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Independent continuous and mapping method of
structural topology optimization based on the global stress approach |
Yunkang SUI1,Jili FENG1,Hongling YE1,Xirong PENG2, |
1.Numerical Simulation
Center for Engineering, Beijing University of Technology, Beijing
100022, China; 2.Harbin Institute of
Technology Shenzhen Graduate School, Shenzhen 518055, China; |
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Abstract There are three difficulties in topology optimization of continuum structures. 1) The topology under multiple load case is more difficult to be optimized than under single load case, because the former becomes a multiple objective based on compliance objective functions. 2) With local constraints, such as an elemental stress limit, the topology is more difficult to be solved than with global constraints, such as the displacement or frequency limits, because the sensitivity analysis of the former has very expensive computation. 3) With the phenomenon of load illness, which is similar with stiffness illness in the structural analysis, it is not easy to get the reasonable final topological structure, because it is difficult to consider different influences between the loads with small forces and big forces, and some topology paths of transferring small forces may disappear during the iteration process. To overcome difficulties above, four measures are adopted. 1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises strength theory, all elements’ stress constraints are transformed into a structural energy constraint. 3) The phenomenon of load illness is divided to classify into three cases. 4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of load illness are solved in terms of different complementary approaches. Several numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of load illness can be solved well by the weighting method that takes the structural energy as a weighting coefficient.
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Keywords
independent continuous mapping (ICM) method
global stresses constraints
topology optimization
continuum structure
load illness
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Issue Date: 05 June 2010
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Sui Y K. Modeling, Transformation and Optimization: New Developmentsof Structural Synthesis Method. Dalian: Dalian University of Technology Press, 1996 (in Chinese)
|
|
Eschenauer H A, Olhoff N. Topology optimization of continuum structures: A review. Appl Mech Rev, 2001, 54(4): 331–390
doi: 10.1115/1.1388075
|
|
Cheng G D, Zhang D X. Topological optimization of plane elastic continuum with stress constraints. Journal of Dalian University of Technology, 1995, 35(1): 1–9 (in Chinese)
|
|
Wang J, Cheng G D. Optimal topology design of thin plate with stress constraints. Acta Mechnica Solida Sinics, 1997, 18(4): 317–322 (in Chinese)
|
|
Guan H S, Grant P, Xie Y M. Evolutionary structural optimizationincorporating tension and compression materials. Advances in Structural Engineering, 1999, 2(4): 273–288
|
|
Rong J H, Jiang J S, Hu D W, Yan D H, Fu J Q. A structural topology evolutionaryoptimization method based on stresses and their sensitivity. Acta Mechnica Sinica, 2003,3535(5): 584–591 (in Chinese)
|
|
Duysinx P, Bendsoe M P. Topology optimization of continuum structures with local stress constraints. International Journal for Numerical Methods inEngineering, 1998, 43(8): 1453–1478
doi: 10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2
|
|
Liu J S, Parks G T, Clarkson P J. Metamorphic development:A new topology optimization method for continuum structures. Structural and Multidisciplinary Optimization, 2000, 20(4): 288–300
doi: 10.1007/s001580050159
|
|
Sui Y K, Yang D Q, Wang P. Topological optimization of continuumstructure with stress and displacement constraints under multipleload cases. Acta Mechanics Sinica, 2000, 32(2): 171–179 (in Chinese)
|
|
Sui Y K, Yu X. The exist-null combination method for the topological optimization of plane membranestructure. Acta Mechanics Sinica, 2001, 3(33): 357–364 (in Chinese)
|
|
Wang J, Cheng G D. Topology optimization design of the continuum structure for multiple loadingconditions with stress constraints. Journal of Mechanical Strength, 2003, 5(1): 55–57
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