The ICM method with objective function transformed by variable discrete condition for continuum structure.

*(English)*Zbl 1200.74117Summary: ICM (Independent Continuous Mapping) method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

##### MSC:

74P15 | Topological methods for optimization problems in solid mechanics |

##### Keywords:

structural topological optimization; ICM method; checkerboard patterns; mesh dependence; the deleting rate
PDF
BibTeX
XML
Cite

\textit{Y. Sui} and \textit{X. Peng}, Acta Mech. Sin. 22, No. 1, 68--75 (2006; Zbl 1200.74117)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Bendsoe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 71, 197–224 (1998) |

[2] | Yang, R.J.: Topological optimization analysis with multiple constraints. American Society of Mechanical Engineers, Design Engineering Division 82, 393–398 (1995) |

[3] | Xie, Y.M., Steven, G.P.: Simple evolutionary procedure for structural optimization. Computers and Structures 49, 885–896 (1993) |

[4] | Sui, Y.K.: Modeling transformation and optimization new developments of structural synthesis method. Dalian University of Technology Press, Dalian, 1996 (in Chinese) |

[5] | Sui, Y.K., Yang, D.Q., Wang, P.: Topological optimization of continuum structure with stress and displacement constraints under multiple loading cases. Acta Mechanica Sinica 32, 171–179 (2000) (in Chinese) |

[6] | Sui, Y.K., Yu, X.: The exist-null combination method for the topological optimization of plane membrane structure. Acta Mechanica Sinica 33, 357–364 (2001) (in Chinese) |

[7] | Sui, Y.K., Yu, X., Ye, B.R.: The uniform model based on the exist-null combination for the truss and membrane topological optimization with stress constraint. Acta Mechanica Solida Sinica 22, 15–22 (2001) |

[8] | Sui, Y.K.: ICM Method of Topological Optimization for Truss, Frame and Continuum Structure. WWCSMO-4, 2001 |

[9] | Bendsoe, M.P., Diaz, A.R., Lipton, R., Taylor, J.E.: Optimal design of material properties and material distribution for multiple loading conditions. International Journal for Numerical Methods in Engineering 38, 1149–1170 (1995) · Zbl 0822.73047 |

[10] | Zhou, M., Rozvany, G.I.N.: On the validity of ESO type methods in topological optimization. Structural and Multidisciplinary Optimization 21, 80–83 (2001) |

[11] | Diaz, A., Sigmund, O.: Checkerboard patterns in layout optimization. Structural Optimization, 10, 40–45 (1995) |

[12] | Jog, C.S., Haber, R.B.: Stability of finite element models for distributed-parameter optimization and topological design. Computer Methods in Applied Mechanics and Engineering 130, 203–226 (1996) · Zbl 0861.73072 |

[13] | Sigmund, O., Petersson, J: Numerical instabilities in topological optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 16, 68–75 (1998) |

[14] | Yuan, Z., Wu, C.C., Zhuan, S.B.: Topological optimization of continuum structure using hybrid elements and artificial material model. Journal of China University of Science and Technology 31, 694–699 (2001) (in Chinese) |

[15] | Petersson, J., Sigmund, O.: Slope constrained topological optimization. International Journal for Numerical Methods in Engineering 41, 1417–1434 (1998) · Zbl 0907.73044 |

[16] | Sigmund, O.: On the design of compliant mechanisms using topological optimization. Mechanics of Structures and Machines 25, 493–524 (1997) |

[17] | Poulsen, T.A., Thomas, A.: A new scheme for imposing a minimum length scale in topological optimization. International Journal for Numerical Methods in Engineering 57, 741–760 (2003) · Zbl 1062.74592 |

[18] | Poulsen, T.A.: Topological optimization in wavelet space. International Journal for Numerical Methods in Engineering 53, 567–582 (2002) · Zbl 1112.74464 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.