Chapter 4: Bibliography

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[2] Bendsøe, M. P., & Sigmund, O. (2003). Topology Optimization: Theory, Methods, and Applications. Berlin, DE: Springer.

[3] Murat, F., & Tartar, L. (1985). Calcul des Variations et Homogénéisation. D. Bergman & al. (Eds.), Les Méthodes de l’Homogénéisation: Théorie et Applications en Physique (pp. 319-369). Coll. Dir. Etudes et Recherches EDF. 57. Paris, FR: Eyrolles.

[4] Dapogny, C., & Frey, P. (2012). Computation of the signed distance function to a discrete contour on adapted triangulation. Calcolo. 49, 193–219

[5] Allaire, G., Jouve, F., & Toader. A.-M. (2004). Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics. 194, 363–393

[6] Bui, C., Dapogny, C., & Frey, P. (2012). An accurate anisotropic adaptation method for solving the level set advection equation. International Journal for Numerical Methods in Fluids.

[7] Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics. 79(1), 12–49.

[8] Allaire, G., Dapogny, C., & Jouve, F. (2021). Shape and Topology Optimization. A. Bonito & R. Nochetto (Eds.), Geometric Partial Differential Equations, Part II (pp. 1–132). Handbook of Numerical Analysis. 22. Elsevier.

[9] Allaire, G., & Schoenauer, M. (2007). Conception optimale de structures. Berlin, DE: Springer.

[10] Shimoda, M., & Liu, Y. (2014). A non-parametric free-form optimization method for shell structures. Structural and Multidisciplinary Optimization. 50, 409–423.

[11] Cheng, L., Zhang, P., Biyikli, E., Bai, J., Robbins, J., & To, A. (2017). Efficient design optimization of variable-density cellular structures for additive manufacturing: theory and experimental validation. Rapid Prototyping Journal. 23(4), 660–677.

[12] Allaire, G. (1992). Homogenization and two-scale convergence. SIAM Journal on Mathematical Analysis. 23(6), 1482–1518.

[13] Allaire, G., Jouve, F., & Michailidis, G. (2016). Thickness control in structural optimization via a level set method. Structural and Multidisciplinary Optimization. 53, 1349–1382.

[14] [Fernández, E., Yang, K. K., Koppen, S., Alarcón, P., Bauduin, S., & Duysinx, P. (2020). Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization. Computer Methods in Applied Mechanics and Engineering. 368, Article 113157.