Abstract
In view of the fact that the follow-up search for an optimal topology is affected by deleting a large number of high-relative-density elements. When the typical density interpolation approach, namely, solid isotropic microstructures with penalization (SIMP), is employed in the continuum structural topology optimization, a new density interpolation approach based on the logistic function is proposed in this paper. This method can weaken low-relative-density elements while enhancing high-relative-density elements by polarization, and then rationally realize polarization of the intermediate density elements. It can reduce the number of gray-scale elements as much as possible to get the optimal topology with distinct boundaries in conjunction with the sensitivity filtering method based on particle swarm optimization (PSO). Several typical numerical examples are given to demonstrate this method.
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Li, S. and Atluri, S.N., The MLPG mixed collocation method for material orientation and topology optimization of anisotropic solids and structures. CMES-Computer Modeling in Engineering & Sciences, 2008, 30: 37–56.
Hu, D., Sun, Z.H., Liang, C. and Han, X., A mesh-free algorithm for dynamic impact analysis of hyperelasticity. Acta Mechanica Solida Sinica, 2013, 26(6): 362–372.
Du, Y., Luo, Z., Tian, Q. and Chen, L., Topology optimization for thermo-mechanical compliant actuators using meshfree methods. Engineering Optimization, 2009, 41: 753–772.
Luo, Z., Gao, W. and Song, C., Design of multi-phase piezoelectric actuators. Journal of Intelligent Material Systems and Structures, 2010, 21(18): 1851–1865.
Huang, X., Xie, Y.M., Jia, B., Li, Q. and Zhou, S.W., Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity. Structural and Multidisciplinary Optimization, 2012, 46: 385–398.
Wang, Y.Q., Luo, Z., Zhang, N. and Kang, Z., Topological shape optimization of microstructural metamaterials using a level set method. Computational Materials Science, 2014, 87: 178–186.
Bendsøe, M.P. and Sigmund, O., Topology optimization: Theory, Methods, and Applications. Springer, Berlin Heidelberg, 2003.
Xie, Y.M. and Steven, G.P., A Simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885–896.
Rozvany, G.I.N., A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009, 37: 217–237.
Bendsøe, M.P. and Sigmund, O., Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69: 635–654.
Takezawa, A., Yoon, G.H., Jeong, S.H. and Kobashi, M., Structural topology optimization with strength and heat conduction constraints. Computer Methods in Applied Mechanics and Engineering, 2014, 276: 341–361.
Allaire, G., Jouve, F. and Toader, A.M., Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, 2004, 194: 363–393.
Luo, Z., Wang, M.Y., Wang, S. and Wei, P., A level set-based parameterization method for structural shape and topology optimization. International Journal for Numerical Methods in Engineering, 2008, 76(1): 1–26.
Sui, Y.K., Yang, D.Q. and Sun, H.C., Uniform ICM theory and method on optimization of structural topology for skeleton and continuum structures. Chinese Journal of Computational Mechanics, 2000, 17(1): 28–33.
Peng, X.R. and Sui, Y.K., Topological optimization of continuum structure with static and displacement and frequency constraints by ICM method. Chinese Journal of Computational Mechanics, 2006, 23(4): 391–396.
Wang, Y., Luo, Z. and Zhang, N., Topological optimization of structures using a multilevel nodal density-based approximant. CMES: Computer Modeling in Engineering & Sciences, 2012, 84(3): 229–252.
Luo, Z., Zhang, N., Wang, Y. and Gao, W., Topology optimization of structures using meshless density variable approximants. International Journal for Numerical Methods in Engineering, 2013, 93: 443–464.
Luo, Z., Chen, L., Yang, J., Zhang, Y. and Abdel-Malek, K., Fuzzy tolerance multilevel approach for structural topology optimization. Computers & structures, 2006, 84(3): 127–140.
Luo, Y., Kang, Z., Luo, Z. and Li, A., Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Structural and Multidisciplinary Optimization, 2009, 39(3): 297–310.
Fuchs, M.B., Jiny, S. and Peleg, N., The SRV constraint for 0/1 topological design. Structural and Multidisciplinary optimization, 2005, 30(4): 320–326.
Wang, M.Y. and Wang, S.Y., Bilateral filtering for structural topology optimization. International Journal for Numerical Methods in Engineering, 2005, 63(13): 1911–1938.
Groenwold, A.A. and Etman, L.F.P., A simple heuristic for gray-scale suppression in optimality criterion-based topology optimization. Structural and Multidisciplinary Optimization, 2009, 39(2): 217–225.
Kang, Z. and Wang, Y.Q., Structural topology optimization based on non-local Shepard interpolation of density field. Computer Methods in Applied Mechanics and Engineering, 2011, 200: 3515–3525.
James, K. and Russell, E., Particle Swarm Optimization. In proceeding(s) IEEE International Conference on Neural Networks, 1995, 4: 1942–1948.
Liu, N., Gao, W., Song, C., Zhang, N. and Pi, Y.L., Interval dynamic response analysis of vehicle-bridge interaction system with uncertainty. Journal of Sound and Vibration, 2013, 332(13): 3218–3231.
Svanberg, K., The method of moving asymptotes: a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359–373.
Sigmund, O., A 99 topology optimization code written in Matlab. Structural and Multidisciplinary optimization, 2001, 21: 120–127.
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Project supported by the National Natural Science Foundation of China (No. 51105229), the National Science Foundation for Distinguished Young Scholars of Hubei Province of China (No. 2013CFA022), the Science and Technology Support Program of Hubei Province of China (No. 2015BHE026) and the Fund Project of Outstanding Dissertation of China Three Gorges University (No. 2014PY026).
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Du, Y., Yan, S., Zhang, Y. et al. A modified interpolation approach for topology optimization. Acta Mech. Solida Sin. 28, 420–430 (2015). https://doi.org/10.1016/S0894-9166(15)30027-6
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DOI: https://doi.org/10.1016/S0894-9166(15)30027-6