Non-probabilistic reliability-based multi-material topology optimization with stress constraint
Source abstract
Abstract
This article aims to develop a novel approach to non-probabilistic reliability-based multi-material topology optimization with stress constraints to address the optimization design problem considering external loading uncertainties. To be specific, the ordered solid isotropic material with penalization multi-material interpolation model is introduced into the non-probabilistic reliability-based topology optimization considering structural volume minimization under stress constraints, the multidimensional ellipsoidal model describes the non-probabilistic uncertainty. By utilizing the first-order reliability method, the failure probability can be estimated, and a non-probabilistic reliability index can be obtained. The global maximum stress is measured by adopting the normalized p-norm function method in combination with relaxation stress. The sensitivity analysis of the stress constraints is derived by the adjoint variable method, and the method of moving asymptote is employed to solve the design variables. Through several numerical examples, the effectiveness and feasibility of the presented method are verified to consider multi-material topology optimization with stress constraints in the absence of accurate probability distribution information of uncertain variables.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Topology Optimization in Engineering · Probabilistic and Robust Engineering Design · Composite Structure Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
Show source-provided references
1. Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363–393 (2004). https://doi.org/10.1016/j.jcp.2003.09.03210.1016/j.jcp.2003.09.032 ↗
2. Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Meth. Appl. Mech. Eng. 71, 197–224 (1988). https://doi.org/10.1016/0045-7825(88)90086-210.1016/0045-7825(88)90086-2 ↗
3. Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optimization. 1, 193–202 (1989). https://doi.org/10.1007/BF0165094910.1007/BF01650949 ↗
4. Ben-Haim, Y., Elishakoff, I.: Convex Models of Uncertainty in Applied Mechanics. Elsevier, Amsterdam (1990)
5. Ben-Haim, Y.: A non-probabilistic concept of reliability. Struct. Saf. 14, 227–245 (1994). https://doi.org/10.1016/0167-4730(94)90013-210.1016/0167-4730(94)90013-2 ↗
6. Bruggi, M.: On an alternative approach to stress constraints relaxation in topology optimization. Struct. Multidiscip. Optim. 36, 125–141 (2008). https://doi.org/10.1007/s00158-007-0203-610.1007/s00158-007-0203-6 ↗
7. Chen, J.L., Zhao, Q.H., Zhang, L.: Multi-material topology optimization of thermo-elastic structures with stress constraint. Mathematics 10, 1216 (2022). https://doi.org/10.3390/math1008121610.3390/math10081216 ↗
8. Chen, Z., Long, K., Wen, P., Nouman, S.: Fatigue-resistance topology optimization of continuum structure by penalizing the cumulative fatigue damage. Adv. Eng. Softw. 150, 102924 (2020). https://doi.org/10.1016/j.advengsoft.2020.10292410.1016/j.advengsoft.2020.102924 ↗
9. Cheng, G.D., Guo, X.: Epsilon-relaxed approach in structural topology optimization. Struct. Optim. 13, 258–266 (1997). https://doi.org/10.1007/BF0119745410.1007/BF01197454 ↗
10. Deng, Z., Guo, Z., Zhang, X.: Interval model updating using perturbation method and radial basis function neural networks. Mech. Syst. Signal Process 84, 699–716 (2017). https://doi.org/10.1016/j.ymssp.2016.09.00110.1016/j.ymssp.2016.09.001 ↗
11. Doan, Q.H., Lee, D., Lee, J., Kang, J.: Multi-material structural topology optimization with decision making of stiffness design criteria. Adv. Eng. Inform. 45, 101098 (2020). https://doi.org/10.1016/j.aei.2020.10109810.1016/j.aei.2020.101098 ↗
12. Elishakoff, I.: Are probabilistic and anti-optimization approaches compatible. In: Whys and Hows in Uncertainty Modelling, pp. 263–355. Springer, Vienna (1999)
13. Gao, J., Xue, H., Gao, L., Luo, Z.: Topology optimization for auxetic metamaterials based on isogeometric analysis. Comput. Meth. Appl. Mech. Eng. 352, 211–236 (2019). https://doi.org/10.1016/j.cma.2019.04.02110.1016/j.cma.2019.04.021 ↗
14. Giraldo-Londoño, O., Russ, J.B., Aguilo, M.A., Paulino, G.H.: Limiting the first principal stress in topology optimization: a local and consistent approach. Struct. Multidiscip. Optim. 65, 9 (2022). https://doi.org/10.1007/s00158-022-03320-y10.1007/s00158-022-03320-y ↗
15. Habashneh, M., Rad, M.M.: Reliability based topology optimization of thermoelastic structures using bi-directional evolutionary structural optimization method. Int. J. Mech. Mater. Des. (2023). https://doi.org/10.1007/s10999-023-09641-010.1007/s10999-023-09641-0 ↗
16. Han, Y.S., Xu, B., Duan, Z.Y., Huang, X.D.: Stress-based bi-directional evolutionary structural topology optimization considering nonlinear continuum damage. Comput. Meth. Appl. Mech. Eng. 396, 115086 (2022). https://doi.org/10.1016/j.cma.2022.11508610.1016/j.cma.2022.115086 ↗
17. Hong, L.X., Li, H.C., Fu, J.F., Li, J., Peng, K.: Hybrid active learning method for non-probabilistic reliability analysis with multi-super-ellipsoidal model. Reliab. Eng. Syst. Saf. 222, 108414 (2022). https://doi.org/10.1016/j.ress.2022.10841410.1016/j.ress.2022.108414 ↗
18. Jeong, S.H., Choi, D.H., Yoon, G.H.: Separable stress interpolation scheme for stress-based topology optimization with multiple homogenous materials. Finite Elem. Anal. Des. 82, 16–31 (2014). https://doi.org/10.1016/j.finel.2013.12.00310.1016/j.finel.2013.12.003 ↗
19. Jiang, C., Bai, Y.C., Han, X., Ning, H.M.: An efficient reliability-based optimization method for uncertain structures based on non-probability interval model. CMC-Comput. Mat. Contin. 18, 21–42 (2010)
20. Jiang, X.D., Ma, J.Q., Teng, X.Y.: Polygonal multiresolution topology optimization of multi-material structures subjected to dynamic loads. Int. J. Mech. Mater. Des. (2023). https://doi.org/10.1007/s10999-022-09631-8(2023).Accessed06February10.1007/s10999-022-09631-8(2023).Accessed06February ↗
21. Kang, Z., Luo, Y.J.: Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput. Meth Appl. Mech. Eng. 198, 3228–3238 (2009). https://doi.org/10.1016/j.cma.2009.06.00110.1016/j.cma.2009.06.001 ↗
22. Khachiyan, L.G.: Rounding of polytopes in the real number model of computation. Math. Oper. Res. 21(2), 307–320 (1996). https://doi.org/10.1287/moor.21.2.30710.1287/moor.21.2.307 ↗
23. Kharmanda, G., Olhoff, N., Mohamed, A.: Reliability-based topology optimization. Struct. Multidiscip. Optim. 26(295), 307 (2004). https://doi.org/10.1007/s00158-003-0322-710.1007/s00158-003-0322-7 ↗
24. Le, C., Norato, J., Bruns, T., Ha, C., Tortorelli, D.: Stress-based topology optimization for continua. Struct. Multidiscip. Optim. 41(4), 605–620 (2010). https://doi.org/10.1007/s00158-009-0440-y10.1007/s00158-009-0440-y ↗
25. Li, X.Q., Zhao, Q.H., Long, K., Zhang, H.X.: Multi-material topology optimization of transient heat conduction structure with functional gradient constraint. Int. Commun. Heat Mass Transf. 131, 105845 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2021.10584510.1016/j.icheatmasstransfer.2021.105845 ↗
26. Long, K., Wang, X., Gu, X.G.: Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm. Eng. Optim. 50, 2091–2107 (2018). https://doi.org/10.1080/0305215X.2017.141740110.1080/0305215X.2017.1417401 ↗
27. Lu, F.Y., Long, K., Zhang, C.W., Zhang, J.H., Tao, T.: A novel design of the offshore wind turbine tripod structure using topology optimization methodology. Ocean Eng. 280, 114607 (2023). https://doi.org/10.1016/j.oceaneng.2023.11460710.1016/j.oceaneng.2023.114607 ↗
28. Meng, Z., Yang, G., Wang, Q., Wang, X., Li, Q.H.: Reliability-based topology optimization of vibrating structures with frequency constraints. Int. J. Mech. Mater. Des. (2023). https://doi.org/10.1007/s10999-022-09637-2(2023).Accessed15January10.1007/s10999-022-09637-2(2023).Accessed15January ↗
29. Moens, D., Vandepitte, D.: Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis. Arch. Comput. Method. Eng. 13, 389–464 (2006). https://doi.org/10.1007/BF0273639810.1007/BF02736398 ↗
30. Moller, B., Beer, M.: Engineering computation under uncertainty-capabilities of non-traditional models. Comput. Struct. 86, 1024–1041 (2007). https://doi.org/10.1016/j.compstruc.2007.05.04110.1016/j.compstruc.2007.05.041 ↗
31. Ni, B.Y., Jiang, C., Huang, Z.L.: Discussions on non-probabilistic convex modelling for uncertain problems. Appl. Math. Model. 59, 54–85 (2018). https://doi.org/10.1016/j.apm.2018.01.02610.1016/j.apm.2018.01.026 ↗
32. Pantelides, C.P., Ganzerli, S.: Design of trusses under uncertain loads using convex models. J. Struct. Eng. 124(3), 318–329 (1998). https://doi.org/10.1061/(ASCE)0733-9445(1998)124:3(318)10.1061/(ASCE)0733-9445(1998)124:3(318) ↗
33. Petersson, J., Sigmund, O.: Slope constrained topology optimization. Int. J. Numer. Meth. Engng. 41, 1417–1434 (1998). https://doi.org/10.1002/(sici)1097-0207(19980430)41:8%3c1417::aid-nme344%3e3.0.co;2-n10.1002/(sici)1097-0207(19980430)41:8<1417::aid-nme344>3.0.co;2-n ↗
34. Rackwitz, R., Flessler, B.: Structural reliability under combined random load sequences. Comput. Struct. 9(5), 489–494 (1978). https://doi.org/10.1016/0045-7949(78)90046-910.1016/0045-7949(78)90046-9 ↗
35. Rosenblatt, M.: Remarks on a multivariate transformation. Ann. Math. Statist. 23(3), 470–472 (1952). https://doi.org/10.1214/aoms/117772939410.1214/aoms/1177729394 ↗
36. Rozvany, G.I.N., Zhou, M., Birker, T.: Generalized shape optimization without homogenization Struct. Optim. 4, 250–252 (1992). https://doi.org/10.1007/bf0174275410.1007/bf01742754 ↗
37. Senhora, F.V., Giraldo-Londoño, O., Menezes, I.F.M., Paulino, G.H.: Topology optimization with local stress constraints: a stress aggregation-free approach. Struct Multidiscip Optim. 62, 1639–1668 (2020). https://doi.org/10.1007/s00158-020-02573-910.1007/s00158-020-02573-9 ↗
38. Sha, W., Xiao, M., Gao, L., Zhang, Y.: A new level set based multi-material topology optimization method using alternating active-phase algorithm. Comput. Methods Appl. Mech. Eng. 377, 113674 (2021). https://doi.org/10.1016/j.cma.2021.11367410.1016/j.cma.2021.113674 ↗
39. Wang, M.Y., Wang, X., Guo, D.: A level set method for structural topology optimization. Comput. Meth. Appl. Mech. Eng. 192, 227–246 (2003). https://doi.org/10.1016/S0045-7825(02)00559-510.1016/S0045-7825(02)00559-5 ↗
40. Wang, X., Meng, Z., Yang, B., Cheng, C.Z., Long, K., Li, J.C.: Reliability-based design optimization of material orientation and structural topology of fiber-reinforced composite structures under load uncertainty. Compos. Struct. 291, 115537 (2022). https://doi.org/10.1016/j.compstruct.2022.11553710.1016/j.compstruct.2022.115537 ↗
41. Xia, H.J., Qiu, Z.P.: An efficient sequential strategy for non-probabilistic reliability-based topology optimization (NRBTO) of continuum structures with stress constraints. Appl. Math. Model. 110, 723–747 (2022). https://doi.org/10.1016/j.apm.2022.06.02110.1016/j.apm.2022.06.021 ↗
42. Xia, L., Zhang, L., Xia, Q., Shi, T.: Stress-based topology optimization using bi-directional evolutionary structural optimization method. Comput. Meth. Appl. Mech. Eng. 333, 356–370 (2018). https://doi.org/10.1016/j.cma.2018.01.03510.1016/j.cma.2018.01.035 ↗
43. Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885–896 (1993). https://doi.org/10.1016/0045-7949(93)90035-C10.1016/0045-7949(93)90035-C ↗
44. Yang, R.J., Chen, C.J.: Stress-based topology optimization. Struct. Optim. 12, 98–105 (1996). https://doi.org/10.1007/BF0119694110.1007/BF01196941 ↗
45. Zhang, L., Zhao, Q.H., Chen, J.L.: Reliability-based topology optimization of thermo-elastic structures with stress constraint. Mathematics. 10, 1091 (2022). https://doi.org/10.3390/math1007109110.3390/math10071091 ↗
46. Zhang, W.S., Guo, X., Wang, M.Y., Wei, P.: Optimal topology design of continuum structures with stress concentration alleviation via level set method. Int. J. Numer. Methods Eng. 93, 942–959 (2013). https://doi.org/10.1002/nme.441610.1002/nme.4416 ↗
47. Zhao, Q.H., Zhang, H.X., Zhang, T.Z., Hua, Q.S., Yuan, L., Wang, W.Y.: An efficient strategy for non-probabilistic reliability-based multi-material topology optimization with evidence theory. Acta Mech. Solida Sin. 32, 803–821 (2019). https://doi.org/10.1007/s10338-019-00121-710.1007/s10338-019-00121-7 ↗
48. Zheng, J., Zhang, G.T., Jiang, C.: Stress-based topology optimization of thermoelastic structures considering self-support constraints. Comput. Meth. Appl. Mech. Eng. 408, 115957 (2023). https://doi.org/10.1016/j.cma.2023.11595710.1016/j.cma.2023.115957 ↗
49. Zuo, W.J., Saitou, K.: Multi-material topology optimization using ordered SIMP interpolation. Struct. Multidiscip. Optim. 55, 477–491 (2017). https://doi.org/10.1007/s00158-016-1513-310.1007/s00158-016-1513-3 ↗