Top

Engineering with Computers

Published in:

01-10-2016 | Original Article

Layout optimization for multi-bi-modulus materials system under multiple load cases

Authors: Jiao Shi, Jing Cao, Kun Cai, Zhenzhong Wang, Qing-Hua Qin

Published in: Engineering with Computers | Issue 4/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

An optimization model is presented for obtaining optimal layout of multiple bi-modulus materials systems under multiple load cases (MLC). In the optimization model, the objective function is the linearly weighted structural compliance under MLC. The bi-modulus materials in a finite element are replaced by isotropic materials according to the stress state of that element. The equivalent mechanical properties of an element are expressed as the power–law function of the volume fractions (design variables) and moduli of the solid phases. Numerical experiments are presented to verify the validity and efficiency of the present algorithm. The effects of factors including the bi-modulus behavior of materials, the load directions and the weighting schemes of MLC are also investigated numerically.

previous article More accurate results for two-dimensional heat equation with Neumann’s and non-classical boundary conditions

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin, pp 117–121

Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–390CrossRef

Cai K, Luo ZJ, Qin Q (2014) Topology optimization of bi-modulus structures using the concept of bone remodeling. Eng Comput 31(7):1361–1378CrossRef

Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH

Rozvany G, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252CrossRef

Qin QH, He XQ (1995) Variational principles, FE and MPT for analysis of non-linear impact-contact problems. Comput Methods Appl Mech Eng 122(3):205–222MathSciNetCrossRefMATH

Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896CrossRef

Huang X, Xie Y-M (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683CrossRef

Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1):227–246MathSciNetCrossRefMATH

10.

Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetCrossRefMATH

11.

Kota S, Joo J, Li Z, Rodgers SM, Sniegowski J (2001) Design of compliant mechanisms: applications to MEMS. Analog Integr Circuits Signal Process 29(1–2):7–15CrossRef

12.

Dühring MB, Jensen JS, Sigmund O (2008) Acoustic design by topology optimization. J Sound Vib 317(3–5):557–575CrossRef

13.

Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidiscip Optim 33(1):1–12CrossRef

14.

Gersborg-Hansen A, Sigmund O, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidiscip Optim 30(3):181–192MathSciNetCrossRefMATH

15.

Shi J, Cai K, Qin QH (2014) Optimal mass distribution prediction for human proximal femur with bi-modulus property. MCB: molecular and cellular. Biomechanics 11(4):235–248

16.

Gersborg-Hansen A, Bendsøe MP, Sigmund O (2006) Topology optimization of heat conduction problems using the finite volume method. Struct Multidiscip Optim 31:251–259MathSciNetCrossRefMATH

17.

Diaz A, Bendsøe M (1992) Shape optimization of structures for multiple loading conditions using a homogenization method. Struct Optim 4(1):17–22CrossRef

18.

Bendsøe MP, Díaz AR, Lipton R, Taylor JE (1995) Optimal design of material properties and material distribution for multiple loading conditions. Int J Numer Methods Eng 38(7):1149–1170MathSciNetCrossRefMATH

19.

Luo Z, Yang J, Chen L-P, Zhang Y-Q, Abdel-Malek K (2006) A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions. Struct Multidiscip Optim 31(1):26–39MathSciNetCrossRefMATH

20.

Sui YK, Du JZ, Guo YQ (2006) Topological optimization of frame structures under multiple loading cases. In: Liu GR et al (eds) Computational methods. Springer, pp 1015–1022

21.

Balamurugan R, Ramakrishnan CV, Swaminathan N (2006) Integrated optimal design of structures under multiple loads for topology and shape using genetic algorithm. Eng Comput 23(1):57–83CrossRefMATH

22.

Luo Z, Tong L, Luo J, Wei P, Wang MY (2009) Design of piezoelectric actuators using a multiphase level set method of piecewise constants. J Comput Phys 228(7):2643–2659MathSciNetCrossRefMATH

23.

Wang MY, Wang X (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193(6–8):469–496MathSciNetCrossRefMATH

24.

Allaire G, Dapogny C, Delgado G, Michailidis G (2013) Multi-phase structural optimization via a level set method. ESAIM: Control, Optim Calc Var 20:576–611MathSciNetCrossRefMATH

25.

Wang Y, Luo Z, Kang Z, Zhang N (2015) A multi-material level set-based topology and shape optimization method. Comput Methods Appl Mec Eng 283:1570–1586MathSciNetCrossRef

26.

Sigmund O (2001) Design of multiphysics actuators using topology optimization-Part II: two-material structures. Comput Methods Applied Mech Eng 190(49–50):6605–6627CrossRefMATH

27.

Luo Z, Gao W, Song C (2010) Design of multi-phase piezoelectric actuators. J Intell Mater Syst Struct 21(18):1851–1865CrossRef

28.

Guo X, Zhang W, Zhong W (2014) Stress-related topology optimization of continuum structures involving multi-phase materials. Comput Methods Appl Mech Eng 268:632–655MathSciNetCrossRefMATH

29.

Han S-Y, Lee S-K (2005) Development of a material mixing method based on evolutionary structural optimization. JSME Int J, Ser A 48(3):132–135MathSciNetCrossRef

30.

Wang MY, Zhou S (2005) Synthesis of shape and topology of multi-material structures with a phase-field method. J Comput-Aided Mater Des 11(2–3):117–138

31.

Ramani A (2009) A pseudo-sensitivity based discrete-variable approach to structural topology optimization with multiple materials. Struct Multidiscip Optim 41(6):913–934MathSciNetCrossRef

32.

Du Z, Guo X (2014) Variational principles and the related bounding theorems for bi-modulus materials. J Mech Phys Solids 73:183–211MathSciNetCrossRef

33.

Achtziger W (1996) Truss topology optimization including bar properties different for tension and compression. Struct Optim 12(1):63–74CrossRef

34.

Chang C, Zheng B, Gea H year (2007)Topology optimization for tension/compression only design. In: Proceedings of the 7th world congress on structural and multidisciplinary optimization. pp 2488–2495

35.

Cai K (2011) A simple approach to find optimal topology of a continuum with tension-only or compression-only material. Struct Multidiscip Optim 43(6):827–835CrossRef

36.

Querin OM, Victoria M, Martí P (2010) Topology optimization of truss-like continua with different material properties in tension and compression. Struct Multidiscip Optim 42(1):25–32CrossRef

37.

Cai K, Gao Z, Shi J (2013) Topology optimization of continuum structures with bi-modulus materials. Eng Optim 46(2):244–260MathSciNetCrossRef

38.

Qin QH, Wang H (2008) Matlab and C programming for Trefftz finite element methods. CRC Press, New YorkCrossRef

39.

Martin HC, Carey GF (1973) Introduction to finite element analysis: theory and applications. McGraw-Hill, New YorkMATH

40.

Qin QH (2000) The Trefftz finite and boundary element method. WIT, SouthamptonMATH

41.

Qin QH (2005) Trefftz finite element method and its applications. Appl Mech Rev 58(5):316–337CrossRef

42.

Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH

43.

Ansys: ANSYS (2012). www.ansys.com

44.

Cai K, Qin QH, Luo Z, Zhang AJ (2013) Robust topology optimisation of bi-modulus structures. Comput Aided Des 45(10):1159–1169CrossRef

Title: Layout optimization for multi-bi-modulus materials system under multiple load cases
Authors: Jiao Shi
Jing Cao
Kun Cai
Zhenzhong Wang
Qing-Hua Qin
Publication date: 01-10-2016
Publisher: Springer London
Published in: Engineering with Computers / Issue 4/2016
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-016-0450-5

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 4/2016

Recognition of virtual loops on 3D CAD models based on the B-rep model

Extreme learning machine assessment for estimating sediment transport in open channels

RETRACTED ARTICLE: Function finding for indirect determination of rock brittleness based on genetic programming and non-linear multiple regression models

More accurate results for two-dimensional heat equation with Neumann’s and non-classical boundary conditions

Back analysis for rock model surrounding underground roadways in coal mine based on black hole algorithm

Application of improved support vector regression model for prediction of deformation modulus of a rock mass