Nodal Evolutionary Computation Enhanced Level Set Algorithm for Structural Topology Optimization

Abstract:

This paper proposes an improved computational algorithm for structure topology optimization. It integrates the merits of Evolutionary Structure Optimization and Level Set Method (LSM) for structure topology optimization. Traditional LSM algorithm has some drawbacks, for instance, its optimal topology configuration is largely dependent on the structural topology initialization. Additionally, new holes cannot be evolved within the updated topology during the optimization iteration. The method proposed in this paper combines the merits of ESO techniques with the LSM scheme, allowing new holes to be automatically inserted in regions with low deformation energy at prescribed iterations of the optimization. The nodal neighboring region is a good selection. For complex structures in which holes cannot be properly inserted in advance, the proposed method considerably improves the ability of LSM to search the optimal topology. In addition to achieving more accurate results, the proposed method also yields higher efficiency during optimization. Benchmark problems are presented to show the effectiveness and robustness of the new proposed algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 337-342
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.337
• Online since: August 2010
• Authors: Hai Peng Jia, Chun Dong Jiang, Bo Liu, Dong Xing Cao, Chun Bo Jiang
• Keywords: Evolutionary Computation, Evolutionary Structure Optimization, Level Set Method (LSM), Structure Optimization, Topological Optimisation

References

[1] Xie Y. M., Steven G. P., Evolutionary structural optimization. Springer-Verlag, Berlin, German, (1997).

[2] John. H. Holland, Adaptation in nature and artificial system: an introductory analysis with applications to biology, control, and artificial intelligence. Cambridge, MA: MIT Press, (1975).

[3] M. P. Bendsøe, Optimal shape design as a material distribution problem, Structural and Multidisciplinary Optimization, Vol. 1(1989), p.193.

DOI: 10.1007/bf01650949

[4] Eschenauer H. A., Olhoff N., Topology optimization of continuum structures: a review, Applied Mechanics Review, Vol. 54(2001), p.331.

DOI: 10.1115/1.1388075

[5] Bendsoe M. P., Kikuchi N., Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Vol. 71(1988), p.197.

DOI: 10.1016/0045-7825(88)90086-2

[6] Makoto Ohsaki, Simultaneous optimization of topology and geometry of a regular plane truss, Computers and Structures, Vol. 66(1998), p.69.

DOI: 10.1016/s0045-7949(97)00050-3

[7] Chyi-Yeu Lin, Shin-Hong Lin, Artificial neural network based hole image interpretation techniques for integrated topology and shape optimization, Computer Methods in Applied Mechanics and Engineering, Vol. 194(2005), p.3817.

DOI: 10.1016/j.cma.2004.09.005

[8] Mehrdad Salami, Tim Hendtlass, A fast evaluation strategy for evolutionary algorithms, Applied Soft Computing, Vol. 2(2003), p.156.

DOI: 10.1016/s1568-4946(02)00067-4

[9] Soon Yu Woon, Liyong Tong, Osvaldo M. Querin and Grant P. Steven, Effective optimization of continuum topologies through a multi-GA system, Computer Methods in Applied Mechanics and Engineering, Vol. 194(2005), p.3416.

DOI: 10.1016/j.cma.2004.12.025

[10] X.Y. Yang, Y.M. Xie and G.P. Steven, Evolutionary methods for topology optimization of continuous structures with design dependent loads, Computers and Structures, Vol. 83(2005), p.956.

DOI: 10.1016/j.compstruc.2004.10.011

[11] Y. M. Xie, G. P. Steven, A simple evolutionary procedure for structure optimization, Computers and Structures, Vol. 49(1993), p.885.

DOI: 10.1016/0045-7949(93)90035-c

[12] G. P. Steven, Q. Li, Y. M. Xie, Multi-criteria optimization that minimizes maximum stress and maximizes stiffness, Computers and Structures, Vol. 80(2002), p.2433.

DOI: 10.1016/s0045-7949(02)00235-3

[13] G. Marckmann P. Bettess and B. Peseux, Self designing structures: a new evolutionary rule for thickness distribution in 2D problems, Communications in Numerical Methods in Engineering, Vol. 18(2002), p.743.

DOI: 10.1002/cnm.534

[14] H. A. Eschenauer, H. A. Kobelev, A. schumacher, Bubble method for topology and shape optimization of structures, Structural and Multidisciplinary Optimization, Vol. 8(1994), p.142.

DOI: 10.1007/bf01742933

[15] Stanley Osher, and Ronald P., Fedkiwy, Level set methods: an overview and some recent results, Journal of Computational Physics, Vol. 169(2001), p.463.

DOI: 10.1006/jcph.2000.6636

[16] J. A. Sethian, Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, Cambridge University Press, (1999).

DOI: 10.1016/s0997-7546(00)01096-7

[17] Stanley J. Osher, Ronald P., Fedkiw. Level set methods and dynamic implicit surfaces，Springer-Verlag, (2000).

[18] Stanley Osher, J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithm based on hamilton-jacobi formulations, Journal of Computational Physics, Vol. 79(1988), p.12.

DOI: 10.1016/0021-9991(88)90002-2

[19] J. A. Sethian and Andreas Wiegmann, Structural boundary design via level set and immersed interface methods, Journal of Computational Physics, Vol. 163(2000), p.489.

DOI: 10.1006/jcph.2000.6581

[20] Stanley J. Osher, Fadil Santosay, Level set methods for optimization problems involving geometry and constraints, Journal of Computational Physics, Vol. 171(2001), p.272.

DOI: 10.1006/jcph.2001.6789

[21] Michael Yu Wang, Xiaoming Wang, Dongming Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, Vol. 192(2003), p.227.

DOI: 10.1016/s0045-7825(02)00559-5

[22] G. Allaire, F. Jouve, A level-set method for vibration and multiple loads structural optimization, Computer Methods in Applied Mechanics and Engineering, Vol. 194(2005), p.3269.

DOI: 10.1016/j.cma.2004.12.018

[23] A. Rietz, Sufficiency of a finite exponent in SIMP (power law) methods, Structural and Multidisciplinary Optimization, Vol. 21(2001), pp.159-163.

DOI: 10.1007/s001580050180

[24] C. Y. Lin, L. S. Chao, Automated image interpretation for integrated topology and shape optimization, Structural and Multidisciplinary Optimization, Vol. 1(2000), p.125.

DOI: 10.1007/s001580050144