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http://dx.doi.org/10.12989/sem.2013.45.6.759

A topology optimization method of multiple load cases and constraints based on element independent nodal density  

Yi, Jijun (School of Mechanical and Electrical Engineering, Central South University)
Rong, Jianhua (School of Mechanical and Electrical Engineering, Changsha University of Science and Technology)
Zeng, Tao (School of Mechanical and Electrical Engineering, Central South University)
Huang, X. (School of Civil, Environmental and Chemical Engineering, RMIT University)
Publication Information
Structural Engineering and Mechanics / v.45, no.6, 2013 , pp. 759-777 More about this Journal
Abstract
In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.
Keywords
topology optimization; element independent nodal density; Shepard interpolation scheme; multiple load cases; multiple constraints; parallel computation;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Bendsoe, M.P. and Sigmund, O. (2003), Topology Optimization: Theory, Methods, and Applications. Springer-Verlag, New York, USA
2 Brodlie, K.W., Asim, M.R. and Unsworth, K. (2005), "Constrained visualization using the shepard interpolation family", Comput. Graphics Forum, 24(4), 809-820.   DOI   ScienceOn
3 Carbonari, R.C., Silva, E.C.N. and Nishiwaki, S. (2004), "Topology optimization applied to the design of multi-actuated piezoelectric micro-tools", Smart Structures and Materials 2004: Modeling, Signal Processing, and Control (Proceedings of SPIE), San Diego, USA, March.
4 Chapman, B., Jost, G. and Pas, R.V.D. (2007), Using OpenMP: Portable Shared Memory Parallel Programming, The MIT Press, Cambridge, Massachusetts, USA.
5 Colominas, I., Parıs, J., Navarrina, F. and Casteleiro, M. (2009), "High performance parallel computing in structural topology optimization", Proceedings of the 12th International Conference on Civil, Structural and Environmental Engineering Computing, Funchal, Portugal, September.
6 Diaz, A. and Sigmund, O. (1995), "Checkerboard patterns in layout optimization", Struct. Optim., 10(1), 40-45.   DOI   ScienceOn
7 Guest, J.K., Prevost, J.H. and Belytschko, T. (2004), "Achieving minimum length scale in topology optimization using nodal design variables and projection functions", Int. J. Numer. Meth. Eng., 61(2), 238-254.   DOI   ScienceOn
8 Huang, X. and Xie, Y. (2007), "Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method", FINITE ELEM. ANAL. DES., 43(14), 1039-1049.   DOI   ScienceOn
9 Huang, X. and Xie, Y.M. (2010), Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, John Wiley & Sons, Chichester, West Sussex, UK.
10 Jog, C.S. and Haber, R.B. (1996), "Stability of finite elements models for distributed-parameter optimization and topology design", Comput. Meth. Appl. Mech. Eng., 130(3-4), 203-226.   DOI   ScienceOn
11 Kang, Z. and Wang, Y.Q. (2011), "Structural topology optimization based on non-local Shepard interpolation of density field", Comput. Meth. Appl. Mech. Eng., 200(49-52), 3515-3525.   DOI   ScienceOn
12 Lee, D.K. (2007), "Combined topology and shape optimization of structures using nodal density as design parameter ", J. ASIAN. ARCHIT. BUILD., 6(1), 159-166.   DOI   ScienceOn
13 Lee, D.K., Kim, J.H., Starossek, U. and Shin, S.M. (2012), "Evaluation of structural outrigger belt truss layouts for tall buildings by using topology optimization", Struct. Eng. Mech., 43(6), 711-724.   DOI   ScienceOn
14 Lee, E.H. and Park, J. (2011), "Structural design using topology and shape optimization", Struct. Eng. Mech., 38(4), 517-527.   DOI   ScienceOn
15 Matsui, K. and Terada, K. (2004), "Continuous approximation of material distribution for topology optimization", Int. J. Numer. Meth. Eng., 59(14), 1925-1944.   DOI   ScienceOn
16 Paulino, G.H. and Le, C.H. (2009), "A modified Q4/Q4 element for topology optimization", Struct. Multidisc. Optim., 37(3), 255-264.   DOI
17 Poulsen, T.A. (2002), "Topology optimization in wavelet space", Int. J. Numer. Meth. Eng., 53(3), 567-582.   DOI   ScienceOn
18 Rahmatalla, S.F. and Swan, C.C. (2004), "A Q4/Q4 continuum structural topology optimization implementation", Struct. Multidisc. Optim., 27(1), 130-135.   DOI
19 Rong, J.H., Li, W.X. and Feng, B. (2010), "A structural topological optimization method based on varying displacement limits and design space adjustments", Adv. Mater. Res., 97-101, 3609.   DOI
20 Rong, J.H. and Liang, Q.Q. (2008), "A level set method for topology optimization of continuum structures with bounded design domains", Comput. Meth. Appl. Mech. Eng., 197(17-18), 1447-1465.   DOI   ScienceOn
21 Rozvany, G.I.N. (2001), "Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics", Struct. Multidisc. Optim., 21(2), 90-108.   DOI   ScienceOn
22 Beckers, M. (1999), "Topology optimization using a dual method with discrete variables", Struct. Optim., 17(1), 14-24.   DOI
23 Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Meth. Appl. Mech. Eng., 71(2), 197-224.   DOI   ScienceOn
24 Bendsoe, M.P. (1989), "Optimal shape design as a material distribution problem", Struct. Multidisc. Optim., 1(4), 193-202.   DOI
25 Sigmund, O. and Petersson, J. (1998), "Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima", Struct. Optim., 16(1), 68-75.   DOI   ScienceOn
26 Rozvany, G.I.N., Zhou, M. and Birker, T. (1992), "Generalized shape optimization without homogenization", Struct. Multidisc. Optim., 4(3-4), 250-254.   DOI
27 Sethian, A. and Wiegmann, A. (2000), "Structural boundary design via level set and immersed interface methods", J. Comput. Phys., 163(2), 489-528.   DOI   ScienceOn
28 Shepard, D. (1968), "A two-dimensional interpolation function for irregularly-spaced data", Proceedings of the 1968 23rd ACM National Conference, New York, January
29 Stolpe, M. and Svanberg, K. (2001), "An alternative interpolation scheme for minimum compliance topology optimization", Struct. Multidisc. Optim., 22(2), 116-124.   DOI   ScienceOn
30 Swan, C.C. and Kosaka, I. (1997), "Voigt-Reuss topology optimization for structures with linear elastic material behaviours", Int. J. Numer. Meth. Eng., 40(16), 3033-3057.   DOI
31 Wang, M.Y., Wang, X.M. and Guo, D.M. (2003), "A level set method for structural topology optimization", Comput. Meth. Appl. Mech. Eng., 192(1), 227-246.   DOI   ScienceOn
32 Xie, Y.M. and Steven, G.P. (1993), "A simple evolutionary procedure for structural optimization", Comput. Struct., 49(5), 885-896.   DOI   ScienceOn
33 Xie, Y.M. and Steven, G.P. (1997), Evolutionary Structural Optimization. Springer, Berlin, Germany.
34 Yang, R.J. and Chuang, C.H. (1994), "Optimal topology design using linear programming", Comput. Struct., 52(2), 265-275.   DOI   ScienceOn