Generating optimal topologies in structural design using a homogenization method
Tài liệu tham khảo
Haftka, 1986, Structural shape optimization—A survey, Comput. Meths. Appl. Mech. Engrg., 57, 91, 10.1016/0045-7825(86)90072-1
Pironneau, 1984
Schanck, 1979, An optimization procedure for stress concentration by the finite element technique, Internat. J. Numer. Meths. Engrg., 14, 115, 10.1002/nme.1620140109
Kikuchi, 1986, Adaptive finite element methods for shape optimization of linearly elastic structures, Comput. Meths. Appl. Mech. Engrg., 57, 67, 10.1016/0045-7825(86)90071-X
Tvergaard, 1975, On the optimum shape of a fillet in a flat bar with restrictions, 181
Tvergaard, 1973
Botkin, 1986, Shape optimization of three-dimensional folded-plate structures, AIAA J., 23-11, 1804
Braibant, 1984, Shape optimal design using B-splines, Comput. Meths. Appl. Mech. Engrg., 44, 247, 10.1016/0045-7825(84)90132-4
Rodrigues, 1988, Shape optimal design of elastic bodies using a mixed variational formulation, Comput. Meths. Appl. Mech. Engrg., 69, 29, 10.1016/0045-7825(88)90164-8
Haug, 1986
Choi, 1983, Shape design sensitivity analysis of elastic structures, J. Structural Mech., 11, 231, 10.1080/03601218308907443
Choi, 1986, A domain method for shape design sensitivity analysis of built-up structures, Comput. Meths. Appl. Mech. Engrg., 57, 1, 10.1016/0045-7825(86)90066-6
Rousselet, 1983, Design sensitivity analysis in structural mechanics, III. Effects of shape variation, J. Structural Mech., 10, 273, 10.1080/03601218208907414
Zolesio, 1981, The material derivative (or speed) method for shape optimization, 1152
Simon, 1980, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim., 2, 649, 10.1080/01630563.1980.10120631
Haber, 1987, A new variational approach to structural shape design sensitivity analysis, 573
Chenais, 1975, On the existence of a solution in a domain identification problem, J. Math. Anal. Appl., 52, 189, 10.1016/0022-247X(75)90091-8
Cheng, 1981, An Investigation Concerning Optimal Design of Solid Elastic Plates, Internat. J. Solids and Structures, 16, 305, 10.1016/0020-7683(81)90065-2
Cheng, 1982, Regularized Formulation for Optimal Design of Axisymmetric Plates, Internat. J. Solids and Structures, 18, 153, 10.1016/0020-7683(82)90023-3
Cea, 1973
Tartar, 1977, Estimation de coefficients homogeneises, 704, 364
Bendsøe, 1986, Generalized plate models and optimal design, 1, 10.1007/978-1-4613-8646-9_1
Gibiansky, 1984, Design of composite plates of extremal rigidity
Lurie, 1982, Regularization of optimal design problems for bars and plates, J. Optim. Theory Appl., 37, 499, 10.1007/BF00934953
Lurie, 1982, Regularization of optimal design problems for bars and plates, J. Optim. Theory Appl., 37, 523, 10.1007/BF00934954
Rozvany, 1987, Least-weight design of perforated plates, Internat. J. Solids and Structures, 23, 521, 10.1016/0020-7683(87)90015-1
Rozvany, 1987, Least-weight design of perforated plates, Internat. J. Solids and Structures, 23, 537, 10.1016/0020-7683(87)90016-3
Goodman, 1986, Numerical study of a relaxed variational problem from optimal design, Comput. Meths. Appl. Mech. Engrg., 57, 107, 10.1016/0045-7825(86)90073-3
Kohn, 1986, Optimal design in elasticity and plasticity, Internat. J. Numer. Meths. Engrg., 22, 183, 10.1002/nme.1620220113
Zochowski, 1988, The design of a two-dimensional domain, Mech. Struct. Mach., 16
Bensousson, 1978
Duvaut, 1976, Analyse fonctionelle et mecanique des milieux continus. Application a l'etude des materiaux composites elastiques a structure periodique-homogeneisation, 119
Sanchez-Palencia, 1980, Non-Homogeneous Media and Vibration Theory, 127
Murat, 1985, Calcul des variations et homogeneisation, 319
Avellaneda, 1987, Optimal bounds and microgeometries for elastic two-phase composites, SIAM J. Appl. Math., 47, 1216, 10.1137/0147082
Francfort, 1986, Homogenization and optimal bounds in linear elasticity, Arch. Rat. Mech. Anal., 94, 307, 10.1007/BF00280908
Kohn, 1986, On bounding the effective conductivity of anisotropic composites, 1, 97
Lurie, 1984, Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion, 99A, 71
Kohn, 1984, A new model for thin plates with rapidly varying thickness, Internat. J. Solids and Structures, 29, 333, 10.1016/0020-7683(84)90044-1
Kohn, 1985, A new model for thin plates with rapidly varying thickness II: A convergence proof, Quart. Appl. Math., 43, 1, 10.1090/qam/782253
Kohn, 1986, A new model for thin plates with rapidly varying thickness III: Comparison of different scalings, Quart. Appl. Math., 44, 35, 10.1090/qam/840441
Kohn, 1986, Optimal design and relaxation of variational problems, Comm. Pure Appl. Math., 39, 1
Kohn, 1986, Optimal design and relaxation of variational problems, Comm. Pure Appl. Math., 39, 139, 10.1002/cpa.3160390202
Kohn, 1986, Optimal design and relaxation of variational problems, Comm. Pure Appl. Math., 39, 353, 10.1002/cpa.3160390305
Bonnetier, 1986
Bendsøe, 1983, On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space, J. Structural Mech., 11, 501, 10.1080/03601218308907455
Francu, 1982, Homogenization of linear elasticity equations, Apl. Mat., 27, 96, 10.21136/AM.1982.103951
Josif'jan, 1982, Asymptotic expansion of a solution of the system of elasticity theory with periodic rapidly oscillating coefficients, Soviet Math. Dokl., 26, 290
Bourgat, 1977, Numerical Experiments of the Homogenization Method for Operators with Periodic Coefficients, 704, 330
Guedes, 1987
Cioranescu, 1979, Homogenization in open sets with holes, J. Math. Anal. Appl., 71, 590, 10.1016/0022-247X(79)90211-7
Olhoff, 1983, On structural optimization, J. Appl. Mech., 50, 1134, 10.1115/1.3167196
Kristensen, 1976, On the optimum shape of fillets in plates subjected to multiple in-plane loading cases, Internat. J. Numer. Meths. Engrg., 10, 1007, 10.1002/nme.1620100504
Pedersen, 1983, Design for minimum stress concentration by finite elements and linear programming, J. Structural Mech., 10, 375, 10.1080/03601218208907419
C.A.M. Soares, H.C. Rodrigues, L.M.O. Faria and E.J. Haug, Optimization of the geometry of shafts using boundary elements, ASME J. Mechanics, Transmissions and Automation in Design 106(2) 199–203.
Rossow, 1973, A finite element method for the optimal design of variable thickness sheets, AIAA J., 11, 1566, 10.2514/3.50631
Rozvany, 1984, Structural layout theory — the present state of knowledge