Skip to main content
SpringerLink
Log in

Meshless approximation combined with implicit topology description for optimization of continua

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

Abstract

The implicit topology description function method is integrated into Reproducing Kernel Particle Method and presents a new implementation of topology optimization of continua. The structural response analysis and the sensitivity analysis are carried out by using the meshless reproducing kernel approximations. Compared with mesh-based methods, the construction of an explicit mesh and the definition of nodal connectivity are avoided. The differences between the finite element method and the meshless method for topology optimization problems are highlighted. Formulations for imposition of concentrated forces and analysis of sensitivity in meshless method are derived in details. Several two-dimensional linear elastic topology optimization problems are solved successfully by the proposed method. The method is found robust and no checkerboarding is found in our numerical examples. Without any worry of mesh-entanglement, the method is expected to be further developed for the topology optimization of nonlinear structures with large deformations.

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

Similar content being viewed by others

References

  • Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overiew and recent developments. Comput Methods Appl Mech Eng 139:3–47

    Article  MATH  Google Scholar 

  • Belytschko T, Xiao SP, Parimi C (2003) Topology optimization with implicit function and regulization. Int J Numer Methods Eng 57:1177–1196

    Article  MATH  Google Scholar 

  • Bendsoe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Germany

    Google Scholar 

  • Bobaru F, Subrata M (2001) Shape sensitivity analysis and shape optimization in planar elasticity using the element-free Galerkin method. Comput Methods Appl Mech Eng 190:4319–4337

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Cho S, Kwak J (2006) Topology design optimization of geometrically non-linear structures using meshfree method. Comput Methods Appl Mech Eng 195:5909–5925

    Article  MATH  MathSciNet  Google Scholar 

  • Grindeanu I, Chang KH, Chen JS (1998) Design sensitivity analysis of hyperelastic structures using a meshless method. AIAA J 36:618–627

    Article  Google Scholar 

  • Guo X, Zhao K, Wang MY (2005) A new approach for simultaneous shape and topology optimization based on dynamic implicit surface functions. Control Cybern 34:255–282

    MathSciNet  Google Scholar 

  • Kim NH, Choi KK, Chen JS (2002) Botkin ME, Meshfree analysis and design sensitivity analysis for shell structures. Int J Numer Methods Eng 53:2087–2116

    Article  MATH  Google Scholar 

  • Kim NH, Choi KK, Botkin ME (2003) Numerical method for shape optimization using meshfree method. Struct Multidiscipl Optim 24:418–429

    Article  Google Scholar 

  • Li S, Liu WK (2002) Meshfree and particle methods and its applications. ASME Appl Mech Rev 55:1–34

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rozvany G, Zhou M (1991) The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336

    Article  Google Scholar 

  • Sethian J, Wiegmann A (2000) Structural boundary design via level-set and immersed interface methods. J Comput Phys 163:489–528

    Article  MATH  MathSciNet  Google Scholar 

  • Wang MY, Zhou S, Ding H (2004) Nonlinear diffusions in topology optimization. Struct Multidiscipl Optim 28:262–276

    Article  MathSciNet  Google Scholar 

  • Wang MY, Wang X, Guo D (2003) A level-set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–240

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Zhang ZQ, Zhou JX, Zhou N, Wang XM, Zhang L (2005) Shape optimization using reproducing kernel particle method and an enriched genetic algorithm. Comput Methods Appl Mech Eng 194:4048–4070

    Article  MATH  MathSciNet  Google Scholar 

  • Zhou JX, Wang XM, Zhang ZQ, Zhang L (2006) On the enhancement of computation and exploration of discretization approaches for meshless shape design sensitivity analysis. Struct Multidiscipl Optim 31:96–104

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    J. X. Zhou & W. Zou

Authors
  1. J. X. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. X. Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, J.X., Zou, W. Meshless approximation combined with implicit topology description for optimization of continua. Struct Multidisc Optim 36, 347–353 (2008). https://doi.org/10.1007/s00158-007-0168-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-007-0168-5

Keywords

Search

Navigation