메뉴 건너뛰기




Volumn 33, Issue 4-5, 2007, Pages 337-349

Exact analytical solutions for some popular benchmark problems in topology optimization II: Three-sided polygonal supports

Author keywords

Benchmark problems; Least weight trusses; Line supports; Michell trusses; Stress controlled trusses

Indexed keywords

BENCHMARKING; NUMERICAL METHODS; PROBLEM SOLVING; TRUSSES;

EID: 33847640957     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0093-7     Document Type: Article
Times cited : (51)

References (30)
  • 1
    • 0001295889 scopus 로고
    • Optimal design for minimum weight and compliance in plane stress using extremal microstructures
    • Allaire G, Kohn RV (1993) Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur J Mech A Solids 12:839-878
    • (1993) Eur J Mech A Solids , vol.12 , pp. 839-878
    • Allaire, G.1    Kohn, R.V.2
  • 2
    • 34250082434 scopus 로고
    • The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: An asymptotic study
    • Bendsøe MP, Haber R (1993) The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study. Struct Optim 6:263-267
    • (1993) Struct Optim , vol.6 , pp. 263-267
    • Bendsøe, M.P.1    Haber, R.2
  • 3
    • 33847611795 scopus 로고
    • Optimum Michell frameworks for three parallel forces. The College of Aeronautics, Cranfield
    • No. 167
    • Chan HSY (1963) Optimum Michell frameworks for three parallel forces. The College of Aeronautics, Cranfield. Report AERO, No. 167
    • (1963) Report AERO
    • Chan, H.S.Y.1
  • 4
    • 33847652427 scopus 로고    scopus 로고
    • Chan HSY (1964) Tabulation of some layouts and virtual displacement fields in the theory of Michell optimum structures. The College of Aeronautics, Cranfield. CoA Note Aero, No. 161
    • Chan HSY (1964) Tabulation of some layouts and virtual displacement fields in the theory of Michell optimum structures. The College of Aeronautics, Cranfield. CoA Note Aero, No. 161
  • 5
    • 4444296958 scopus 로고
    • Half-plane slip-line fields and Michell structures
    • Chan HSY (1967) Half-plane slip-line fields and Michell structures. Q J Mech Appl Math 20:453-469
    • (1967) Q J Mech Appl Math , vol.20 , pp. 453-469
    • Chan, H.S.Y.1
  • 6
    • 17444370334 scopus 로고
    • Symmetric plane frameworks of least weight
    • Sawczuk A, Mróz Z eds, Springer, Berlin Heidelberg New York, pp
    • Chan HSY (1975) Symmetric plane frameworks of least weight. In: Sawczuk A, Mróz Z (eds) Optimization in structural design. Springer, Berlin Heidelberg New York, pp 313-326
    • (1975) Optimization in structural design , pp. 313-326
    • Chan, H.S.Y.1
  • 7
    • 25844493554 scopus 로고    scopus 로고
    • The lightest plane structures of a bounded stress level, transmitting a point load to a circular support
    • Graczykowski C, Lewiński T (2005) The lightest plane structures of a bounded stress level, transmitting a point load to a circular support. Control Cybern 34:227-253
    • (2005) Control Cybern , vol.34 , pp. 227-253
    • Graczykowski, C.1    Lewiński, T.2
  • 8
    • 33749254970 scopus 로고    scopus 로고
    • Graczykowski C, Lewiński T (2006) Michell cantilevers constructed within trapezoidal domains. Part I: geometry of Hencky nets. Part II: virtual displacement fields. Part III: force fields. Part IV: complete exact solutions of selected optimal designs and their approximations by trusses of finite number of joints. Struct Multidisc Optim Part I 32:347-368;
    • Graczykowski C, Lewiński T (2006) Michell cantilevers constructed within trapezoidal domains. Part I: geometry of Hencky nets. Part II: virtual displacement fields. Part III: force fields. Part IV: complete exact solutions of selected optimal designs and their approximations by trusses of finite number of joints. Struct Multidisc Optim Part I 32:347-368;
  • 9
    • 33847664033 scopus 로고    scopus 로고
    • Part II 32:463-471;
    • Part II 32:463-471;
  • 10
    • 33847646555 scopus 로고    scopus 로고
    • Part III 33:27-46;
    • Part III 33:27-46;
  • 11
    • 33847655424 scopus 로고    scopus 로고
    • Part IV- 33:113-129
    • Part IV- 33:113-129
  • 15
    • 0028436504 scopus 로고
    • Extended exact solutions for least-weight truss layouts. Part I: Cantilever with a horizontal axis of symmetry
    • Lewiński T, Zhou M, Rozvany GIN (1994a) Extended exact solutions for least-weight truss layouts. Part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36:375-398
    • (1994) Int J Mech Sci , vol.36 , pp. 375-398
    • Lewiński, T.1    Zhou, M.2    Rozvany, G.I.N.3
  • 16
    • 0028433884 scopus 로고    scopus 로고
    • Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts. Part II: unsymmetric cantilevers. Ibidem 399-419
    • Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts. Part II: unsymmetric cantilevers. Ibidem 399-419
  • 17
    • 0001694169 scopus 로고
    • The limits of economy of material in frame-structures
    • Michell AGM (1904) The limits of economy of material in frame-structures. Phil Mag 8:589-597
    • (1904) Phil Mag , vol.8 , pp. 589-597
    • Michell, A.G.M.1
  • 18
    • 0000604772 scopus 로고
    • On optimal orientation of orthotropic materials
    • Pedersen P (1989) On optimal orientation of orthotropic materials. Struct Optim 1:101-106
    • (1989) Struct Optim , vol.1 , pp. 101-106
    • Pedersen, P.1
  • 19
    • 0001939298 scopus 로고
    • Bounds on elastic energy in solids of orthotropic material
    • Pedersen P (1990) Bounds on elastic energy in solids of orthotropic material. Struct Optim 2:55-63
    • (1990) Struct Optim , vol.2 , pp. 55-63
    • Pedersen, P.1
  • 20
    • 33847681669 scopus 로고    scopus 로고
    • Pedersen P (1993) Optimal orientation of anisotropic materals. Optimal distribution of anisotropic materials. Optimal shape design with anisotropic materials. In: Rozvany GIN (ed) Optimization of large structural systems. Proceedings of the NATO ASI, Berchtesgaden, 1991, II. Kluwer, Dordrecht, pp 649-681
    • Pedersen P (1993) Optimal orientation of anisotropic materals. Optimal distribution of anisotropic materials. Optimal shape design with anisotropic materials. In: Rozvany GIN (ed) Optimization of large structural systems. Proceedings of the NATO ASI, Berchtesgaden, 1991, vol. II. Kluwer, Dordrecht, pp 649-681
  • 21
    • 0001832207 scopus 로고
    • Optimization of structural geometry
    • Bednarek AR, Cesari L eds, New York, Academic Press
    • Prager W, Rozvany GIN (1977) Optimization of structural geometry. In: Bednarek AR, Cesari L (eds) Dynamical systems. New York, Academic Press
    • (1977) Dynamical systems
    • Prager, W.1    Rozvany, G.I.N.2
  • 23
    • 0031997969 scopus 로고    scopus 로고
    • Exact analytical solutions for some popular benchmark problems in topology optimization
    • Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Optim 15:42-48
    • (1998) Struct Optim , vol.15 , pp. 42-48
    • Rozvany, G.I.N.1
  • 24
    • 0035302167 scopus 로고    scopus 로고
    • Stress ratio and compliance based methods in topology optimization - a critical review
    • Rozvany GIN (2001) Stress ratio and compliance based methods in topology optimization - a critical review. Struct Multidisc Optim 21:109-119
    • (2001) Struct Multidisc Optim , vol.21 , pp. 109-119
    • Rozvany, G.I.N.1
  • 26
    • 0025564949 scopus 로고
    • Michell layouts for various combinations of line supports - I
    • Rozvany GIN, Gollub W (1990) Michell layouts for various combinations of line supports - I. Int J Mech Sci 32:1021-1043
    • (1990) Int J Mech Sci , vol.32 , pp. 1021-1043
    • Rozvany, G.I.N.1    Gollub, W.2
  • 27
    • 0031256981 scopus 로고    scopus 로고
    • Exact Michell layouts for various combinations of line supports - II
    • Rozvany GIN, Gollub W, Zhou M (1997) Exact Michell layouts for various combinations of line supports - II. Struct Optim 14:138-149
    • (1997) Struct Optim , vol.14 , pp. 138-149
    • Rozvany, G.I.N.1    Gollub, W.2    Zhou, M.3
  • 30
    • 0004785706 scopus 로고
    • The minimum weight of certain redundant structures
    • Sved G (1954) The minimum weight of certain redundant structures. Aust J Appl Sci 5:1-8
    • (1954) Aust J Appl Sci , vol.5 , pp. 1-8
    • Sved, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.