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Volumn 39, Issue 5, 2009, Pages 487-501

Effects of planar element formulation and numerical integration order on checkerboard material layouts

Author keywords

Checkerboard; Drilling degrees of freedom; Homogenization; Reduced integration

Indexed keywords

4-NODE ELEMENT; CHECKERBOARD; DRILLING DEGREES OF FREEDOM; ELEMENT FORMULATION; ELEMENT LEVEL; GAUSS QUADRATURE RULES; HOMOGENIZATION; INTEGRATION SCHEME; MATERIAL LAYOUT; NUMERICAL INTEGRATIONS; PLANAR FINITE ELEMENTS; QUADRATIC ELEMENT; REDUCED INTEGRATION; SUPPRESS SPURIOUS; TOPOLOGY OPTIMIZATION; ZERO ENERGY MODES;

EID: 70350212598     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-008-0345-1     Document Type: Article
Times cited : (2)

References (45)
  • 1
    • 0023983940 scopus 로고
    • A quadrilateral finite element including vertex rotations for plane elasticity analysis
    • 0633.73073 10.1002/nme.1620260314
    • D Allman 1988 A quadrilateral finite element including vertex rotations for plane elasticity analysis Int J Numer Methods Eng 26 717 730 0633.73073 10.1002/nme.1620260314
    • (1988) Int J Numer Methods Eng , vol.26 , pp. 717-730
    • Allman, D.1
  • 2
    • 0001695416 scopus 로고
    • Optimal shape design as a material distribution problem
    • 10.1007/BF01650949
    • M Bendsøe 1989 Optimal shape design as a material distribution problem Struct Optim 1 193 202 10.1007/BF01650949
    • (1989) Struct Optim , vol.1 , pp. 193-202
    • Bendsøe, M.1
  • 4
    • 0024105011 scopus 로고
    • Generating optimal topologies in structural design using a homogenization method
    • 10.1016/0045-7825(88)90086-2
    • M Bendsøe N Kikuchi 1988 Generating optimal topologies in structural design using a homogenization method Comput Methods Appl Mech Eng 71 197 224 10.1016/0045-7825(88)90086-2
    • (1988) Comput Methods Appl Mech Eng , vol.71 , pp. 197-224
    • Bendsøe, M.1    Kikuchi, N.2
  • 5
    • 0001241926 scopus 로고    scopus 로고
    • Material interpolation schemes in topology optimization
    • 10.1007/s004190050248
    • M Bendsøe O Sigmund 1999 Material interpolation schemes in topology optimization Arch Appl Mech 69 635 654 10.1007/s004190050248
    • (1999) Arch Appl Mech , vol.69 , pp. 635-654
    • Bendsøe, M.1    Sigmund, O.2
  • 7
    • 0035896055 scopus 로고    scopus 로고
    • Topology optimization of non-linear elastic structures and compliant mechanisms
    • DOI 10.1016/S0045-7825(00)00278-4, PII S0045782500002784
    • T Bruns D Tortorelli 2001 Topology optimization of non-linear elastic structures and compliant mechanisms Comput Methods Appl Mech Eng 190 3443 3459 1014.74057 10.1016/S0045-7825(00)00278-4 (Pubitemid 32379192)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , Issue.26-27 , pp. 3443-3459
    • Bruns, T.E.1    Tortorelli, D.A.2
  • 9
    • 84987014302 scopus 로고
    • Solutions to shape and topology eigenvalue optimization problems using a homogenization method
    • 0767.73046 10.1002/nme.1620350707
    • A Díaz N Kikuchi 1992 Solutions to shape and topology eigenvalue optimization problems using a homogenization method Int J Numer Methods Eng 35 1487 1502 0767.73046 10.1002/nme.1620350707
    • (1992) Int J Numer Methods Eng , vol.35 , pp. 1487-1502
    • Díaz, A.1    Kikuchi, N.2
  • 10
    • 0029356773 scopus 로고
    • Checkerboard patterns in layout optimization
    • 10.1007/BF01743693
    • A Díaz O Sigmund 1995 Checkerboard patterns in layout optimization Struct Optim 10 40 45 10.1007/BF01743693
    • (1995) Struct Optim , vol.10 , pp. 40-45
    • Díaz, A.1    Sigmund, O.2
  • 12
    • 0037294231 scopus 로고    scopus 로고
    • On reduced integration and locking of flat shell finite elements with drilling rotations
    • DOI 10.1002/cnm.567
    • S Geyer A Groenwold 2003 On reduced integration and locking of flat shell finite elements with drilling rotations Commun Numer Methods Eng 19 85 97 1024.74040 10.1002/cnm.567 (Pubitemid 36290331)
    • (2003) Communications in Numerical Methods in Engineering , vol.19 , Issue.2 , pp. 85-97
    • Geyer, S.1    Groenwold, A.A.2
  • 13
    • 0015399446 scopus 로고
    • A method of computing numerically integrated stiffness matrices
    • 0242.73042 10.1002/nme.1620050108
    • A Gupta B Mohraz 1972 A method of computing numerically integrated stiffness matrices Int J Numer Methods Eng 5 83 89 0242.73042 10.1002/nme.1620050108
    • (1972) Int J Numer Methods Eng , vol.5 , pp. 83-89
    • Gupta, A.1    Mohraz, B.2
  • 14
    • 0032301899 scopus 로고    scopus 로고
    • A review of homogenization and topology opimization II-analytical and numerical solution of homogenization equations
    • 10.1016/S0045-7949(98)00132-1
    • B Hassani E Hinton 1998 A review of homogenization and topology opimization II-analytical and numerical solution of homogenization equations Comput Struct 69 719 738 10.1016/S0045-7949(98)00132-1
    • (1998) Comput Struct , vol.69 , pp. 719-738
    • Hassani, B.1    Hinton, E.2
  • 15
    • 0032305382 scopus 로고    scopus 로고
    • A review of homogenization and topology optimization I-homogenization theory for media with periodic structure
    • 0948.74048 10.1016/S0045-7949(98)00131-X
    • B Hassani E Hinton 1998 A review of homogenization and topology optimization I-homogenization theory for media with periodic structure Comput Struct 69 707 717 0948.74048 10.1016/S0045-7949(98)00131-X
    • (1998) Comput Struct , vol.69 , pp. 707-717
    • Hassani, B.1    Hinton, E.2
  • 16
    • 0032292348 scopus 로고    scopus 로고
    • A review of homogenization and topology optimization III-topology optimization using optimality criteria
    • 10.1016/S0045-7949(98)00133-3
    • B Hassani E Hinton 1998 A review of homogenization and topology optimization III-topology optimization using optimality criteria Comput Struct 69 739 756 10.1016/S0045-7949(98)00133-3
    • (1998) Comput Struct , vol.69 , pp. 739-756
    • Hassani, B.1    Hinton, E.2
  • 17
    • 0024304211 scopus 로고
    • On drilling degrees of freedom
    • 0691.73015 10.1016/0045-7825(89)90124-2 978290
    • T Hughes F Brezzi 1989 On drilling degrees of freedom Comput Methods Appl Mech Eng 72 105 121 0691.73015 10.1016/0045-7825(89)90124-2 978290
    • (1989) Comput Methods Appl Mech Eng , vol.72 , pp. 105-121
    • Hughes, T.1    Brezzi, F.2
  • 18
    • 0025471178 scopus 로고
    • A robust quadrilateral membrane finite element with drilling degrees of freedom
    • 0729.73207 10.1002/nme.1620300305
    • A Ibrahimbegovic R Taylor E Wilson 1990 A robust quadrilateral membrane finite element with drilling degrees of freedom Int J Numer Methods Eng 30 445 457 0729.73207 10.1002/nme.1620300305
    • (1990) Int J Numer Methods Eng , vol.30 , pp. 445-457
    • Ibrahimbegovic, A.1    Taylor, R.2    Wilson, E.3
  • 19
    • 84985407445 scopus 로고
    • Quadrature rules for brick based finite elements
    • 0259.65027 10.1002/nme.1620030213
    • B Irons 1971 Quadrature rules for brick based finite elements Int J Numer Methods Eng 3 293 294 0259.65027 10.1002/nme.1620030213
    • (1971) Int J Numer Methods Eng , vol.3 , pp. 293-294
    • Irons, B.1
  • 20
    • 0030123599 scopus 로고    scopus 로고
    • Stability of finite element models for distributed-parameter optimization and topology design
    • C Jog R Haber 1996 Stability of finite element models for distributed-parameter optimization and topology design Comput Methods Appl Mech Eng 130 203 226 0861.73072 10.1016/0045-7825(95)00928-0 1393566 (Pubitemid 126382777)
    • (1996) Computer Methods in Applied Mechanics and Engineering , vol.130 , Issue.3-4 , pp. 203-226
    • Jog, C.S.1    Haber, R.B.2
  • 21
    • 0007480823 scopus 로고
    • A displacement-based topology design method with self-adaptive layered materials
    • M. Bendsøe C. Mota Soares (eds). Kluwer Academic Dordrecht
    • Jog C, Haber R, Bendsøe M (1993) A displacement-based topology design method with self-adaptive layered materials. In: Bendsøe M, Mota Soares C (eds) Topology design of structures. Kluwer Academic, Dordrecht
    • (1993) Topology Design of Structures
    • Jog, C.1    Haber, R.2    Bendsøe, M.3
  • 24
    • 70350251722 scopus 로고    scopus 로고
    • Implications of finite element formulation in optimal topology design
    • Zingoni A (ed) Cape Town, 5-7 July 2004
    • Long C, Groenwold A, Loveday P (2004) Implications of finite element formulation in optimal topology design. In: Zingoni A (ed) Progress in structural engineering, mechanics and computation, Cape Town, 5-7 July 2004, pp 1015-1019
    • (2004) Progress in Structural Engineering, Mechanics and Computation , pp. 1015-1019
    • Long, C.1    Groenwold, A.2    Loveday, L.3
  • 26
    • 33645403646 scopus 로고    scopus 로고
    • A numerical study of the effect of penalty parameters for membrane elements with independent rotation fields and penalized equilibrium
    • 10.1016/j.finel.2005.12.001
    • C Long S Geyer A Groenwold 2006 A numerical study of the effect of penalty parameters for membrane elements with independent rotation fields and penalized equilibrium Finite Elem Anal Des 42 757 765 10.1016/j.finel.2005.12. 001
    • (2006) Finite Elem Anal des , vol.42 , pp. 757-765
    • Long, C.1    Geyer, S.2    Groenwold, A.3
  • 27
    • 0034244686 scopus 로고    scopus 로고
    • Maximization of eigenvalues using topology optimization
    • DOI 10.1007/s001580050130
    • N Pedersen 2000 Maximization of eigenvalues using topology optimization Struct Multidisc Optim 20 2 11 10.1007/s001580050130 (Pubitemid 30967899)
    • (2000) Structural and Multidisciplinary Optimization , vol.20 , Issue.1 , pp. 2-11
    • Pedersen, N.L.1
  • 29
    • 0036865690 scopus 로고    scopus 로고
    • A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization
    • 10.1007/s00158-002-0251-x
    • T Poulsen 2002 A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization Struct Multidisc Optim 24 396 399 10.1007/s00158-002-0251-x
    • (2002) Struct Multidisc Optim , vol.24 , pp. 396-399
    • Poulsen, T.1
  • 31
    • 0035301717 scopus 로고    scopus 로고
    • Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics
    • DOI 10.1007/s001580050174
    • G Rozvany 2001 Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics Struct Multidisc Optim 21 90 108 10.1007/s001580050174 (Pubitemid 32535045)
    • (2001) Structural and Multidisciplinary Optimization , vol.21 , Issue.2 , pp. 90-108
    • Rozvany, G.I.N.1
  • 32
    • 56449087079 scopus 로고    scopus 로고
    • A critical review of established methods of structural topology optimization
    • Rozvany G (2008) A critical review of established methods of structural topology optimization. Struct Multidisc Optim. doi: 10.1007/s00158-007-0217-0
    • (2008) Struct Multidisc Optim
    • Rozvany, G.1
  • 33
    • 0025867747 scopus 로고
    • Applications of the COC algorithm in layout optimization
    • Rozvany G, Zhou M (1991) Applications of the COC algorithm in layout optimization. In: Eschenauer H, Matteck C, Olhoff N (eds) Engineering optimization in design processes, Proc. Int. Conf. held in Karlsruhe, Germany, Sept. 1990. Springer, Berlin, pp 59-70 (Pubitemid 21724009)
    • (1991) Lecture Notes in Engineering , Issue.63 , pp. 59-70
    • Rozvany, G.I.N.1    Zhou, M.2
  • 34
    • 0000177670 scopus 로고
    • Generalized shape optimization without homogenization
    • 10.1007/BF01742754
    • G Rozvany M Zhou T Birker 1992 Generalized shape optimization without homogenization Struct Optim 4 250 252 10.1007/BF01742754
    • (1992) Struct Optim , vol.4 , pp. 250-252
    • Rozvany, G.1    Zhou, M.2    Birker, T.3
  • 35
    • 56449106736 scopus 로고    scopus 로고
    • Checkerboards, element chains and hinges in topology optimization: Causes and prevention
    • Gosling P (ed) Univ. Newcastle-upon-Tyne. UK
    • th ASMO-UK/ISSMO conf., Univ. Newcastle-upon-Tyne. UK, pp 149-159
    • (2002) th ASMO-UK/ISSMO Conf. , pp. 149-159
    • Rozvany, G.1    Querin, O.2
  • 36
    • 0347603492 scopus 로고    scopus 로고
    • Pomezanski Weight increasing effect of topology simplification
    • 10.1007/s00158-003-0334-3
    • G Rozvany O Querin V Z Gaspar 2003 Pomezanski Weight increasing effect of topology simplification Struct Multidisc Optim 25 459 465 10.1007/s00158-003- 0334-3
    • (2003) Struct Multidisc Optim , vol.25 , pp. 459-465
    • Rozvany, G.1    Querin, O.2    Gaspar, V.Z.3
  • 37
    • 0028499421 scopus 로고
    • Materials with prescribed constitutive parameters: An inverse homogenization problem
    • 0946.74557 10.1016/0020-7683(94)90154-6 1287768
    • O Sigmund 1994 Materials with prescribed constitutive parameters: an inverse homogenization problem Int J Solids Struct 31 2313 2329 0946.74557 10.1016/0020-7683(94)90154-6 1287768
    • (1994) Int J Solids Struct , vol.31 , pp. 2313-2329
    • Sigmund, O.1
  • 38
    • 0031270912 scopus 로고    scopus 로고
    • On the design of compliant mechanisms using topology optimization
    • O Sigmund 1997 On the design of compliant mechanisms using topology optimization Mech Struct Mach 25 495 526
    • (1997) Mech Struct Mach , vol.25 , pp. 495-526
    • Sigmund, O.1
  • 39
    • 0035850702 scopus 로고    scopus 로고
    • Design of multiphysics actuators using topology optimization - Part I: One-material structures
    • DOI 10.1016/S0045-7825(01)00251-1, PII S0045782501002511
    • O Sigmund 2001 Design of multiphysics actuators using topology optimization-Part I: one-material structures Comput Methods Appl Mech Eng 190 6577 6604 1116.74407 10.1016/S0045-7825(01)00251-1 (Pubitemid 33030866)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , Issue.49-50 , pp. 6577-6604
    • Sigmund, O.1
  • 40
    • 0035850686 scopus 로고    scopus 로고
    • Design of multiphysics actuators using topology optimization - Part II: Two-material structures
    • DOI 10.1016/S0045-7825(01)00252-3, PII S0045782501002523
    • O Sigmund 2001 Design of multiphysics actuators using topology optimization - Part II: Two-material structures Comput Methods Appl Mech Eng 190 6605 6627 10.1016/S0045-7825(01)00252-3 (Pubitemid 33033624)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , Issue.49-50 , pp. 6605-6627
    • Sigmund, O.1
  • 41
    • 0032137868 scopus 로고    scopus 로고
    • Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
    • O Sigmund J Petersson 1998 Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima Struct Multidisc Optim 16 68 75
    • (1998) Struct Multidisc Optim , vol.16 , pp. 68-75
    • Sigmund, O.1    Petersson, J.2
  • 42
    • 0026203039 scopus 로고
    • The COC algorithm, Part II: Topological, geometrical and generalized shape optimization
    • 10.1016/0045-7825(91)90046-9
    • M Zhou G Rozvany 1991 The COC algorithm, Part II: topological, geometrical and generalized shape optimization Comput Methods Appl Mech Eng 89 309 336 10.1016/0045-7825(91)90046-9
    • (1991) Comput Methods Appl Mech Eng , vol.89 , pp. 309-336
    • Zhou, M.1    Rozvany, G.2
  • 45
    • 0015051922 scopus 로고
    • Reduced integration techniques in general analysis of plates and shells
    • 0253.73048 10.1002/nme.1620030211
    • O Zienkiewicz R Taylor J Too 1971 Reduced integration techniques in general analysis of plates and shells Int J Numer Methods Eng 3 275 290 0253.73048 10.1002/nme.1620030211
    • (1971) Int J Numer Methods Eng , vol.3 , pp. 275-290
    • Zienkiewicz, O.1    Taylor, R.2    Too, J.3


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