, Shape optimization by the homogenization method, 2001.
, Conception optimale de structures, Mathématiques et Applications, vol.58, 2006.
, A new approach for the optimal distribution of assemblies in a nuclear reactor, Numerische Mathematik, vol.89, issue.1, pp.1-29, 2001.
DOI : 10.1007/PL00005459
, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032
, 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
, Optimal design in small amplitude homogenization, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.3, pp.543-574, 2007.
DOI : 10.1051/m2an:2007026
, Lecture notes on geometric evolution problems, distance function and viscosity solutions, in Calculus of Variations and Partial Differential Equations, pp.5-93, 1999.
, An optimal design problem with perimeter penalization, Calc, pp.55-69, 1993.
DOI : 10.1007/bf02163264
, Topology Optimization. Theory, Methods, and Applications, 2003.
, Sensitivity of Darcy's law to discontinuities, Chinese Ann, Math. Ser. B, vol.24, issue.2, pp.205-214, 2003.
, Representation of equilibrium solutions to the table problem of growing sandpiles, Journal of the European Mathematical Society, vol.6, pp.1-30, 2004.
DOI : 10.4171/JEMS/16
, 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
, A Density Result in Two-Dimensional Linearized Elasticity, and Applications, Archive for Rational Mechanics and Analysis, vol.167, issue.3, pp.211-233, 2003.
DOI : 10.1007/s00205-002-0240-7
, On the existence of a solution in a domain identification problem, Journal of Mathematical Analysis and Applications, vol.52, issue.2, pp.189-289, 1975.
DOI : 10.1016/0022-247X(75)90091-8
, Variational Methods for Structural Optimization, 2000.
DOI : 10.1007/978-1-4612-1188-4
, Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.343-367, 2006.
DOI : 10.1137/050624108
, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2011.
DOI : 10.1137/1.9780898719826
, Shape identification via metrics constructed from the oriented distance function, Control and Cybernetics, vol.34, issue.1, pp.137-164, 2005.
, Measure theory and fine properties of functions, 1992.
, Curvature measures, Transactions of the American Mathematical Society, vol.93, issue.3, pp.418-491, 1959.
DOI : 10.1090/S0002-9947-1959-0110078-1
, Reconciling distance functions and level sets, Scale-Space Theories in Computer Vision, pp.70-81, 1999.
, Optimum composite material design, RAIRO M2AN, pp.657-686, 1995.
DOI : 10.1051/m2an/1995290606571
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.1336
, Variation et optimisation de formes, une analyse géométrique, Mathématiques et Applications, vol.48, 2005.
DOI : 10.1007/3-540-37689-5
, The determination of a discontinuity in a conductivity from a single boundary measurement, Inverse Problems, vol.14, issue.1, pp.67-82, 1998.
DOI : 10.1088/0266-5611/14/1/008
, Reconstruction of pressure velocities and boundaries of thin layers in thinly-stratified layers, J. Inverse Ill-Posed Probl, pp.371-388, 2010.
, Design of functionally graded composite structures in the presence of stress constraints, International Journal of Solids and Structures, vol.39, issue.9, pp.2575-2586, 2002.
DOI : 10.1016/S0020-7683(02)00129-4
, Hamilton--Jacobi Equations and Distance Functions on Riemannian Manifolds, Applied Mathematics and Optimization, vol.47, issue.1, pp.1-25, 2002.
DOI : 10.1007/s00245-002-0736-4
URL : http://arxiv.org/abs/math/0201296
, Strongly Elliptic Systems and Boundary Integral Equations, 2000.
, A level set method for structural topology optimization with multi-constraints and multi-materials, Acta Mechanica Sinica, vol.20, issue.5, 2004.
, A level set method for structural topology optimization and its applications Advances in Engineering software, pp.415-441, 2004.
, The theory of composites, 2001.
DOI : 10.1017/CBO9780511613357
, Sur le contrôle par un domaine géométrique, 1976.
, Numerical optimization, 2006.
DOI : 10.1007/b98874
, Existence of the residual functional derivative with respect to a coordinate of gap point of medium
, On Discretization and Differentiation of Operators with Application to Newton???s Method, SIAM Journal on Numerical Analysis, vol.3, issue.1, pp.143-156, 1966.
DOI : 10.1137/0703010
, 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
, Level-Set Methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics , computer vision and materials science, 1999.
, Design of materials with extreme thermal expansion using a three-phase topology optimization method, Journal of the Mechanics and Physics of Solids, vol.45, issue.6, pp.1037-1067, 1997.
DOI : 10.1016/S0022-5096(96)00114-7
, Design of multiphysics actuators using topology optimization-part ii: Two-material structures, Computer methods in applied mechanics and engineering, pp.6605-6627, 2001.
, Modeling holes and inclusions by level sets in the extended finite-element method, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.46-47, pp.6183-6200, 2001.
DOI : 10.1016/S0045-7825(01)00215-8
URL : https://hal.archives-ouvertes.fr/hal-01007065
, Fundamentals of functionally graded materials [48] V. ? Sverak, On optimal shape design, Institute of Materials, pp.537-551, 1993.
, Voigt-Reuss topology optimization for structures with linear elastic material behaviors, Int. J. Numer. Methods Engrg, p.40, 1997.
, The general theory of homogenization. A personalized introduction, Lecture Notes of the Unione Matematica Italiana, vol.7, 2009.
, Understanding Solids: The Science of, Materials, 2004.
DOI : 10.1002/0470020849
, A multiphase level set framework for image segmentation using the Mumford and Shah model, International Journal of Computer Vision, vol.50, issue.3, pp.271-293, 2002.
DOI : 10.1023/A:1020874308076
, Design of Multimaterial Compliant Mechanisms Using Level-Set Methods, Journal of Mechanical Design, vol.127, issue.5, pp.941-956, 2005.
DOI : 10.1115/1.1909206
, ???Color??? level sets: a multi-phase method for structural topology optimization with multiple materials, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.6-8, pp.469-496, 2004.
DOI : 10.1016/j.cma.2003.10.008
, A level-set based variational method for design and optimization of heterogeneous objects, Computer-Aided Design, vol.37, issue.3, pp.321-337, 2005.
DOI : 10.1016/j.cad.2004.03.007
, Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme, Structural and Multidisciplinary Optimization, vol.23, issue.1, pp.49-62, 2001.
DOI : 10.1007/s00158-001-0165-z
, Computational design of multi-phase microstructural materials for extremal conductivity, Computational Materials Science, vol.43, issue.3, pp.549-564, 2008.
DOI : 10.1016/j.commatsci.2007.12.021
, Multimaterial structural topology optimization with a generalized Cahn???Hilliard model of multiphase transition, Structural and Multidisciplinary Optimization, vol.60, issue.2, pp.89-111, 2007.
DOI : 10.1007/s00158-006-0035-9