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The ICM method with objective function transformed by variable discrete condition for continuum structure. (English) Zbl 1200.74117
Summary: 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
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##### 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
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