optimization - theory, methods and applications. Springer
Bruns T (2007) Topology optimization of convection-dominated, steady-state heat transfer problems. Int J Heat Mass Transfer 50(15–16):2859–2873. doi:10.1016/j.ijheatmasstransfer.2007.01.039
Coffin P, Maute K (2015) Level set topology optimization of cooling and heat devices using a simplified convection model. Structural and Multidisciplinary Optimization, available online 10.1007/s00158-015-1343-8
COMSOL-Multiphysics (2015) Version 5-1 COMSOL, Inc
Dede E, Joshi SN, Zhou F (2015) Topology optimization, additive layer manufacturing, and experimental testing of an air-cooled heat sink. ASME Journal of Mechanical Design (available online). doi:10.1115/1.4030989
Gersborg AR, Andreasen CS (2011) An explicit parameterization for casting constraints in gradient driven topology optimization. Struct Multidiscip Optim 44:875–881. doi:10.1007/s00158-011-0632-0
Guest J, Prévost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254. doi:10.1002/nme.1064
Iga A, Nishiwaki S, Izui K, Yoshimura M (2009) Topology optimization for thermal conductors considering design-dependent effects, including heat conduction and convection. Int J Heat Mass Transfer 52(11–12):2721–2732. doi:10.1016/j.ijheatmasstransfer.2008.12.013
Sigmund O (2001) Design of multiphysics actuators using topology optimization part i: One-material structures. Comput Method Appl M 190:6577–6604. doi:10.1016/S0045-7825(01)00251-1
SIMULIA-Abaqus (2015) Manual, Dassault Systèmes Simulia
SIMULIA-Tosca (2015) Manual, Dassault Systèmes Simulia
Yin L, Ananthasuresh G (2002) A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisms. Sensors Actuators 97–98:599–609. doi:10.1016/S0924-4247(01)00853-6
Yoon GH (2010) Topological design of heat dissipating structure with forced convective heat transfer. J Mech Sci Technol 24(6):1225–1233. doi:10.1007/s12206-010-0328-1
Yoon GH, Kim YY (2005) The element connectivity parameterization formulation for the topology design optimization of multiphysics systems. Int J Numer Methods Eng 64(12):1649–1677. doi:10.1002/nme.1422
Zhou M, Lazarov BS, Wang F, Sigmund O (2015) Minimum length scale in topology optimization by geometric constraints. Comput Methods Appl Mech Eng 293:266–282. doi:10.1016/j.cma.2015.05.003
Acknowledgments
The authors acknowledge the financial support received from the EU research project “LaScISO” (Large Scale Industrial Structural Optimisation), grant agreement No.: 285782, and from the research project “Sapere Aude TOpTEn” (Topology Optimization of Thermal ENergy systems) from the Danish Council for Independent Research, grant: DFF-4005-00320. The authors thank Daniel Kurfeß and Pratik Upadhyay from Dassault Systèmes Deutschland GmbH SIMULIA Office for the support in this project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, M., Alexandersen, J., Sigmund, O. et al. Industrial application of topology optimization for combined conductive and convective heat transfer problems. Struct Multidisc Optim 54, 1045–1060 (2016). https://doi.org/10.1007/s00158-016-1433-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-016-1433-2