Topology optimization and additive manufacturing
G. Allaire, M. Bihr, B. Bogosel, Support optimization in additive manufacturing for geometric and thermo-mechanical constraints, SMO, 61, pp. 2377-2399 (2020). HAL preprint: hal-02468684
G. Allaire, C. Dapogny, A. Faure, G. Michailidis, Shape optimization of a layer by layer mechanical constraint for additive manufacturing, C. R. Math. Acad. Sci. Paris, 355, no. 6, 699-717 (2017). Open Access manuscript: CRAS Série I
G. Allaire, L. Jakabcin, Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing, M3AS 28(12), 2313-2366 (2018). HAL preprint: hal-01666081.
M. Boissier, G. Allaire, C. Tournier, Additive Manufacturing Scanning Paths Optimization Using Shape Optimization Tools, SMO, 61, pp. 2437-2466 (2020). HAL preprint: hal-02410481v1.
Density based methods
Sigmund, O. and J. Petersson. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16.1 (1998): 68-75. PDF
Borrvall, Thomas, and Joakim Petersson. Topology optimization of fluids in Stokes flow. International journal for numerical methods in fluids 41.1 (2003): 77-107. PDF
Jang, In Gwun, and Il Yong Kim. Computational study of Wolff’s law with trabecular architecture in the human proximal femur using topology optimization. Journal of biomechanics 41.11 (2008): 2353-2361. PDF
Larsen, Ulrik Darling, O. Signund, and S. Bouwsta. Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. Journal of microelectromechanical systems 6.2 (1997): 99-106. PDF
Christiansen, Rasmus E., and Ole Sigmund. Inverse design in photonics by topology optimization: tutorial. JOSA B 38.2 (2021): 496-509. PDF
Optimization algorithms in topology optimization
Svanberg, K. The method of moving asymptotes—a new method for structural optimization. International journal for numerical methods in engineering 24.2 (1987): 359-373. PDF
Dunning, Peter D., and H. Alicia Kim. Introducing the sequential linear programming level-set method for topology optimization. Structural and Multidisciplinary Optimization 51.3 (2015): 631-643. PDF
F. V. Senhora et al. Topology optimization with local stress constraints: a stress aggregation-free approach. Structural and Multidisciplinary Optimization 62.4 (2020): 1639-1668. PDF
The Hadamard’s method in shape optimization
Topology optimization of large scale systems
H. Li, T. Kondoh, P. Jolivet, K. Furuta, T. Yamada, B. Zhu and S. Nishiwaki. Three-dimensional topology optimization of a fluid–structure system using body-fitted mesh adaption based on the level-set method. Applied Mathematical Modelling, 101, 276-308 (2022) PDF
S. Kambampati et al. Large-scale level set topology optimization for elasticity and heat conduction. Structural and Multidisciplinary Optimization 61.1 (2020): 19-38. PDF
N. Aage et al. Giga-voxel computational morphogenesis for structural design. Nature 550.7674 (2017): 84-86.
N. Aage, E. Andreassen, and B. S. Lazarov. Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework. Structural and Multidisciplinary Optimization 51.3 (2015): 565-572. PDF
Inverse homogenization
G. Allaire, P. Geoffroy-Donders, and O. Pantz. Topology optimization of modulated and oriented periodic microstructures by the homogenization method. Computers & Mathematics with Applications 78.7 (2019): 2197-2229. PDF
J. Wu, O. Sigmund, and J. P. Groen. Topology optimization of multi-scale structures: a review. Structural and Multidisciplinary Optimization 63.3 (2021): 1455-1480. PDF
F.C. Stutz, J.P. Groen, O. Sigmund and J.A. Bærentzen, 2020. Singularity aware de-homogenization for high-resolution topology optimized structures. Structural and Multidisciplinary Optimization, 62(5), pp.2279-2295. PDF
Geometric constraints in shape optimization
Machine learning approach to topology optimization
H. Chi et al. Universal machine learning for topology optimization. Computer Methods in Applied Mechanics and Engineering 375 (2021): 112739. PDF
Kazemi, Hesaneh, Carolyn Seepersad, and H. Alicia Kim. Topology Optimization Integrated Deep Learning for Multiphysics Problems. AIAA SCITECH 2022 Forum. 2022. PDF