Skip to main content
SpringerLink
Log in

On topology optimization of linear and nonlinear plate problems

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper we propose a new restriction method based on employing C 0-continuous fields of density defined on a set of meshes different from the one used for the finite element analysis. The optimization procedure starts with using a coarse density-mesh compared to the finite element one. Once the convergence is obtained in the optimization steps, a finer density-mesh is nominated for the further steps. Linear and nonlinear plate behaviors are considered and formulated by Kirchhoff or Mindlin–Reissner hypothesis. Comparison is made with element/nodal based approaches using filter. The results show excellent and robust performance 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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Bendsøe MP, Sigmund O (2003) Topology optimization. Springer, Berlin

    Google Scholar 

  • Bourdin B (2001) Filters in topology optimization. Int J Numer Meth Eng 50:2143–2158

    Article  MATH  MathSciNet  Google Scholar 

  • Bruyneel M, Duysinx P, Fleury C (2002) A family of MMA approximations for structural optimization. Struct Multidisc Optim 24:263–276

    Article  Google Scholar 

  • Hughes TJR, Cohen M (1978) The “heterosis” finite element for plate bending. Comput Struct 9:445–450

    Article  MATH  Google Scholar 

  • Jog CS, Haber RB (1996) Stability of finite element models for distributed-parameter optimization and topology design. Comput Meth Appl Mech Eng 130:203–226

    Article  MATH  MathSciNet  Google Scholar 

  • Kemmler R, Lipka A, Ramm E (2005) Large deformations and stability in topology optimization. Struct Multidisc Optim 30:459–476

    Article  MathSciNet  Google Scholar 

  • Matsui K, Terada K (2004) Continuous approximation of material distribution for topology optimization. Int J Numer Meth Eng 59:1925–1944

    Article  MATH  MathSciNet  Google Scholar 

  • Pedersen NL (2001) On topology optimization of plates with prestress. Int J Numer Meth Eng 51:225–239

    Article  MATH  Google Scholar 

  • Rahmatalla S, Swan CC (2003) Continuum topology optimization of buckling-sensitive structures. AIAA J 41:1180–1189

    Article  Google Scholar 

  • Rahmatalla SF, Swan CC (2004) A Q4/Q4 Continuum structural topology optimization formulation. Struct Multidisc Optim 27:130–135

    Article  Google Scholar 

  • Reddy JN (2007) Theory and analysis of elastic plates and shells. CRC, New York

    Google Scholar 

  • Rozvany GIN (2001) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Multidisc Optim 21:90–108

    Article  Google Scholar 

  • Sigmund O (2001) A 99 line topology optimization code written in MATLAB. Struct Multidisc Optim 21:120–127

    Article  Google Scholar 

  • Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424

    Article  Google Scholar 

  • Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three phase topology optimization method. J Mech Phys Solids 46(7):1037–1067

    Article  MathSciNet  Google Scholar 

  • Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboard, mesh-dependencies and local minima. Struct Optim 16:68–75

    Article  Google Scholar 

  • Stegmann J, Lund E (2005) Nonlinear topology optimization of layered shell structures. Struct Multidisc Optim 29:349–360

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Svanberg K (1995) A globally convergent version of MMA without line search. In: Olhoff N, Rozvany GIN (eds) Proceedings of the first world congress of structural and multidisciplinary optimization-WCSMO1. Goslar, Germany, pp 9–16

    Google Scholar 

  • Timoshenko SP, Woinowsky-Krieger S (1970) Theory of plates and shells. McGraw-Hill, Singapore

    Google Scholar 

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

    Article  Google Scholar 

  • Zienkiewicz OC, Cheung YK (1964) The finite element method for analysis of elastic isotropic and orthotropic slabs. Proc Inst Civ Eng 28:471–488

    Google Scholar 

  • Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heineman, Stoneham, MA

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    B. Boroomand & A. R. Barekatein

Authors
  1. B. Boroomand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. R. Barekatein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Boroomand.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boroomand, B., Barekatein, A.R. On topology optimization of linear and nonlinear plate problems. Struct Multidisc Optim 39, 17–27 (2009). https://doi.org/10.1007/s00158-008-0311-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-008-0311-y

Keywords

Search

Navigation