Different effects of economic and structural performance indexes on model construction of structural topology optimization. (English) Zbl 1345.74094
Summary: The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper. The influences of their different roles in model construction of structural topology optimization are also discussed. Furthermore, two structural topology optimization models, optimizing a performance index under the limitation of an economic index, represented by the minimum compliance with a volume constraint (MCVC) model, and optimizing an economic index under the limitation of a performance index, represented by the minimum weight with a displacement constraint (MWDC) model, are presented. Based on a comparison of numerical example results, the conclusions can be summarized as follows: (1) under the same external loading and displacement performance conditions, the results of the MWDC model are almost equal to those of the MCVC model; (2) the MWDC model overcomes the difficulties and shortcomings of the MCVC model; this makes the MWDC model more feasible in model construction; (3) constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering, which have remained unchanged since the early days of mechanical engineering.
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
Keywords:
economic index; performance index; structural topology optimization models; MCVC model; MWDC model; safety and economySoftware:
top.mReferences:
| [1] | Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods and Applications. Springer, Berlin (2003) · Zbl 1059.74001 |
| [2] | Rozvany, G.I.N.: A critical review of established methods of structural topology optimization. Struct. Multidiscip. Optim. 37, 217-237 (2009) · Zbl 1274.74004 |
| [3] | Michell, A.G.M.: The limits of economy of material in frame structures. Philos. Mag. 8, 589-597 (1904) · JFM 35.0828.01 |
| [4] | Rozvany, G.I.N., Gollub, W.: Michell layouts for various combinations of line support. Int. J. Mech. Sci. 32, 1021-1043 (1990) · Zbl 0733.73053 |
| [5] | Rozvany, G.I.N.: Some shortcomings in Michell’s truss theory. Struct. Optim. 12, 244-250 (1996) · Zbl 0983.74050 |
| [6] | Sokół, T.: A 99 line code for discretized Michell truss optimization written in Mathematica. Struct. Multidiscip. Optim. 43, 181-190 (2011) · Zbl 1274.74008 |
| [7] | Rozvany, G.I.N., Sokół, T.: Exact truss topology optimization: allowance for support costs and different permissible stresses in tension and compression—extensions of a classical solution by Michell. Struct. Multidiscip. Optim. 45, 367-376 (2012) · Zbl 1274.74387 |
| [8] | Rozvany, G.I.N., Sokół, T., Pomezanski, V.: Extension of Michell’s theory to exact stress-based multi-load truss optimization. In: 10th World Congress on Structural and Multidisciplinary Optimization, Orlando, 19-24 May 2013 |
| [9] | Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197-224 (1988) · Zbl 0671.73065 |
| [10] | Hagishita, T., Ohsaki, M.: Topology optimization of trusses by growing ground structure method. Struct. Multidiscip. Optim. 37, 377-393 (2009) |
| [11] | Sokół, T.: Topology optimization of large-scale trusses using ground structure approach with selective subsets of active bars. In: CMM 2011 International Conference Computer Methods in Mechanics, Warsaw, 9-12 May 2011 |
| [12] | Tenek, L.H., Hagiwara, I.: Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization method. Comput. Methods Appl. Mech. Eng. 115, 111-124 (1994) |
| [13] | Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193-202 (1989) |
| [14] | Zhou, M., Rozvany, G.I.N.: The COC algorithm. Part II: Topological, geometry and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89, 309-336 (1991) |
| [15] | Rozvany, G.I.N., Zhou, M., Birker, T.: Generalized shape optimization without homogenization. Struct. Optim. 4, 250-252 (1992) |
| [16] | Lee, S.J., Bae, J.E., Hinton, E.: Shell topology optimization using the layered artificial material model. Int. J. Numer. Methods Eng. 47, 843-867 (2000) · Zbl 0983.74050 · doi:10.1002/(SICI)1097-0207(20000210)47:4<843::AID-NME801>3.0.CO;2-5 |
| [17] | Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885-896 (1993) |
| [18] | Tanskanen, P.: The evolutionary structural optimization method: theoretical aspects. Comput. Methods Appl. Mech. Eng. 191, 5485-5498 (2002) · Zbl 1083.74572 |
| [19] | Cervera, E., Trevelyan, J.: Evolutionary structural optimization based on boundary representation of NURBS. Part I: 2D algorithms. Comput. Struct. 83, 1902-1916 (2005) · doi:10.1016/j.compstruc.2005.02.016 |
| [20] | Sui, Y.K.: Modeling, Transformation and Optimization—New Developments of Structural Synthesis Method. Dalian University of Technology Press, Dalian (1996) |
| [21] | Sui, Y.K., Yang, D.Q.: A new method for structural topological optimization based on the concept of independent continuous variables and smooth model. Acta. Mech. Sin. 14, 179-185 (1998) |
| [22] | Sui, Y.K., Du, J.Z., Guo, Y.Q.: Topological optimization of frame structures under multiple loading cases. In: International Conference on Computational Methods, Singapore, 15-17 Dec. (2004) |
| [23] | Sui, Y.K., Peng, X.R.: The ICM method with objective function transformed by variable discrete condition for continuum structure. Acta. Mech. Sin. 22, 68-75 (2006) · Zbl 1200.74117 |
| [24] | Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163, 489-528 (2000) · Zbl 0994.74082 |
| [25] | Wang, M., Wang, X., Guo, D.: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192, 227-246 (2003) · Zbl 1083.74573 |
| [26] | Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363-393 (2004) · Zbl 1136.74368 |
| [27] | Guest, J.K., Asadpoure, A., Ha, S.H.: Eliminating beta-continuation from Heaviside projection and density filter algorithms. Struct. Multidiscip. Optim. 44, 443-453 (2011) · Zbl 1274.74337 |
| [28] | Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on Heaviside functions. Struct. Multidiscip. Optim. 41, 495-505 (2010) · Zbl 1274.74419 |
| [29] | Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33, 401-424 (2007) |
| [30] | Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 43, 767-784 (2011) · Zbl 1274.74409 |
| [31] | Guo, X., Zhang, W., Zhong, W.: Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J. Appl. Mech. 81, 081009-1-081009-12 (2014) |
| [32] | Sigmund, O.: A 99 line topology optimization code written in Matlab. Struct. Multidiscip. Optim. 21, 120-127 (2001) |
| [33] | Hibbeler, R.C.: Structural Analysis, 8th edn. Prentice Hall, Inc., Englewood Cliffs (2012) |
| [34] | Sun, H.C., Wang, Y.F., Chai, S.: Effects of hypothesis of static determinate on solutions of structural optimum designs. J. Dalian Univ. Technol. 45, 161-165 (2005) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
