Abstract
Reliability and optimization are two key elements for structural design. The reliability-based topology optimization (RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach (the performance measure approach, PMA) and the decoupled approaches (the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method (SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.
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Bendsøe, M.P. and Kikuchi, N., Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224.
Bendsøe, M.P. and Sigmund, O., Topology Optimization: Theory, Methods and Applications. Berlin: Springer-Verlag Berlin Heidelberg Company, 2003.
Chen, C.Y., Pan, J. and Wang, D.Y., The satellite structure topology optimization based on homogenization method and its size sensitivity analysis. Acta Mechanica Solida Sinica, 2005, 18(2): 173–180.
Lee, J.O., Yang, Y.S. and Ruy, W.S., A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Computers & Structures, 2002, 80(3–4): 257–269.
Maute, K. and Frangopol, D.M., Reliability-based design of MEMS mechanisms by topology optimization. Computers & Structures, 2003, 81(8): 813824.
Kim, C., Wang, S.Y, Bae, K.R., Moon, H. and Choi, K.K., Reliability-based topology optimization with uncertainties. Journal of Mechanical Science and Technology, 2006, 20(4): 494–504.
Cho, K.H., Park, J.Y., Im, M.G. and Han, S.Y., Reliability-based topology optimization of electro-thermal-compliant mechanisms with a new material mixing method. International Journal of Precision Engineering and Manufacturing, 2012, 13(5): 693–699.
Kharmanda, G., Olhoff, N., Mohamed, A. and Lemaire, M., Reliability-based topology optimization. Structural and Multidisciplinary Optimization, 2004, 26(5): 295–307.
Silva, M., Tortorelli, D.A., Norato, J.A., Ha, C. and Bae, H.R., Component and system reliability-based topology optimization using a single-loop method. Structural and Multidisciplinary Optimization, 2010, 41(1): 87–106.
Nguyen, T.H., Song, J. and Paulino, G.H., Single-loop system reliability-based topology optimization considering statistical dependence between limit-states. Structural and Multidisciplinary Optimization, 2011, 44(5): 593–611.
Yoo, K.S., Eom, Y.S., Park, J.Y., et al., Reliability-based topology optimization using successive standard response surface method. Finite Elem Anal Des, 2011, 47(8): 843–849.
Eom, Y.S., Yoo, K.S., Park, J.Y. and Han, S.Y., Reliability-based topology optimization using a standard response surface method for three-dimensional structures. Structural and Multidisciplinary Optimization, 2011, 43(2): 287–295.
Suzuki, K. and Kikuchi, N., A homogenization method for shape and topology optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 93 (3): 291–318.
Bendsøe, M.P., Optimal shape design as a material distribution problem. Computers & Structures, 1989, 1(4): 193–202.
Xie, Y.M. and Steven, G.P., A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885–896.
Wang, M.Y., Wang, X. and Guo, D., A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1–2): 227–246.
Eschenauer, H.A. and Olhoff, N., Topology optimization of continuum structures: a review. Applied Mechanics Reviews, 2001, 54(4): 331–389.
Lee, S.H. and Chen, W., A comparative study of uncertainty propagation methods for black-box-type problems. Structural and Multidisciplinary Optimization, 2009, 37(3): 239–253.
Hasofer, A.M. and Lind, N.C., An exact and invariant first order reliability format. Journal of Engineering Mechanics—ASCE, 1974, 100(1): 111–121.
Rosenblatt, M., Remarks on a Multivariate Transformation. Annals of Mathematical Statistics, 1952, 23(3): 470–472.
Liu, P.L. and Kiureghian, A.D., Multivariate distribution models with prescribed marginals and covariances. Probabilistic Engineering Mechanics, 1986, 1(2): 105–112.
Tu, J. and Choi, K.K., A new study on reliability-based design optimization. Journal of Mechanical Design-ASME, 1999, 121(4): 557–564.
Wu, Y.T., Millwater, H.R. and Cruse, T.A., Advanced probabilistic structural analysis method for implicit performance functions. AIAA Journal, 1990, 28(9): 1663–1669.
Grujicic, M., Arakere, G., Bell, W.C., Marvi, H., Yalavarthy, H.V., Pandurangan, B., Haque, I. and Fadel, G.M., Reliability-Based Design Optimization for Durability of Ground Vehicle Suspension System Components. Journal of Materials Engineering and Performance, 2010, 19(3): 301–313.
Du, X. and Chen, W., Sequential optimization and reliability assessment method for efficient probabilistic design. Journal of Mechanical Design-ASME, 2004, 126(2): 225–233.
Isukapalli, S.S., Roy, A. and Georgopoulos, P.G., Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems. Risk Analysis, 1998, 18(3): 351–363.
Xiong, F.F., Chen, W., Xiong, Y. and Yang, S., Weighted stochastic response surface method considering sample weights. Structural and Multidisciplinary Optimization, 2011, 43(6): 837–849.
Smolyak, S.A., Quadrature and interpolation formulas for tensor products of certain classes of functions. Doklady Akademii nauk SSSR, 1963, 1(4): 240–243.
Yserentant, H., On the multi-level splitting of finite element spaces. Numerische Mathematik, 1986, 49(4): 379–412.
Xiong, F.F., Greene, S., Chen, W., Xiong, Y. and Yang, S.X., A new sparse grid based method for uncertainty propagation. Structural and Multidisciplinary Optimization, 2010, 41(3): 335–349.
Gerstner, T. and Griebel, M., Numerical integration using sparse grids. Numerical Algorithms, 1998, 18(3–4): 209–232.
Clenshaw, C.W. and Curtis, A.R., A method for numerical integration on an automatic computer. Numerische Mathematik, 1960, 2(1): 197–205.
Svanberg, K., The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359–373.
Sigmund, O., Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization, 2007, 33(4–5): 401–424.
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Project supported by the National Natural Science Foundation of China (Nos. 51275040 and 50905017), and the Programme of Introducing Talents of Discipline to Universities (No. B12022). The authors are also grateful to Krister Svanberg for providing his implementation of the MMA algorithm.
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Zhao, Q., Chen, X., Ma, Z. et al. A Comparison of Deterministic, Reliability-Based Topology Optimization under Uncertainties. Acta Mech. Solida Sin. 29, 31–45 (2016). https://doi.org/10.1016/S0894-9166(16)60005-8
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DOI: https://doi.org/10.1016/S0894-9166(16)60005-8