SpringerLink
Log in

A Multi-point constraints based integrated layout and topology optimization design of multi-component systems

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The integrated layout and topology optimization is to find proper layout of movable components and topology patterns of their supporting structures, where two kinds of design variables, i.e. the structural pseudo-densities and the components’ locations are optimized simultaneously. The purpose of this paper is to demonstrate a new multi-point constraints (MPC) based method where the rivets or bolts connections between the components and their supporting structures are introduced. The displacement consistence involved in the MPC is strictly maintained which makes the components to carry the loads together with the supporting structures. Moreover, more benefits like avoidance of finite element remeshing and precise geometry of the components can be obtained. In particular, sensitivities with respect to the components’ locations can be analytically and efficiently achieved by deriving the MPC equations. Finally, several numerical examples are tested and discussed to demonstrate the validity of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Ainsworth M (2001) Essential boundary conditions and multi-point constraints in finite element analysis. Comput Methods Appl Mech Eng 190:6323–6339

    Article  MATH  MathSciNet  Google Scholar 

  • Allaire G, Jouve F, Maillot H (2004) Topology optimization for minimum stress design with the homogenization method. Struct Multidiscip Optim 28:87–98

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization: theory, method and application. Springer-Verlag, Berlin Heidelberg

    Google Scholar 

  • Bojczuk D, Mroz Z (1998) On optimal design of supports in beam and frame structures. Struct Multidiscip Optim 16:47–57

    Article  Google Scholar 

  • Bruyneel M, Duysinx P (2004) Note on topology optimization of continuum structures including self-weight. Struct Multidiscip Optim 29:245–256

    Article  Google Scholar 

  • Buhl T (2001) Simultaneous topology optimization of structure and supports. Struct Multidiscip Optim 23:336–346

    Article  Google Scholar 

  • Chickermane H, Gea HC (1997) Design of multi-component structural systems for optimal layout topology and joint locations. Engineering with Computers 13:235–243

    Article  Google Scholar 

  • Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49:1–38

    Article  MathSciNet  Google Scholar 

  • Guo X, Cheng G D (2010) Recent development in structural design and optimization. Acta Mech Sinica 26(6):807–823

    Article  MATH  MathSciNet  Google Scholar 

  • Kang Z, Wang YQ (2013) Integrated topology optimization with embedded movable holes based on combined description by material density and level sets. Comput Methods Appl Mech Eng 255:1–13

    Article  MATH  MathSciNet  Google Scholar 

  • Lee WS, Youn SK (2004) Topology optimization of rubber isolators considering static and dynamic behaviours. Struct Multidiscip Optim 27(4):284–294

    Article  Google Scholar 

  • Li Q, Steven GP, **e YM (2001) Evolutionary structural optimization for connection topology design of multi-component systems. Eng Comput 18:460–479

    Article  MATH  Google Scholar 

  • Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidiscip Optim 27:27–42

    Article  Google Scholar 

  • Ma ZD, Kikuchi N, Pierre C, Raju B (2006) Multidomain topology optimization for structural and material designs. J Appl Mech 73:565–573

    Article  MATH  MathSciNet  Google Scholar 

  • Niu B, Yan J, Cheng GD (2009) Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Struct Multidiscip Optim 39:115–132

    Article  Google Scholar 

  • Qian ZY, Ananthasuresh GK (2004) Optimal embedding of rigid objects in the topology design of structures. Mech Based Des Struct Mach 32:165–193

    Article  Google Scholar 

  • Radovcic Y, Remouchamps A (2002) BOSS QUATTRO: an open system for parametric design. Struct Multidiscip Optim 23(2):140–152

    Article  Google Scholar 

  • Remouchamps A, Bruyneel M, Fleury C, Grihon S (2011) Application of a bi-level scheme including topology optimization to the design of an aircraft pylon. Struct Multidiscip Optim 44(6):739–750

    Article  Google Scholar 

  • Shan P (2008) Optimal embedding objects in the topology design of structure. Master thesis of Dalian University of Technology.

  • Svanberg K (2007) On a globally convergent version of MMA. 7th World Congress on Structural and Multidisciplinary Optimization, COEX Seoul

    Google Scholar 

  • **a L, Zhu JH, Zhang WH (2012a) Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems. Comput Methods Appl Mech Eng 241-244:142–154

    Article  MathSciNet  Google Scholar 

  • **a L, Zhu JH, Zhang WH (2012b) A superelement formulation for the efficient layout design of complex multi-component system. Struct Multidiscip Optim 45:643–655

    Article  MATH  MathSciNet  Google Scholar 

  • **a L, Zhu JH, Zhang WH, Piotr B (2013) An implicit model for the integrated optimization of component layout and structure topology. Comput Methods Appl Mech Eng 257:87–102

    Article  MATH  Google Scholar 

  • Yan J, Liu L, Cheng GD, Liu ST (2008a) Concurrent material and structural optimization of hollow plate with truss-like material. Struct Multidiscip Optim 35:153–163

    Article  Google Scholar 

  • Yan J, Cheng GD, Liu L (2008b) A uniform optimum material based model for concurrent optimization of thermoelastic structures and materials. Int J Simul Multidiscip Des Optim 2:259–266

    Article  Google Scholar 

  • Yang XW, Li YM (2012) Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment

  • Yoon KH, Heo SP, Song KN, Jung YH (2004) Dynamic impact analysis of the grid structure using multi-point constraint (MPC) equation under the lateral impact load. Comput Struct 82(23–26):2221–2228

    Article  Google Scholar 

  • Zhang J, Zhang WH, Zhu JH (2012) Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput Methods Appl Mech Eng 245-246:75–89

    Article  Google Scholar 

  • Zhang WH, Zhu JH (2006) A new finite-circle family method for optimal multi-component packing design. WCCM VII, Los Angeles

    Google Scholar 

  • Zhang WS, Sun G, Guo X, Shan P (2013) A level set-based approach for simultaneous optimization of the structural topology and the layout of embedding structural components. Eng Mech 30(7):22–27

    Google Scholar 

  • Zhu JH, Zhang WH (2006) Coupled Design of Components Layout and Supporting Structures Using Shape and Topology Optimization. Proceedings of CJK-OSM IV 2006, Kunming China

  • Zhu JH, Zhang WH (2010) Integrated layout design of supports and structures. Comput Methods Appl Mech Eng 199(9-12):557– 569

    Article  MATH  Google Scholar 

  • Zhu JH, Zhang WH, Beckers P (2009) Integrated layout design of multi-component system. Int J Numer Methods Eng 78:631–651

    Article  MATH  Google Scholar 

  • Zhu JH, Zhang WH, Beckers P, Chen YZ, Guo ZZ (2008) Simultaneous design of components layout and supporting structures using coupled shape and topology optimization. Struct Multidiscip Optim 36(1):29–41

    Article  MATH  MathSciNet  Google Scholar 

  • Zhu JH, Zhang WH, **a L, Zhang Q, Bassir D (2012) Optimal Packing Configuration Design with Finite-Circle Method. J Intell Robot Syst 67:185–199

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China (90916027, 51275424, 11172236), 973 Program (2011CB610304), the 111 Project(B07050), Science and Technology Research and development projects in Shaanxi Province(2014KJXX-37), the Fundamental Research Funds for the Central Universities (3102014JC02020505).

Author information

Authors and Affiliations

  1. Engineering Simulation and Aerospace Computing (ESAC), Northwestern Polytechnical University, **’an, Shaanxi, 710072, China

    Ji-Hong Zhu, Huan-Huan Gao, Wei-Hong Zhang & Ying Zhou

Authors
  1. Ji-Hong Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huan-Huan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei-Hong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ying Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ji-Hong Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, JH., Gao, HH., Zhang, WH. et al. A Multi-point constraints based integrated layout and topology optimization design of multi-component systems. Struct Multidisc Optim 51, 397–407 (2015). https://doi.org/10.1007/s00158-014-1134-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-014-1134-7

Keywords

Search

Navigation