Concurrent Design of Structures and Materials Based on the Bi-Directional Evolutionary Structural Optimization

Abstract:

Different from the independent optimization of macrostructures or materials, a two-scale topology optimization algorithm is developed in this paper based on the bi-directional evolutionary structural optimization (BESO) method for concurrently designing a macrostructure and its composite microstructure. The objective is to minimize the mean compliance of the structure which is composed of a two-phase composite. The effective properties of the composite are calculated through the homogenization method and integrated into the finite element analysis of the structure. Sensitivity analysis for the structure and microstructure is conducted by the adjoint method. Based on the derived sensitivity numbers, the BESO approach is applied for iteratively updating the topologies for both the structure at the macro level and the microstructure of composite at the micro level. Numerical examples are presented to validate the effectiveness of the proposed optimization algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 438-439)
• Pages: 445-450
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.438-439.445
• Online since: October 2013
• Authors: Xiao Lei Yan, Xiao Dong Huang, Yi Min Xie
• Keywords: BESO, Concurrent Design, Homogenization, Topology Optimization

References

[1] M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71 (1988) 197-224.

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

[2] M. P. Bends, O. Sigmund, Topology Optimization: Theory, Methods and Applications, Springer-Verlag, Berlin, (2003).

[3] Y. M. Xie, G. P. Steven, A simple evolutionary procedure for structural optimization. Computers & Structures, 49 (1993) 885-896.

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

[4] J. A. Sethian, A. Wiegmann, Structural boundary design via level set and immersed interface methods, Journal of Computational Physics, Vol. 163 2 (2000) 489-528.

DOI: 10.1006/jcph.2000.6581

[5] X. Huang, Y. M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, John Wiley & Sons, Chichester, (2010).

[6] O. Sigmund, Tailoring materials with prescribed elastic properties, Mechanics of Materials, 20 (1995) 351-368.

DOI: 10.1016/0167-6636(94)00069-7

[7] J. K. Guest, J. H. Prévost, Design of maximum permeability material structures, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 1006-1017.

DOI: 10.1016/j.cma.2006.08.006

[8] X. Huang, A. Radman, Y. M. Xie, Topological design of microstructures of cellular materials for maximum bulk or shear modulus, Computational Materials Science, 50 (2011) 1861-1870.

DOI: 10.1016/j.commatsci.2011.01.030

[9] H. Rodrigues, J. M. Guedes, M. P. Bendsøe, Hierarchical optimization of material and structure, Structural and Multidisciplinary Optimization, Vol. 24 1 (2002) 1-10.

DOI: 10.1007/s00158-002-0209-z

[10] J. D. Deng, J. Yan, G. D. Cheng, Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material, Structural and Multidisciplinary Optimization, Vol. 47 4 (2013) 583-597.

DOI: 10.1007/s00158-012-0849-6

[11] X. Huang, S. W. Zhou, Y. M. Xie, Q. Li, Topology optimization of microstructures of cellular materials and composites for structures, Computational Materials Science, 67 (2013) 397-407.

DOI: 10.1016/j.commatsci.2012.09.018

[12] X. Huang, Y. M. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method, Finite Element in Analysis and Design, Vol. 43 14 (2007) 1039-1049.

DOI: 10.1016/j.finel.2007.06.006

[13] X. Huang, Y. M. Xie, Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials, Computational Mechanics, Vol. 43 3 (2009) 393-401.

DOI: 10.1007/s00466-008-0312-0