Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 1965. ,
Sobolev spaces, 2003. ,
Shape optimization by the homogenization method, 2001. ,
Conception optimale de structures, Mathématiques & Applications, vol.58, 2006. ,
Shape optimization by the homogenization method, Numerische Mathematik, vol.76, issue.1, pp.27-68, 1997. ,
DOI : 10.1007/s002110050253
Multi-phase optimization via a level set method, ESAIM: Control, Optimization and Calculus of Variations, pp.576-611, 2014. ,
Damage and fracture evolution in brittle materials by shape optimization methods, Journal of Computational Physics, vol.230, issue.12, pp.5010-5044, 2011. ,
DOI : 10.1016/j.jcp.2011.03.024
URL : https://hal.archives-ouvertes.fr/hal-00784048
An optimal design problem with perimeter penalization, Calculus of Variations and Partial Differential Equations, pp.1-55, 1993. ,
Polarization and Moment Tensors; With Applications to Inverse Problems and Effective Medium Theory, p.162, 2007. ,
Sensitivity analysis with respect to a local perturbation of the material property, Asympt. Anal, vol.49, pp.87-108, 2006. ,
Analysis of a level set method for topology optimization, Optimization Methods and Software, pp.555-573, 2011. ,
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization, Structural and Multidisciplinary Optimization, vol.37, issue.4, pp.755-765, 2011. ,
DOI : 10.1137/S0363012997323230
URL : https://hal.archives-ouvertes.fr/hal-01325799
A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, vol.216, issue.2, pp.573-588, 2006. ,
DOI : 10.1016/j.jcp.2005.12.015
Topology optimization using a dual method with discrete variables, Structural Optimization, pp.14-24, 1999. ,
Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988. ,
DOI : 10.1016/0045-7825(88)90086-2
Material interpolation schemes in topology optimization, Archive of Applied Mechanics, pp.635-654, 1999. ,
Topology Optimization. Theory, Methods, and Applications, 2003. ,
Asymptotic analysis of periodic structures, 1978. ,
The topological derivative in anisotropic elasticity, The Quarterly Journal of Mechanics and Applied Mathematics, vol.66, issue.4, pp.557-586, 2013. ,
DOI : 10.1093/qjmam/hbt018
URL : https://hal.archives-ouvertes.fr/hal-00852248
Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids, vol.24, issue.1, pp.41-77, 2003. ,
DOI : 10.1007/978-3-662-12613-4
Filters in topology optimization, International Journal for Numerical Methods in Engineering, vol.18, issue.9, pp.2143-2158, 2001. ,
DOI : 10.1007/BF01210686
Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2000. ,
DOI : 10.1007/978-0-387-70914-7
Topology optimization of non-linear elastic structures and compliant mechanisms, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.26-27, pp.3443-3459, 2001. ,
DOI : 10.1016/S0045-7825(00)00278-4
Variational Methods in Shape Optimization Problems, Birkäuser, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00414080
Conception optimale ou identification de formes, calcul rapide de la d??riv??e directionnelle de la fonction co??t, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.3, pp.371-420, 1986. ,
DOI : 10.1051/m2an/1986200303711
The shape and topological optimizations connection, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.4, pp.713-726, 2000. ,
DOI : 10.1016/S0045-7825(99)00357-6
Shape optimization, level set methods on unstructured meshes and mesh evolution, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-00916224
Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2011. ,
DOI : 10.1137/1.9780898719826
Theory and Practice of Finite Elements, 2004. ,
DOI : 10.1007/978-1-4757-4355-5
Topology optimization of slightly compressible fluids, ZAMM, vol.40, issue.3, pp.46-62, 2006. ,
DOI : 10.1080/08905459708945415
Topological sensitivity analysis in heterogeneous anisotropic elasticity problem. Theoretical and computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.311, pp.311-134, 2016. ,
DOI : 10.1016/j.cma.2016.08.004
A new approach to variable-topology shape design using a constraint on perimeter, Structural Optimization, pp.1-12, 1996. ,
Variation et optimisation de formes, une analyse géométrique, Mathématiques et Applications, vol.48, 2005. ,
DOI : 10.1007/3-540-37689-5
Variational approach to shape derivatives, ESAIM: Control, Optimisation and Calculus of Variations, vol.14, issue.3, pp.517-539, 2008. ,
DOI : 10.1051/cocv:2008002
URL : http://www.esaim-cocv.org/articles/cocv/pdf/2008/03/cocv0641.pdf
Fundamental Solutions for partial differential operators, and applications, 1996. ,
Filters in topology optimization based on Helmholtz-type differential equations, International Journal for Numerical Methods in Engineering, vol.79, issue.11, pp.765-781, 2011. ,
DOI : 10.1002/nme.2579
Sur le contrôle par un domaine géométrique, 1976. ,
Calculus of Variations and Homogenization, in Topics in the mathematical modelling of composite materials, Progr. NonLinear Differential Equations, pp.139-173, 1997. ,
Remarks on strongly elliptic partial differential equations, Communications on Pure and Applied Mathematics, vol.7, issue.4, pp.649-675, 1955. ,
DOI : 10.7146/math.scand.a-10364
Topological derivatives in shape optimization, 2012. ,
DOI : 10.1007/978-3-642-35245-4
URL : https://hal.archives-ouvertes.fr/hal-01304757
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5, pp.333-337, 2005. ,
DOI : 10.1016/j.crma.2005.07.005
Some convergence results in perimeter-controlled topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.1-2, pp.123-140, 1999. ,
DOI : 10.1016/S0045-7825(98)00248-5
Slope constrained topology optimization, International Journal for Numerical Methods in Engineering, vol.89, issue.8, pp.41-1417, 1998. ,
DOI : 10.1016/0045-7825(91)90044-7
Numerical Models for Differential Problems, 2014. ,
Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999. ,
On the design of compliant mechanisms using topology optimization, Mechanical Structures and Machines, pp.493-524, 1997. ,
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization, vol.89, issue.1, pp.68-75, 1998. ,
DOI : 10.1007/BF01214002
Introduction to Shape Optimization; Shape Sensitivity Analysis, 1992. ,
A homogenization method for shape and topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.93, issue.3, pp.291-318, 1991. ,
DOI : 10.1016/0045-7825(91)90245-2