Structural topology optimization subject to overhang angle constraint with overhang length relaxation in additive manufacturing

This paper studies additive manufacturing (AM) oriented structural topology optimization (TO). The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is considered. Although the overhang length relaxation allows additi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Science China. Technological sciences Jg. 65; H. 6; S. 1213 - 1231
Hauptverfasser: Zhang, KaiQing, Cheng, GengDong, Wang, Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beijing Science China Press 01.06.2022
Springer Nature B.V
Schlagworte:
ISSN:1674-7321, 1869-1900
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract This paper studies additive manufacturing (AM) oriented structural topology optimization (TO). The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is considered. Although the overhang length relaxation allows additional flexibility for AM product design, there have been very limited studies on it. This paper elucidates that the overhang angle constraint we proposed can identify the lower boundary element that violates the overhang angle constraint. Taking advantage of this fact, we achieve the overhang length relaxation by specifying that the volume fraction of the elements that violate the overhang angle constraint in each local area of the design domain is less than a specified upper bound. A formula for estimating the maximum allowable overhang length of this method is proposed and verified. The horizontal minimum length constraint is also employed in this paper. While controlling the horizontal length size of the structural member, this constraint together with the overhang angle constraint with overhang length relaxation suppresses the hanging feature. The gradient-based optimization algorithm method of moving asymptotic (MMA) is used to solve the TO formulation. Numerical examples show the effectiveness of this method. It is observed that the new constraint alleviates the main issues of traditional overhang angle constraints, i.e., gray element issue, stress concentration issue, and shattered structure issue. Compared with the strict traditional overhang angle constraint, the new formulation reduces structural compliance.
AbstractList This paper studies additive manufacturing (AM) oriented structural topology optimization (TO). The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is considered. Although the overhang length relaxation allows additional flexibility for AM product design, there have been very limited studies on it. This paper elucidates that the overhang angle constraint we proposed can identify the lower boundary element that violates the overhang angle constraint. Taking advantage of this fact, we achieve the overhang length relaxation by specifying that the volume fraction of the elements that violate the overhang angle constraint in each local area of the design domain is less than a specified upper bound. A formula for estimating the maximum allowable overhang length of this method is proposed and verified. The horizontal minimum length constraint is also employed in this paper. While controlling the horizontal length size of the structural member, this constraint together with the overhang angle constraint with overhang length relaxation suppresses the hanging feature. The gradient-based optimization algorithm method of moving asymptotic (MMA) is used to solve the TO formulation. Numerical examples show the effectiveness of this method. It is observed that the new constraint alleviates the main issues of traditional overhang angle constraints, i.e., gray element issue, stress concentration issue, and shattered structure issue. Compared with the strict traditional overhang angle constraint, the new formulation reduces structural compliance.
Author Zhang, KaiQing
Cheng, GengDong
Wang, Yu
Author_xml – sequence: 1
  givenname: KaiQing
  surname: Zhang
  fullname: Zhang, KaiQing
  organization: Department of Engineering Mechanics, Dalian University of Technology
– sequence: 2
  givenname: GengDong
  surname: Cheng
  fullname: Cheng, GengDong
  email: chenggd@dlut.edu.cn
  organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology
– sequence: 3
  givenname: Yu
  surname: Wang
  fullname: Wang, Yu
  organization: Department of Engineering Mechanics, Dalian University of Technology
BookMark eNp9kF1L5TAQhsPiwupZf8DeBbyum0napr0U8QsEL3SvQ5qkxxx6kpqk6vHGv266FQRBA0NmmHnm4z1Ae847g9AfIMdACP8bAUoGBaFQQNvWxe4H2oembnNEyF72a14WnFH4hQ5j3JD8WNMSKPfR620Kk0pTkANOfvSDX--wH5Pd2heZrHc4Tt3GqJSz2D-acC_dGmcbDFbexRSkdQk_2XT_kR6MW-c4mEE-L02sw1Jrm-yjwVvppl7OM61b_0Y_ezlEc_j-r9C_87O708vi-ubi6vTkulAM6lToShumKWEVk6qqm0ZyrllpWC0brrku21aRTjakVX1HgZZMdw3QnnNOe-AdW6Gjpe8Y_MNkYhIbPwWXRwpac1ZDxZoqV_GlSgUfYzC9UDb9v2C-cxBAxCy4WAQXWXAxCy52mYRP5BjsVobdtwxdmDjOUpjwsdPX0BtY9Jj8
CitedBy_id crossref_primary_10_1016_j_istruc_2024_107359
crossref_primary_10_1007_s11430_024_1526_3
crossref_primary_10_1007_s00158_023_03732_4
crossref_primary_10_1007_s00158_024_03808_9
crossref_primary_10_1016_j_tws_2023_111439
crossref_primary_10_1007_s11431_022_2198_4
crossref_primary_10_1088_1361_665X_ada07d
crossref_primary_10_1016_j_addma_2023_103919
Cites_doi 10.1016/0045-7825(91)90046-9
10.1016/0045-7825(88)90086-2
10.1007/s10409-017-0679-2
10.1016/j.cma.2015.02.011
10.1002/nme.1620240207
10.1007/s00158-009-0452-7
10.1007/s00158-016-1551-x
10.1007/s10409-009-0240-z
10.1007/s00158-008-0250-7
10.1002/nme.1064
10.1007/s00419-015-1106-4
10.1016/j.cma.2011.08.006
10.3934/mbe.2020255
10.2351/1.4885235
10.1016/j.cma.2012.09.005
10.1007/s00158-018-2168-z
10.1016/j.cma.2018.04.040
10.1002/nme.2724
10.1002/nme.5461
10.1016/j.cma.2017.08.018
10.1016/j.cma.2018.01.037
10.1016/j.cma.2017.05.003
10.1016/j.cma.2012.08.020
10.1016/j.cma.2020.113385
10.1007/s00158-016-1459-5
10.1016/S0045-7825(00)00278-4
10.1016/j.cma.2009.06.001
10.1007/s00158-010-0602-y
10.1016/j.cma.2014.08.027
10.1007/s00158-018-2114-0
10.1016/j.compstruc.2018.10.011
10.1115/1.4028620
10.1080/17452759.2019.1637023
10.1007/s00158-009-0443-8
10.1002/nme.5575
10.1016/j.jcp.2017.09.041
10.1007/s00158-021-03077-w
10.1002/nme.285
10.1007/s00158-020-02607-2
10.1007/BF01650949
10.1007/s00170-012-4271-4
10.1007/s00158-016-1522-2
10.2514/6.2014-2036
10.7712/100016.2065.5873
ContentType Journal Article
Copyright Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2022
Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
Copyright_xml – notice: Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2022
– notice: Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
DBID AAYXX
CITATION
DOI 10.1007/s11431-021-1996-y
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1869-1900
EndPage 1231
ExternalDocumentID 10_1007_s11431_021_1996_y
GroupedDBID -5B
-5G
-BR
-EM
-SC
-S~
-Y2
-~C
.VR
06D
0R~
0VY
1N0
29~
2B.
2C.
2J2
2JN
2JY
2KG
2KM
2LR
2VQ
2~H
30V
4.4
406
40D
40E
5VR
5VS
8TC
8UJ
92E
92I
92Q
93N
95-
95.
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAXDM
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABDZT
ABECU
ABFTD
ABFTV
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACZOJ
ADHIR
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADYOE
ADZKW
AEBTG
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEMSY
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFLOW
AFQWF
AFUIB
AFWTZ
AFYQB
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHSBF
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMTXH
AMXSW
AMYLF
AOCGG
ARMRJ
ASPBG
AVWKF
AXYYD
AZFZN
B-.
BDATZ
BSONS
CAG
CAJEC
CCEZO
CEKLB
CHBEP
CJPJV
COF
CSCUP
CW9
DDRTE
DNIVK
DPUIP
EBLON
EBS
EIOEI
EJD
ESBYG
FA0
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
H13
HG6
HMJXF
HRMNR
HVGLF
HZ~
IJ-
IKXTQ
IWAJR
IXD
I~Z
J-C
JBSCW
JZLTJ
KOV
LLZTM
MA-
N2Q
NB0
NPVJJ
NQJWS
O9J
P9P
PF0
PT4
Q--
QOS
R89
RIG
ROL
RSV
S16
S3B
SAP
SCL
SEG
SHX
SISQX
SJYHP
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
TCJ
TGP
TR2
TSG
TUC
U1G
U2A
U5M
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
YLTOR
Z5O
Z7R
Z7S
Z7V
Z7X
Z7Y
Z7Z
Z85
Z88
ZMTXR
~A9
AAPKM
AAYXX
ABBRH
ABDBE
ABRTQ
ADHKG
AFDZB
AFOHR
AGQPQ
AHPBZ
ATHPR
AYFIA
CITATION
ID FETCH-LOGICAL-c316t-d5de3d20353ac5688a77d34e36a87d7d499c0ba809cfb21243db812f7772f17b3
IEDL.DBID RSV
ISICitedReferencesCount 8
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000797766700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1674-7321
IngestDate Thu Sep 25 00:44:44 EDT 2025
Sat Nov 29 05:32:41 EST 2025
Tue Nov 18 21:28:14 EST 2025
Fri Feb 21 02:49:21 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 6
Keywords overhang angle constraint
design for manufacturability
additive manufacturing
topology optimization
overhang length relaxation
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c316t-d5de3d20353ac5688a77d34e36a87d7d499c0ba809cfb21243db812f7772f17b3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2673615385
PQPubID 2043625
PageCount 19
ParticipantIDs proquest_journals_2673615385
crossref_citationtrail_10_1007_s11431_021_1996_y
crossref_primary_10_1007_s11431_021_1996_y
springer_journals_10_1007_s11431_021_1996_y
PublicationCentury 2000
PublicationDate 2022-06-01
PublicationDateYYYYMMDD 2022-06-01
PublicationDate_xml – month: 06
  year: 2022
  text: 2022-06-01
  day: 01
PublicationDecade 2020
PublicationPlace Beijing
PublicationPlace_xml – name: Beijing
– name: Heidelberg
PublicationTitle Science China. Technological sciences
PublicationTitleAbbrev Sci. China Technol. Sci
PublicationYear 2022
Publisher Science China Press
Springer Nature B.V
Publisher_xml – name: Science China Press
– name: Springer Nature B.V
References Guest, Prévost, Belytschko (CR15) 2004; 61
Li, Chen, Liu (CR22) 2016; 54
Zhang, Cheng (CR3) 2020; 35
Deng, To (CR37) 2020; 366
Liu, Yu (CR41) 2009; 142
Liu, Zhu, Sun (CR23) 2018; 58
Wang, Yang, Yi (CR28) 2013; 65
Zhou, Rozvany (CR32) 1991; 89
Pellens, Lombaert, Lazarov (CR42) 2019; 59
Poulsen (CR25) 2002; 53
Luo, Sigmund, Li (CR36) 2020; 372
Lazarov, Wang, Sigmund (CR17) 2016; 86
Johnson, Gaynor (CR12) 2018; 24
Schevenels, Lazarov, Sigmund (CR21) 2011; 200
CR8
Kang, Luo (CR19) 2009; 198
Svanberg (CR50) 1987; 24
Garaigordobil, Ansola, Fernandez de Bustos (CR40) 2021; 64
Qian (CR10) 2017; 111
Bruns, Tortorelli (CR48) 2001; 190
Gaynor, Guest (CR9) 2016; 54
Fu, Rolfe, Chiu (CR34) 2019; 14
Bendsøe (CR31) 1989; 1
Ven, Ayas, Langelaar (CR35) 2017
Wang, Gao, Kang (CR7) 2018; 339
Mertens, Clijsters, Kempen (CR30) 2014; 136
CR14
Zhang, Zhou (CR6) 2018; 334
Langelaar (CR13) 2016; 12
Bendsøe, Kikuchi (CR1) 1988; 71
Clausen, Aage, Sigmund (CR45) 2015; 290
Qian, Sigmund (CR20) 2013; 253
Zhang, Cheng, Xu (CR2) 2019; 212
Guest (CR43) 2009; 37
Wu, Clausen, Sigmund (CR44) 2017; 326
Kranz, Herzog, Emmelmann (CR29) 2015; 27
Xu, Cai, Cheng (CR47) 2010; 41
Groen, Sigmund (CR27) 2018; 113
Bourdin (CR49) 2001; 50
Langelaar (CR4) 2017; 55
Sigmund (CR52) 2009; 25
Fu (CR39) 2020; 17
Guo, Zhou, Zhang (CR11) 2017; 323
Guest, Smith Genut (CR26) 2010; 81
Clausen, Andreassen, Sigmund (CR46) 2017; 33
Zhou, Sigmund, Zhang (CR38) 2011; 396
Zhou, Liu, Wei (CR33) 2020; 61
Wang, Lazarov, Sigmund (CR51) 2011; 43
Zhang, Zhong, Guo (CR16) 2014; 282
Nguyen, Paulino, Song (CR24) 2010; 41
Allaire, Dapogny, Estevez (CR5) 2007; 351
Guo, Zhang, Zhang (CR18) 2013; 253
L Zhou (1996_CR38) 2011; 396
O Sigmund (1996_CR52) 2009; 25
B S Lazarov (1996_CR17) 2016; 86
W Zhang (1996_CR6) 2018; 334
S Xu (1996_CR47) 2010; 41
E Ven (1996_CR35) 2017
D Wang (1996_CR28) 2013; 65
X Qian (1996_CR10) 2017; 111
Y F Fu (1996_CR39) 2020; 17
J Wu (1996_CR44) 2017; 326
J K Guest (1996_CR43) 2009; 37
J K Liu (1996_CR41) 2009; 142
K Q Zhang (1996_CR3) 2020; 35
J Kranz (1996_CR29) 2015; 27
Q Li (1996_CR22) 2016; 54
A Clausen (1996_CR45) 2015; 290
Z Kang (1996_CR19) 2009; 198
H Deng (1996_CR37) 2020; 366
K Zhang (1996_CR2) 2019; 212
X Guo (1996_CR18) 2013; 253
M Zhou (1996_CR33) 2020; 61
T H Nguyen (1996_CR24) 2010; 41
J K Guest (1996_CR26) 2010; 81
Y Wang (1996_CR7) 2018; 339
M Zhou (1996_CR32) 1991; 89
M P Bendsøe (1996_CR31) 1989; 1
J P Groen (1996_CR27) 2018; 113
R Mertens (1996_CR30) 2014; 136
G Allaire (1996_CR5) 2007; 351
T E Johnson (1996_CR12) 2018; 24
T E Bruns (1996_CR48) 2001; 190
Y F Luo (1996_CR36) 2020; 372
Y F Fu (1996_CR34) 2019; 14
A Clausen (1996_CR46) 2017; 33
M Langelaar (1996_CR13) 2016; 12
J Pellens (1996_CR42) 2019; 59
X Qian (1996_CR20) 2013; 253
B Bourdin (1996_CR49) 2001; 50
A Garaigordobil (1996_CR40) 2021; 64
M Schevenels (1996_CR21) 2011; 200
J K Guest (1996_CR15) 2004; 61
M Langelaar (1996_CR4) 2017; 55
X Guo (1996_CR11) 2017; 323
A T Gaynor (1996_CR9) 2016; 54
1996_CR8
C Liu (1996_CR23) 2018; 58
W Zhang (1996_CR16) 2014; 282
F Wang (1996_CR51) 2011; 43
1996_CR14
T A Poulsen (1996_CR25) 2002; 53
K Svanberg (1996_CR50) 1987; 24
M P Bendsøe (1996_CR1) 1988; 71
References_xml – volume: 89
  start-page: 309
  year: 1991
  end-page: 336
  ident: CR32
  article-title: The COC algorithm, part II: topological, geometrical and generalized shape optimization
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/0045-7825(91)90046-9
– volume: 396
  start-page: 114110
  year: 2011
  ident: CR38
  article-title: Self-supporting structure design with feature-driven optimization approach for additive manufacturing
  publication-title: Comput Methods Appl Mech Eng
– volume: 71
  start-page: 197
  year: 1988
  end-page: 224
  ident: CR1
  article-title: Generating optimal topologies in structural design using a homogenization method
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/0045-7825(88)90086-2
– volume: 33
  start-page: 778
  year: 2017
  end-page: 791
  ident: CR46
  article-title: Topology optimization of 3D shell structures with porous infill
  publication-title: Acta Mech Sin
  doi: 10.1007/s10409-017-0679-2
– volume: 290
  start-page: 524
  year: 2015
  end-page: 541
  ident: CR45
  article-title: Topology optimization of coated structures and material interface problems
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2015.02.011
– volume: 24
  start-page: 359
  year: 1987
  end-page: 373
  ident: CR50
  article-title: The method of moving asymptotes—a new method for structural optimization
  publication-title: Int J Numer Meth Engng
  doi: 10.1002/nme.1620240207
– volume: 24
  start-page: 667
  year: 2018
  end-page: 686
  ident: CR12
  article-title: Three-dimensional projection-based topology optimization for prescribed-angle self-supporting additively manufactured structures
  publication-title: Addit Manuf
– volume: 41
  start-page: 495
  year: 2010
  end-page: 505
  ident: CR47
  article-title: Volume preserving nonlinear density filter based on Heaviside functions
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0452-7
– volume: 54
  start-page: 1157
  year: 2016
  end-page: 1172
  ident: CR9
  article-title: Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1551-x
– volume: 25
  start-page: 227
  year: 2009
  end-page: 239
  ident: CR52
  article-title: Manufacturing tolerant topology optimization
  publication-title: Acta Mech Sin
  doi: 10.1007/s10409-009-0240-z
– ident: CR8
– volume: 37
  start-page: 463
  year: 2009
  end-page: 473
  ident: CR43
  article-title: Imposing maximum length scale in topology optimization
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-008-0250-7
– volume: 61
  start-page: 238
  year: 2004
  end-page: 254
  ident: CR15
  article-title: Achieving minimum length scale in topology optimization using nodal design variables and projection functions
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.1064
– volume: 86
  start-page: 189
  year: 2016
  end-page: 218
  ident: CR17
  article-title: Length scale and manufacturability in density-based topology optimization
  publication-title: Arch Appl Mech
  doi: 10.1007/s00419-015-1106-4
– volume: 200
  start-page: 3613
  year: 2011
  end-page: 3627
  ident: CR21
  article-title: Robust topology optimization accounting for spatially varying manufacturing errors
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2011.08.006
– volume: 366
  start-page: 113093
  year: 2020
  ident: CR37
  article-title: Linear and nonlinear topology optimization design with projection-based ground structure method (P-GSM)
  publication-title: Int J Numer Methods Eng
– volume: 17
  start-page: 4631
  year: 2020
  end-page: 4656
  ident: CR39
  article-title: Recent advances and future trends in exploring Pareto-optimal topologies and additive manufacturing oriented topology optimization
  publication-title: Math Biosci Eng
  doi: 10.3934/mbe.2020255
– volume: 27
  start-page: S14001
  year: 2015
  end-page: 1
  ident: CR29
  article-title: Design guidelines for laser additive manufacturing of lightweight structures in TiAl6V4
  publication-title: J Laser Appl
  doi: 10.2351/1.4885235
– volume: 142
  start-page: 1
  year: 2009
  end-page: 19
  ident: CR41
  article-title: Self-support topology optimization with horizontal overhangs for additive manufacturing
  publication-title: J Manuf Sci Eng-Trans ASME
– volume: 253
  start-page: 356
  year: 2013
  end-page: 368
  ident: CR18
  article-title: Robust structural topology optimization considering boundary uncertainties
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2012.09.005
– volume: 59
  start-page: 2005
  year: 2019
  end-page: 2022
  ident: CR42
  article-title: Combined length scale and overhang angle control in minimum compliance topology optimization for additive manufacturing
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-018-2168-z
– volume: 339
  start-page: 591
  year: 2018
  end-page: 614
  ident: CR7
  article-title: Level set-based topology optimization with overhang constraint: Towards support-free additive manufacturing
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2018.04.040
– volume: 81
  start-page: 1019
  year: 2010
  end-page: 1045
  ident: CR26
  article-title: Reducing dimensionality in topology optimization using adaptive design variable fields
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.2724
– volume: 111
  start-page: 247
  year: 2017
  end-page: 272
  ident: CR10
  article-title: Undercut and overhang angle control in topology optimization: A density gradient based integral approach
  publication-title: Int J Numer Meth Engng
  doi: 10.1002/nme.5461
– volume: 326
  start-page: 358
  year: 2017
  end-page: 375
  ident: CR44
  article-title: Minimum compliance topology optimization of shell-infill composites for additive manufacturing
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2017.08.018
– volume: 12
  start-page: 60
  year: 2016
  end-page: 70
  ident: CR13
  article-title: Topology optimization of 3D self-supporting structures for additive manufacturing
  publication-title: Addit Manuf
– volume: 334
  start-page: 56
  year: 2018
  end-page: 78
  ident: CR6
  article-title: Topology optimization of self-supporting structures with polygon features for additive manufacturing
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2018.01.037
– volume: 323
  start-page: 27
  year: 2017
  end-page: 63
  ident: CR11
  article-title: Self-supporting structure design in additive manufacturing through explicit topology optimization
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2017.05.003
– volume: 253
  start-page: 237
  year: 2013
  end-page: 251
  ident: CR20
  article-title: Topological design of electromechanical actuators with robustness toward over- and under-etching
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2012.08.020
– volume: 372
  start-page: 113385
  year: 2020
  ident: CR36
  article-title: Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2020.113385
– ident: CR14
– volume: 54
  start-page: 971
  year: 2016
  end-page: 984
  ident: CR22
  article-title: Structural topology optimization considering connectivity constraint
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1459-5
– volume: 190
  start-page: 3443
  year: 2001
  end-page: 3459
  ident: CR48
  article-title: Topology optimization of non-linear elastic structures and compliant mechanisms
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/S0045-7825(00)00278-4
– volume: 198
  start-page: 3228
  year: 2009
  end-page: 3238
  ident: CR19
  article-title: Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2009.06.001
– volume: 35
  start-page: 101224
  year: 2020
  ident: CR3
  article-title: Three-dimensional high resolution topology optimization considering additive manufacturing constraints
  publication-title: Addit Manuf
– volume: 43
  start-page: 767
  year: 2011
  end-page: 784
  ident: CR51
  article-title: On projection methods, convergence and robust formulations in topology optimization
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-010-0602-y
– volume: 282
  start-page: 71
  year: 2014
  end-page: 86
  ident: CR16
  article-title: An explicit length scale control approach in SIMP-based topology optimization
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2014.08.027
– volume: 58
  start-page: 2455
  year: 2018
  end-page: 2479
  ident: CR23
  article-title: An efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-018-2114-0
– volume: 212
  start-page: 86
  year: 2019
  end-page: 100
  ident: CR2
  article-title: Topology optimization considering overhang constraint in additive manufacturing
  publication-title: Comput Struct
  doi: 10.1016/j.compstruc.2018.10.011
– volume: 136
  start-page: 61012
  year: 2014
  ident: CR30
  article-title: Optimization of scan strategies in selective laser melting of aluminum parts with downfacing areas
  publication-title: J Manuf Sci Eng
  doi: 10.1115/1.4028620
– volume: 14
  start-page: 382
  year: 2019
  end-page: 394
  ident: CR34
  article-title: Design and experimental validation of self-supporting topologies for additive manufacturing
  publication-title: Virtual Phys Prototyp
  doi: 10.1080/17452759.2019.1637023
– volume: 50
  start-page: 2143
  year: 2001
  end-page: 2158
  ident: CR49
  article-title: Filters in topology optimization
  publication-title: J Manuf Sci Eng-Trans ASME
– volume: 41
  start-page: 525
  year: 2010
  end-page: 539
  ident: CR24
  article-title: A computational paradigm for multiresolution topology optimization (MTOP)
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0443-8
– volume: 113
  start-page: 1148
  year: 2018
  end-page: 1163
  ident: CR27
  article-title: Homogenization-based topology optimization for high-resolution manufacturable microstructures
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.5575
– volume: 351
  start-page: 295
  year: 2007
  end-page: 328
  ident: CR5
  article-title: Structural optimization under overhang constraints imposed by additive manufacturing technologies
  publication-title: J Comput Phys
  doi: 10.1016/j.jcp.2017.09.041
– volume: 64
  start-page: 4065
  year: 2021
  end-page: 4078
  ident: CR40
  article-title: On preventing the dripping effect of overhang constraints in topology optimization for additive manufacturing
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-021-03077-w
– volume: 53
  start-page: 567
  year: 2002
  end-page: 582
  ident: CR25
  article-title: Topology optimization in wavelet space
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.285
– volume: 61
  start-page: 2423
  year: 2020
  end-page: 2435
  ident: CR33
  article-title: Topology optimization of easy-removal support structures for additive manufacturing
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-020-02607-2
– volume: 1
  start-page: 193
  year: 1989
  end-page: 202
  ident: CR31
  article-title: Optimal shape design as a material distribution problem
  publication-title: Struct Optim
  doi: 10.1007/BF01650949
– volume: 65
  start-page: 1471
  year: 2013
  end-page: 1484
  ident: CR28
  article-title: Research on the fabricating quality optimization of the overhanging surface in SLM process
  publication-title: Int J Adv Manuf Technol
  doi: 10.1007/s00170-012-4271-4
– volume: 55
  start-page: 871
  year: 2017
  end-page: 883
  ident: CR4
  article-title: An additive manufacturing filter for topology optimization of print-ready designs
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1522-2
– year: 2017
  ident: CR35
  article-title: A PDE-based approach to constrain the minimum overhang angle in topology optimization for additive manufacturing
  publication-title: Advances in Structural and Multidisciplinary Optimization
– volume: 50
  start-page: 2143
  year: 2001
  ident: 1996_CR49
  publication-title: J Manuf Sci Eng-Trans ASME
– volume: 14
  start-page: 382
  year: 2019
  ident: 1996_CR34
  publication-title: Virtual Phys Prototyp
  doi: 10.1080/17452759.2019.1637023
– volume: 326
  start-page: 358
  year: 2017
  ident: 1996_CR44
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2017.08.018
– volume: 142
  start-page: 1
  year: 2009
  ident: 1996_CR41
  publication-title: J Manuf Sci Eng-Trans ASME
– volume: 366
  start-page: 113093
  year: 2020
  ident: 1996_CR37
  publication-title: Int J Numer Methods Eng
– volume: 59
  start-page: 2005
  year: 2019
  ident: 1996_CR42
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-018-2168-z
– volume: 113
  start-page: 1148
  year: 2018
  ident: 1996_CR27
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.5575
– volume: 334
  start-page: 56
  year: 2018
  ident: 1996_CR6
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2018.01.037
– volume: 339
  start-page: 591
  year: 2018
  ident: 1996_CR7
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2018.04.040
– volume: 111
  start-page: 247
  year: 2017
  ident: 1996_CR10
  publication-title: Int J Numer Meth Engng
  doi: 10.1002/nme.5461
– volume: 212
  start-page: 86
  year: 2019
  ident: 1996_CR2
  publication-title: Comput Struct
  doi: 10.1016/j.compstruc.2018.10.011
– volume: 190
  start-page: 3443
  year: 2001
  ident: 1996_CR48
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/S0045-7825(00)00278-4
– volume: 61
  start-page: 2423
  year: 2020
  ident: 1996_CR33
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-020-02607-2
– volume: 41
  start-page: 525
  year: 2010
  ident: 1996_CR24
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0443-8
– volume: 17
  start-page: 4631
  year: 2020
  ident: 1996_CR39
  publication-title: Math Biosci Eng
  doi: 10.3934/mbe.2020255
– volume: 71
  start-page: 197
  year: 1988
  ident: 1996_CR1
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/0045-7825(88)90086-2
– volume: 396
  start-page: 114110
  year: 2011
  ident: 1996_CR38
  publication-title: Comput Methods Appl Mech Eng
– volume: 323
  start-page: 27
  year: 2017
  ident: 1996_CR11
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2017.05.003
– volume: 58
  start-page: 2455
  year: 2018
  ident: 1996_CR23
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-018-2114-0
– volume: 1
  start-page: 193
  year: 1989
  ident: 1996_CR31
  publication-title: Struct Optim
  doi: 10.1007/BF01650949
– volume: 282
  start-page: 71
  year: 2014
  ident: 1996_CR16
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2014.08.027
– volume: 43
  start-page: 767
  year: 2011
  ident: 1996_CR51
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-010-0602-y
– volume: 136
  start-page: 61012
  year: 2014
  ident: 1996_CR30
  publication-title: J Manuf Sci Eng
  doi: 10.1115/1.4028620
– volume: 64
  start-page: 4065
  year: 2021
  ident: 1996_CR40
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-021-03077-w
– volume: 54
  start-page: 1157
  year: 2016
  ident: 1996_CR9
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1551-x
– ident: 1996_CR8
  doi: 10.2514/6.2014-2036
– volume: 198
  start-page: 3228
  year: 2009
  ident: 1996_CR19
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2009.06.001
– volume: 27
  start-page: S14001
  year: 2015
  ident: 1996_CR29
  publication-title: J Laser Appl
  doi: 10.2351/1.4885235
– volume: 253
  start-page: 237
  year: 2013
  ident: 1996_CR20
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2012.08.020
– volume: 53
  start-page: 567
  year: 2002
  ident: 1996_CR25
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.285
– volume: 61
  start-page: 238
  year: 2004
  ident: 1996_CR15
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.1064
– volume: 12
  start-page: 60
  year: 2016
  ident: 1996_CR13
  publication-title: Addit Manuf
– volume: 86
  start-page: 189
  year: 2016
  ident: 1996_CR17
  publication-title: Arch Appl Mech
  doi: 10.1007/s00419-015-1106-4
– volume: 81
  start-page: 1019
  year: 2010
  ident: 1996_CR26
  publication-title: Int J Numer Meth Eng
  doi: 10.1002/nme.2724
– volume: 35
  start-page: 101224
  year: 2020
  ident: 1996_CR3
  publication-title: Addit Manuf
– volume: 89
  start-page: 309
  year: 1991
  ident: 1996_CR32
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/0045-7825(91)90046-9
– volume: 253
  start-page: 356
  year: 2013
  ident: 1996_CR18
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2012.09.005
– volume: 41
  start-page: 495
  year: 2010
  ident: 1996_CR47
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0452-7
– volume: 65
  start-page: 1471
  year: 2013
  ident: 1996_CR28
  publication-title: Int J Adv Manuf Technol
  doi: 10.1007/s00170-012-4271-4
– volume: 372
  start-page: 113385
  year: 2020
  ident: 1996_CR36
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2020.113385
– volume: 25
  start-page: 227
  year: 2009
  ident: 1996_CR52
  publication-title: Acta Mech Sin
  doi: 10.1007/s10409-009-0240-z
– volume: 24
  start-page: 667
  year: 2018
  ident: 1996_CR12
  publication-title: Addit Manuf
– volume: 24
  start-page: 359
  year: 1987
  ident: 1996_CR50
  publication-title: Int J Numer Meth Engng
  doi: 10.1002/nme.1620240207
– volume: 54
  start-page: 971
  year: 2016
  ident: 1996_CR22
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1459-5
– volume: 37
  start-page: 463
  year: 2009
  ident: 1996_CR43
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-008-0250-7
– volume: 55
  start-page: 871
  year: 2017
  ident: 1996_CR4
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-016-1522-2
– volume: 200
  start-page: 3613
  year: 2011
  ident: 1996_CR21
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2011.08.006
– volume: 290
  start-page: 524
  year: 2015
  ident: 1996_CR45
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/j.cma.2015.02.011
– ident: 1996_CR14
  doi: 10.7712/100016.2065.5873
– volume: 33
  start-page: 778
  year: 2017
  ident: 1996_CR46
  publication-title: Acta Mech Sin
  doi: 10.1007/s10409-017-0679-2
– volume: 351
  start-page: 295
  year: 2007
  ident: 1996_CR5
  publication-title: J Comput Phys
  doi: 10.1016/j.jcp.2017.09.041
– volume-title: Advances in Structural and Multidisciplinary Optimization
  year: 2017
  ident: 1996_CR35
SSID ssj0000389014
Score 2.326161
Snippet This paper studies additive manufacturing (AM) oriented structural topology optimization (TO). The minimum compliance design subject to overhang angle...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1213
SubjectTerms Additive manufacturing
Algorithms
Asymptotic methods
Design optimization
Engineering
Manufacturing
Optimization
Product design
Stress concentration
Structural members
Topology optimization
Upper bounds
Title Structural topology optimization subject to overhang angle constraint with overhang length relaxation in additive manufacturing
URI https://link.springer.com/article/10.1007/s11431-021-1996-y
https://www.proquest.com/docview/2673615385
Volume 65
WOSCitedRecordID wos000797766700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAVX
  databaseName: SpringerLink Contemporary
  customDbUrl:
  eissn: 1869-1900
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000389014
  issn: 1674-7321
  databaseCode: RSV
  dateStart: 20100101
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEF60etCDb7FaZQ-elECSTbLbo4jFgxSxKr2FfQUKbSq2FXvyrzuzSRoVFfSQQ7KbJdnHzOzsfN8Qcmq5iaUKAs9KWE2RYqEnBQs8oxMdKniWMQcUvuHdruj327cljntSRbtXR5JOUtdgN1DtsPUNA89Fzs6XyQpoO4H5Gu56jwvHCjLG-Y7TGwPsPc7CoDrN_K6Vz_qoNjK_nIs6ddPZ_NeHbpGN0rqkF8V02CZLNt8h6x84B3fJW88xxiLbBp0WGRLmdAyCY1QiMulkptA5A6UU4zvRo0zhGlqq0ZjEnBJTiv7buhjTscA9AmNei0YGOcVQJRSmdCTzGQIoHCJyjzx0ru4vr70yC4OnWZBMPRMby0zos5hJHSdCSM4NiyxLpOCGG9gyaV9J4bd1pkARRswosBoyDnZ7FnDF9kkjH-f2gFAWZyppt6XQEVhhAci3zBrta8FVpn2pm8SvxiLVJUU5_tUwrcmVsW9T6NsU-zadN8nZ4pWngp_jt8qtaoDTcqlO0hAj21Dux01yXg1oXfxjY4d_qn1E1kIETjj_TYs0YKjtMVnVL9PB5PnEzeB3P5HvuQ
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB50FdSDb3F95uBJKbRN23SPIoriuogvvJW8CgtaxV3FPfnXncm2WxUV9NBDmzS0mWRmMpnvC8COFSaWKgg8K3E2RYqHnkx54Bmd6FDhs5w7oHBbdDrp7W3rvMRx96ps92pL0mnqGuyGph2XvmHguczZwThMRGiwiDD_4vJmFFghxjjfcXpTgr0neBhUu5nftfLZHtVO5pd9UWdujub-9aHzMFt6l2x_OBwWYMwWizDzgXNwCd4uHWMssW2w_vCEhAF7QMVxXyIyWe9ZUXAGSxnld1JEmeF1Z5kmZ5LOlOgzit_WxXQcC94TMOZ12Ei3YJSqRMqU3cvimQAUDhG5DNdHh1cHx155CoOneZD0PRMby03o85hLHSdpKoUwPLI8kakwwuCSSftKpn5L5woNYcSNQq8hF-i354FQfAUaxUNhV4HxOFdJqyVTHaEXFqB-y63Rvk6FyrUvdRP8ShaZLinK6a_usppcmfo2w77NqG-zQRN2R688Dvk5fqu8UQk4K6dqLwsps430ftyEvUqgdfGPja39qfY2TB1fnbWz9knndB2mQwJRuFjOBjRQ7HYTJvVLv9t72nKj-R2EL_Kd
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB50FdGDb3F11Rw8KcW2aZvuUdRFUZaFVdlbyauwsFvFdsU9-dfN9GFVVBAPPbRJQ5tJMpPJfN8AHGqmfC4cx9LczCZPUNfiIXUsJQPpCvMspjlQ-IZ1u-Fg0O6VeU7TKtq9OpIsMA3I0pRkJ48qPqmBb0bNm22w61h5FO10FuY8jKPH7Xr__t3Jguxxds7vjcH2FqOuU51sftfKZ91UG5xfzkhz1dNZ-fdHr8JyaXWS02KYrMGMTtZh6QMX4Qa89nMmWWThIFmROWFKHsyCMi6RmiSdCHTamFKCcZ_oaSbmGmki0cjEXBMZQb9uXYxpWsw9AmZeikaGCcEQJlxkyZgnEwRW5EjJTbjrXNyeXVpldgZLUifILOUrTZVrU59y6QdhyBlT1NM04CFTTJmtlLQFD-22jIVRkB5VwlgTMTP2fOwwQbegkTwkehsI9WMRtNs8lJ6xzhyz7sVaSVuGTMTS5rIJdiWXSJbU5fhXo6gmXca-jUzfRti30bQJR--vPBa8Hb9VblXCjsopnEYuRryhPvCbcFwJty7-sbGdP9U-gIXeeSe6uepe78Kii9iK3MXTgoaRut6DefmcDdOn_XxgvwFLd_uB
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Structural+topology+optimization+subject+to+overhang+angle+constraint+with+overhang+length+relaxation+in+additive+manufacturing&rft.jtitle=Science+China.+Technological+sciences&rft.au=Zhang%2C+KaiQing&rft.au=Cheng%2C+GengDong&rft.au=Wang%2C+Yu&rft.date=2022-06-01&rft.pub=Science+China+Press&rft.issn=1674-7321&rft.eissn=1869-1900&rft.volume=65&rft.issue=6&rft.spage=1213&rft.epage=1231&rft_id=info:doi/10.1007%2Fs11431-021-1996-y&rft.externalDocID=10_1007_s11431_021_1996_y
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1674-7321&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1674-7321&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1674-7321&client=summon