References
- Allaire, G., F. Jouve, and A. M. Toader. 2004. “Structural Optimization Using Sensitivity Analysis and a Level-Set Method.” Journal of Computational Physics 194 (1): 363–393. doi: https://doi.org/10.1016/j.jcp.2003.09.032
- Andreassen, E., A. Clausen, M. Schevenels, B. S. Lazarov, and O. Sigmund. 2011. “Efficient Topology Optimization in MATLAB Using 88 Lines of Code.” Structural and Multidisciplinary Optimization 43: 1–16. doi: https://doi.org/10.1007/s00158-010-0594-7
- Bendsøe, M., and O. Sigmund. 2003. Topology Optimization: Theory, Method and Applications. New York: Springer.
- Brunes, T. E. 2007. “Topology Optimization of Convection-Dominated, Steady-State Heat Transfer Problems.” International Journal of Heat and Mass Transfer 50 (15–16): 2859–2873. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2007.01.039
- Da, D. 2019. Topology Optimization Design of Heterogeneous Materials and Structures. Hoboken, NJ: John Wiley & Sons.
- Da, D., X. Cui, K. Long, Y. Cai, and G. Li. 2019. “Multiscale Concurrent Topology Optimization of Structures and Microscopic Multi-phase Materials for Thermal Conductivity.” Engineering Computations 36 (1): 126–146. doi: https://doi.org/10.1108/EC-01-2018-0007
- Farhat, C., K. C. Park, and Y. Dubois-Pelerin. 1991. “An Unconditionally Stable Staggered Algorithm for Transient Finite Element Analysis of Coupled Thermoelastic Problems.” Computer Methods in Applied Mechanics and Engineering 85 (3): 349–365. doi: https://doi.org/10.1016/0045-7825(91)90102-C
- Filipov, S., and I. Farago. 2018. “Implicit Euler Time Discretization and FDM with Newton Method in Nonlinear Heat Transfer Modeling.” International Scientific Journal Mathematical Modeling 3: 94–98.
- Guest J, J. Prevost, and T. Belytschko. 2004. “Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions.” International Journal for Numerical Methods in Engineering 61 (2): 238–254. doi: https://doi.org/10.1002/nme.1064
- Guirguis, D., W. W. Melek, and M. F. Aly. 2018. “High-Resolution Non-Gradient Topology Optimization.” Journal of Computational Physics 372 (21): 107–125. doi: https://doi.org/10.1016/j.jcp.2018.06.025
- Ha, S. H., and S. Cho. 2005. “Topological Shape Optimization of Heat Conduction Problems Using Level Set Approach.” Numerical Heat Transfer, Part B: Fundamentals. A n International Journal of Computation and Methodology 48 (1): 67–88. doi: https://doi.org/10.1080/10407790590935966
- Ha, S. H., and S. Cho. 2008. “Level Set-Based Topological Shape Optimization of Nonlinear Heat Conduction Problems.” Numerical Heat Transfer, Part B: Fundamentals. A n International Journal of Computation and Methodology 54: 454–475. doi: https://doi.org/10.1080/10407790802483408
- Huang, X., and Y. M. Xie. 2010. Evolutionary Topology Optimization of Continuum Structures. Chichester: John Wiley & Sons.
- Joo, Y., I. Lee, and S. J. Kim. 2017. “Topology Optimization of Heat Sinks in Natural Convection Considering the Effect of Shape-Dependent Heat Transfer Coefficient.” International Journal of Heat and Mass Transfer 109 (7): 123–133. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2017.01.099
- Lewis, R. W., P. Nithiarasu, and K. N. Seetharamu. 2004. Fundamentals of the Finite Element Method for Heat and Fluid Flow. Chichester: John Wiley & Sons.
- Li, Q., G. P. Steven, Y. M. Xie, and O. M. Querin. 2004. “Evolutionary Topology Optimization for Temperature Reduction of Heat Conducting Fields.” International Journal of Heat and Mass Transfer 47 (23): 5071–5083. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2004.06.010
- Lienemann, J., A. Yousefi, and J. G. Korvink. 2003. “Nonlinear Heat Transfer Modeling.” Dimension Reduction of Large-Scale Systems. In Proceedings of a Workshop, Germany: Oberwolfach, October 19–25.
- Liu, G. R. 2005. An Introduction to Meshfree Methods and Their Programming. Netherlands: Springer.
- Pironneau, O. 1983. Optimal Shape Design for Elliptic System. New York: Springer.
- Sethian, J. A . 1999. Level Set Methods and Fast Marching Methods. Cambridge: Cambridge University Press.
- Sigmund, O. 2001. “A 99 Line Topology Optimization Code Written in Matlab.” Structural and Multidisciplinary Optimization 21 (2): 120–127. doi: https://doi.org/10.1007/s001580050176
- Sigmund, O. 2007. “Morphology-Based Black and White Filters for Topology Optimization.” Structural and Multidisciplinary Optimization 33: 401–424. doi: https://doi.org/10.1007/s00158-006-0087-x
- Sigmund, O., and K. Maute. 2013. “Topology Optimization Approaches A Comparative Review.” Structural and Multidisciplinary Optimization 48: 1031–1055. doi: https://doi.org/10.1007/s00158-013-0978-6
- Sokolowski, J., and J. P. Zolesio. 1992. Introduction to Shape Optimization: Shape Sensitivity Analysis. New York: Springer.
- Svanberg, K. 2002. “A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations.” SIAM Journal on Optimization 12 (2): 555–573. doi: https://doi.org/10.1137/S1052623499362822
- Tang, L., T. Gao, L. Song, L. Meng, C. Zhang, and W. Zhang. 2019. “Topology Optimization of Nonlinear Heat Conduction Problems Involving Large Temperature Gradient.” Computer Methods in Applied Mechanics and Engineering 357: 1–24.
- Wang, S. Y., and M. Y. Wang. 2006. “Radial Basis Functions and Level Set Method for Structural Topology Optimization.” International Journal for Numerical Methods in Engineering 65 (12): 2060–2090. doi: https://doi.org/10.1002/nme.1536
- Wang, M. Y., X. Wang, and D. Guo. 2003. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 192 (1–2): 227–246. doi: https://doi.org/10.1016/S0045-7825(02)00559-5
- Wei, P., Z. Li, X. Li, and M. Y. Wang. 2018. “An 88-Line MATLAB Code for the Parameterized Level Set Method Based Topology Optimization Using Radial Basis Functions.” Structural and Multidisciplinary Optimization 58: 831–849. doi: https://doi.org/10.1007/s00158-018-1904-8
- Wu, C., J. Fang, and Q. Lia. 2019. “Multi-material Topology Optimization for Thermal Buckling Criteria.” Computer Methods in Applied Mechanics and Engineering 346 (1): 1136–1155. doi: https://doi.org/10.1016/j.cma.2018.08.015
- Wu, S., Y. Zhang, and S. Liu. 2019. “Topology Optimization for Minimizing the Maximum Temperature of Transient Heat Conduction Structure.” Structural and Multidisciplinary Optimization 60: 69–82. doi: https://doi.org/10.1007/s00158-019-02196-9
- Xia, Q., T. Shi, and L. Xia. 2018. “Topology Optimization for Heat Conduction by Combining Level Set Method and BESO Method.” International Journal of Heat and Mass Transfer 127 (Part C) 200–209. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.036
- Yamada, T., K. Izui, and S. Nishiwaki. 2011. “A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects.” Journal of Mechanical Design 133 (3): 031011.1–031011.9. doi: https://doi.org/10.1115/1.4003684
- Yan, S., F. Wang, and O. Sigmund. 2018. “On the Non-Optimality of Tree Structures for Heat Conduction.” International Journal of Heat and Mass Transfer 122 (7): 660–680. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.114
- Zeidan S., O. Sigmund, and B. S. Lazarov. 2016. “Topology Optimization for Transient Heat Transfer Problems.” ECCOMAS Congress 5–10 Jun 2016, Hersonissos, Greece.
- Zhu, J. H., W. H. Zhang, and L. Xia. 2016. “Topology Optimization in Aircraft and Aerospace Structures Design.” Archives of Computational Methods in Engineering 23: 595–622. doi: https://doi.org/10.1007/s11831-015-9151-2
- Zhuang, C. G., Z. H. Xiong, and H. Ding. 2007. “A Level Set Method for Topology Optimization of Heat Conduction Problem Under Multiple Load Cases.” Computer Methods in Applied Mechanics and Engineering 196 (4–6): 1074–1084. doi: https://doi.org/10.1016/j.cma.2006.08.005