Evolutionary topology optimization of continuum structures with stress constraints
Tóm tắt
In this work, we propose to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization design subject to both constraints on volume fraction and maximum von Mises stress. To this end, the aggregated p-norm global stress measure is first adopted to approximate the maximum stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one or multiple Lagrange multipliers. The Lagrange multipliers are employed to yield compromised designs of the compliance and the p-norm stress. An empirical scheme is developed for the determination of the Lagrange multipliers such that the maximum von Mises stress could be effectively constrained through the controlling of the aggregated p-norm stress. To further enforce the satisfaction of stress constraints, the stress norm parameter p is assigned to a higher value after attaining the objective volume. The update of the binary design variables lies in the computationally efficient sensitivity numbers derived using the adjoint method. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.
Tài liệu tham khảo
Allaire G, Jouve F (2008) Minimum stress optimal design with the level set method. Eng Anal Bound Elem 32:909–918
Cai S, Zhang W, Zhu J, Gao T (2014) Stress constrained shape and topology optimization with fixed mesh: a b-spline finite cell method combined with level set function. Comput Methods Appl Mech Eng 278:361–387
Cheng GD, Guo X (1997) ε-relaxed approach in structural topology optimization. Struct Multidiscip Optim 13:258–266
Cheng GD, Jiang Z (1992) Study on topology optimization with stress constraints. Eng Optim 20:129–148
Da D, Yvonnet J, Xia L, Li G (2018) Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage. Int J Numer Methods Eng 115(5):604–626
Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38
Duysinx P (1999) Topology optimization with different stress limits in tension and compression. Proceedings of the 3rd World Congress of Structural and Multidisciplinary Optimization WCSMO3
Duysinx P, Bendsøe M (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43:1453–1478
Duysinx P, Sigmund O (1998) New development in handling stress constraints in optimal material distribution. In: Proc. 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization. A collection of technical papers (held in St. Louis, Missouri), 3:1501–1509
Guo X, Zhang W, Wang M, Wei P (2011) Stress-related topology optimization via level set approach. Comput Methods Appl Mech Eng 200(47–48):3439–3452
Guo X, Zhang W, Zhong W (2014) Stress-related topology optimization of continuum structures involving multi-phase materials. Comput Methods Appl Mech Eng 268:632–655
Huang X, Xie YM (2007) Convergent and mesh-independent solutions for bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43:1039–1049
Huang X, Xie YM (2010) Evolutionary topology optimization of continuum structures with an additional displacement constraint. Struct Multidiscip Optim 40:409–416
Kirsch U (1990) On singular topologies in optimum structural design. Struct Multidiscip Optim. 2:133–142
Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41:605–620
Li Z, Shi T, Xia Q (2017) Eliminate localized eigenmodes in level set based topology optimization for the maximization of the first eigenfrequency of vibration. Adv Eng Softw 107:59–70
Luo Y, Wang MY, Kang Z (2013) An enhanced aggregation method for topology optimization with local stress constraints. Comput Methods Appl Mech Eng 254:31–41
Picelli R, Townsend S, Brampton C, Norato J, Kim H (2018) Stress-based shape and topology optimization with the level set method. Comput Methods Appl Mech Eng 329:1–23
Rozvany G (2001) On design-dependent constraints and singular topologies. Struct Multidiscip Optim 21:164–172
Rozvany G, Birker T (1994) On singular topologies in exact layout optimization. Struct Multidiscip Optim 8:228–235
Rozvany G, Sobieszczanski-Sobieski J (1992) New optimality criteria methods: forcing uniqueness of the adjoint strains by corner rounding at constraint intersections. Struct Multidiscip Optim 4:244–246
van Miegroet LV, Duysinx P (2007) Stress concentration minimization of 2D filets using X-fem and level set description. Struct Multidiscip Optim 33(4):425–438
Wei P, Wang MY (2009) Piecewise constant level set method for structural topology optimization. Int J Numer Methods Eng 78(4):379–402
Xia Q, Shi T, Liu S, Wang MY (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90-91:55–64
Xia Q, Shi T, Liu S, Wang MY (2013) Shape and topology optimization for tailoring stress in a local region to enhance performance of piezoresistive sensors. Comput Struct 114:98–105
Xia L, Da D, Yvonnet J (2018a) Topology optimization for maximizing the fracture resistance of quasi-brittle composites. Comput Methods Appl Mech Eng 15(332):234–254
Xia L, Xia Q, Huang X, Xie Y (2018b) Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch Comput Methods Eng 25(2):437–478
Xia L, Zhang L, Xia Q, Shi T (2018c) Stress-based topology optimization using bi-directional evolutionary structural optimization method. Comput Methods Appl Mech Eng 333:356–370
Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896
Yang R, Chen C (1996) Stress-based topology optimization. Struct Multidiscip Optim 12:98–105
Zhang W, Guo X, Wang MY, Wei P (2013) Optimal topology design of continuum structures with stress concentration alleviation via level set method. Int J Numer Methods Eng 93(9):942–959
Zhang W, Yuan J, Zhang J, Guo X (2016) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim 53(6):1243–1260
Zhang W, Chen J, Zhu X, Zhou J, Xue D, Lei X, Guo X (2017) Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach. Comput Methods Appl Mech Eng 322:590–614
Zhang W, Li D, Zhou J, Du Z, Li B, Guo X (2018) A Moving Morphable Void (MMV)-based explicit approach for topology optimization considering stress constraints. Comput Methods Appl Mech Eng 334:381–413
Zhou M, Sigmund O (2017) On fully stressed design and p-norm measures in structural optimization. Struct Multidiscip Optim 56(3):731–736
Zhu J, Zhang W, Xia L (2016) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng 23(4):595–622
Zuo ZH, Xie YM, Huang X (2012) Evolutionary topology optimization of structures with multiple displacement and frequency constraints. Adv Struct Eng 15(2):359–372