The shape optimization of underground caverns based on strain energy criterion via explicit interface tracking methods

Le, C., Bruns, T., Tortorelli, D.: A gradient-based parameter-free approach to shape optimization. Comput. Methods Appl. Mech. Eng. 200(9–12), 985–996 (2011)

Lian, H., Kerfriden, P., Bordas, S.P.A.: Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int. J. Numer. Meth. Eng. 106(12), 972–1017 (2016)

Lian, H., Kerfriden, P., Bordas, S.P.A.: (2017) Shape optimization directly from CAD: an isogeometric boundary element approach. Comput. Methods Appl. Mech. Eng. 317, 1–41 (2017)

Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194(1), 363–393 (2004)

Wang, M., Wang, X., Guo, D.: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192(1), 227–246 (2003)

Bendøe, M.P., Sigmund, O.: Topol. Optim. Theory Methods Appl., 2nd edn. Springer Verlag, Berlin (2003)

Misztal, M.K., Bærentzen, J.A.: Topology adaptive interface tracking using the deformable simplicial complex. ACM Trans. Graph. 31(3), 1–12 (2012)

Christiansen, A.N., Nobel-Jørgensen, M., Aage, N., Sigmund, O., Bærentzen, J.A.: Topology optimization using an explicit interface representation. Struct. Multidiscip. Optim. 399, 387–399 (2014)

Christiansen, A.N., Bærentzen, J.A., Nobel-Jørgensen, M., Aage, N., Sigmund, O.: Combined shape and topology optimization of 3D structures. Comput. Gr. 46, 25–35 (2015)

Lian, H., Christiansen, A.N., Tortorelli, D.A., Sigmund, O., Aage, N.: Combined shape and topology optimization for minimization of maximal von Mises stress. Struct. Multidiscip. Optim. 55, 1541–1557 (2017)

Lian, H., Aage, N., Sigmund, O.: Combined shape and topology optimization for stokes flow problems. In 11th world congress of structural and multidisciplinary optimization. Sydney, Australia (2015)

Zhou, M., Lian, H., Sigmund, O., Aage, N.: Shape optimization of fluid flow problems using an explicit boundary tracking approach. Int. J. Numer. Meth. Fluids 88(6), 296–313 (2018)

Svanberg, K.: The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Meth. Eng. 24(2), 359–373 (1987)