메뉴 건너뛰기




Volumn 8, Issue 2, 2007, Pages 163-192

On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs

Author keywords

Convex mixed integer programming; Topology optimization

Indexed keywords

HOMOGENIZATION METHOD; INTEGER PROGRAMMING; LINEAR PROGRAMMING; QUADRATIC PROGRAMMING; STIFFNESS; STRUCTURAL DESIGN; STRUCTURAL LOADS;

EID: 34548245521     PISSN: 13894420     EISSN: 15732924     Source Type: Journal    
DOI: 10.1007/s11081-007-9005-3     Document Type: Article
Times cited : (34)

References (39)
  • 1
    • 13944271956 scopus 로고    scopus 로고
    • Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs
    • Adams W, Forrester R, Glover F (2004) Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs. Discret Optim 1:99-120
    • (2004) Discret Optim , vol.1 , pp. 99-120
    • Adams, W.1    Forrester, R.2    Glover, F.3
  • 3
    • 0002309872 scopus 로고
    • An optimal design problem with perimeter penalization
    • Ambrosio L, Buttazzo G (1993) An optimal design problem with perimeter penalization. Calc Var 1:55-69
    • (1993) Calc Var , vol.1 , pp. 55-69
    • Ambrosio, L.1    Buttazzo, G.2
  • 4
    • 0001695416 scopus 로고
    • Optimal shape design as a material distribution problem
    • Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193-202
    • (1989) Struct Optim , vol.1 , pp. 193-202
    • Bendsøe, M.1
  • 6
    • 0024105011 scopus 로고
    • Generating optimal topologies in structural design using a homogenization method
    • Bendsøe M, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197-224
    • (1988) Comput Methods Appl Mech Eng , vol.71 , Issue.2 , pp. 197-224
    • Bendsøe, M.1    Kikuchi, N.2
  • 8
    • 0035015695 scopus 로고    scopus 로고
    • Optimal design of truss structures by logical-based branch and cut
    • Bollapragada S, Ghattas O, Hooker J (2001) Optimal design of truss structures by logical-based branch and cut. Oper Res 49(1):42-51
    • (2001) Oper Res , vol.49 , Issue.1 , pp. 42-51
    • Bollapragada, S.1    Ghattas, O.2    Hooker, J.3
  • 10
    • 0037428358 scopus 로고    scopus 로고
    • Topology optimization of fluids in Stokes flow
    • Borrvall T, Petersson J (2003) Topology optimization of fluids in Stokes flow. Int J Numer Methods Eng 41:77-107
    • (2003) Int J Numer Methods Eng , vol.41 , pp. 77-107
    • Borrvall, T.1    Petersson, J.2
  • 12
    • 0002412766 scopus 로고
    • Automatic design of optimal structures
    • Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Méc 3:25-52
    • (1964) J Méc , vol.3 , pp. 25-52
    • Dorn, W.1    Gomory, R.2    Greenberg, H.3
  • 13
    • 0000905135 scopus 로고    scopus 로고
    • Topology optimization of continuum structures: A review
    • Eschenauer H, Olhoff N (2001) Topology optimization of continuum structures: A review. Appl Mech Rev 54(4):331-390
    • (2001) Appl Mech Rev , vol.54 , Issue.4 , pp. 331-390
    • Eschenauer, H.1    Olhoff, N.2
  • 15
    • 0034159025 scopus 로고    scopus 로고
    • Multiphase composites with extremal bulk modulus
    • Gibiansky L, Sigmund O (2000) Multiphase composites with extremal bulk modulus. J Mech Phys Solids 48:461-498
    • (2000) J Mech Phys Solids , vol.48 , pp. 461-498
    • Gibiansky, L.1    Sigmund, O.2
  • 16
    • 0016619730 scopus 로고
    • Improved linear integer programming formulations on nonlinear integer programs
    • Glover F (1975) Improved linear integer programming formulations on nonlinear integer programs. Manag Sci 22(4):455-460
    • (1975) Manag Sci , vol.22 , Issue.4 , pp. 455-460
    • Glover, F.1
  • 17
    • 0342758158 scopus 로고
    • An improved MIP formulation for products of discrete and continuous variables
    • Glover F (1984) An improved MIP formulation for products of discrete and continuous variables. J Inf Optim Sci 5:469-471
    • (1984) J Inf Optim Sci , vol.5 , pp. 469-471
    • Glover, F.1
  • 18
    • 0037572457 scopus 로고
    • Mixed-integer linear programming formulations of some nonlinear discrete design optimization problems
    • In: Floudas C, Pardalos P (eds) Princeton University Press, Princeton
    • Grossman I, Voudouris V, Ghattas O (1992) Mixed-integer linear programming formulations of some nonlinear discrete design optimization problems. In: Floudas C, Pardalos P (eds) Recent advances in global optimization. Princeton University Press, Princeton
    • (1992) Recent Advances in Global Optimization
    • Grossman, I.1    Voudouris, V.2    Ghattas, O.3
  • 19
    • 0025505232 scopus 로고
    • Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
    • Guedes J, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83:143-198
    • (1990) Comput Methods Appl Mech Eng , vol.83 , pp. 143-198
    • Guedes, J.1    Kikuchi, N.2
  • 20
    • 0022093646 scopus 로고
    • Simultaneous analysis and design
    • Haftka R (1985) Simultaneous analysis and design. AIAA J 23(7)
    • (1985) AIAA J , vol.23 , Issue.7
    • Haftka, R.1
  • 23
    • 0037030824 scopus 로고    scopus 로고
    • Topology design of structures subjected to periodic loading
    • Jog C (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687-709
    • (2002) J Sound Vib , vol.253 , Issue.3 , pp. 687-709
    • Jog, C.1
  • 25
    • 0003915726 scopus 로고
    • Design of material structures using topology optimization
    • PhD thesis, Department of Solid Mechanics, Technical University of Denmark. DCAMM Report S 69
    • Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, Department of Solid Mechanics, Technical University of Denmark. DCAMM Report S 69
    • (1994)
    • Sigmund, O.1
  • 26
    • 0029325144 scopus 로고
    • Tailoring materials with prescribed elastic properties
    • Sigmund O (1995) Tailoring materials with prescribed elastic properties. Mech Mater 20:351-368
    • (1995) Mech Mater , vol.20 , pp. 351-368
    • Sigmund, O.1
  • 28
    • 0033891005 scopus 로고    scopus 로고
    • A new class of extremal composites
    • Sigmund O (2000) A new class of extremal composites. J Mech Phys Solids 48:397-428
    • (2000) J Mech Phys Solids , vol.48 , pp. 397-428
    • Sigmund, O.1
  • 29
    • 0035850702 scopus 로고    scopus 로고
    • Design of multiphysics actuators using topology optimization, part I: One-material structures
    • Sigmund O (2001a) Design of multiphysics actuators using topology optimization, part I: One-material structures. Comput Methods Appl Mech Eng 190(49-50):6577-6604
    • (2001) Comput Methods Appl Mech Eng , vol.190 , Issue.49-50 , pp. 6577-6604
    • Sigmund, O.1
  • 30
    • 0035850686 scopus 로고    scopus 로고
    • Design of multiphysics actuators using topology optimization, part II: Two-material structures
    • Sigmund O (2001b) Design of multiphysics actuators using topology optimization, part II: Two-material structures. Comput Methods Appl Mech Eng 190(49-50):6605-6627
    • (2001) Comput Methods Appl Mech Eng , vol.190 , Issue.49-50 , pp. 6605-6627
    • Sigmund, O.1
  • 31
    • 85020829255 scopus 로고    scopus 로고
    • Topology optimization of elastic band gap structures and waveguides
    • In: H. Mang, F. Rammerstorfer, and J. Eberhardsteiner (eds) Vienna, July 7-12 2002
    • Sigmund O, Jensen J (2002) Topology optimization of elastic band gap structures and waveguides. In: H. Mang, F. Rammerstorfer, and J. Eberhardsteiner (eds) Proceedings of the fifth world congress on computational mechanics WCCM V, Vienna, July 7-12 2002
    • (2002) Proceedings of the Fifth World Congress on Computational Mechanics WCCM V
    • Sigmund, O.1    Jensen, J.2
  • 32
    • 0141976799 scopus 로고    scopus 로고
    • Systematic design of phononic band gap materials and structures by topology optimization
    • Sigmund O, Jensen J (2003) Systematic design of phononic band gap materials and structures by topology optimization. Philos Trans Math Phys Eng Sci 361(1806):1001-1019
    • (2003) Philos Trans Math Phys Eng Sci , vol.361 , Issue.1806 , pp. 1001-1019
    • Sigmund, O.1    Jensen, J.2
  • 33
    • 0001424622 scopus 로고    scopus 로고
    • Composites with extremal thermal expansion coefficients
    • Sigmund O, Torquato S (1996) Composites with extremal thermal expansion coefficients. Appl Phys Lett 69(21):3203-3205
    • (1996) Appl Phys Lett , vol.69 , Issue.21 , pp. 3203-3205
    • Sigmund, O.1    Torquato, S.2
  • 34
    • 0031169474 scopus 로고    scopus 로고
    • Design of materials with extreme thermal expansion using a three-phase topology optimization method
    • Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45:1037-1067
    • (1997) J Mech Phys Solids , vol.45 , pp. 1037-1067
    • Sigmund, O.1    Torquato, S.2
  • 35
    • 21144458232 scopus 로고    scopus 로고
    • Design of planar articulated mechanisms using branch and bound
    • Stolpe M, Kawamoto A (2005) Design of planar articulated mechanisms using branch and bound. Math Program 103(2):357-398
    • (2005) Math Program , vol.103 , Issue.2 , pp. 357-398
    • Stolpe, M.1    Kawamoto, A.2
  • 36
    • 0038608021 scopus 로고    scopus 로고
    • Modeling topology optimization problems as linear mixed 0-1 programs
    • Stolpe M, Svanberg K (2003) Modeling topology optimization problems as linear mixed 0-1 programs. Int J Numer Methods Eng 57(5):723-739
    • (2003) Int J Numer Methods Eng , vol.57 , Issue.5 , pp. 723-739
    • Stolpe, M.1    Svanberg, K.2
  • 37
    • 0023287947 scopus 로고
    • The method of moving asymptotes - A new method for structural optimization
    • Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359-373
    • (1987) Int J Numer Methods Eng , vol.24 , pp. 359-373
    • Svanberg, K.1
  • 38
    • 0036013025 scopus 로고    scopus 로고
    • A class of globally convergent optimization methods based on conservative convex separable approximations
    • Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12(2):555-573
    • (2002) SIAM J Optim , vol.12 , Issue.2 , pp. 555-573
    • Svanberg, K.1
  • 39
    • 0026203039 scopus 로고
    • The COC algorithm, part II: Topological, geometry and generalized shape optimization
    • Zhou M, Rozvany G (1991) The COC algorithm, part II: Topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:197-224
    • (1991) Comput Methods Appl Mech Eng , vol.89 , pp. 197-224
    • Zhou, M.1    Rozvany, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.