Abstract
Unsymmetrical complex plate and shell structure is one of the common engineering structures. In practice, more redundant materials exist because of the irrationality of this kind of structure with heavy load and multiple working conditions, and the study of its topology optimization has become an engaging topic. Using the SIMP model, topological results show that one side of the main web is a hollow structure, and the other side of the auxiliary web is a truss structure. According to the topological results and considering manufacturable processing, a new structure is redesigned, the size and shape of the redesigned structure is secondary optimized, and the final structure is obtained. The method in this paper not only meets the performance requirements of the unsymmetrical complex plate and shell structures, but also realizes the topology and lightweight. The effectiveness scientific research value of the proposed method is verified by engineering examples.
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Abbreviations
- X :
-
Design variable
- x e :
-
Relative density of the unit
- E :
-
Equivalent elastic modulus of the material
- E 0 :
-
Original elastic modulus of the material
- p :
-
Penalty factor
- C :
-
Compliance of the structure
- F :
-
External force vector of the structure
- U :
-
Displacement vector of the structure
- K :
-
Stiffness matrix of the structure
- u e :
-
Displacement column vector of material element
- k 0 :
-
Element stiffness matrix
- f :
-
Optimized ratio of material volume
- V 0 :
-
Initial volume of the design domain
- V :
-
Volume of the optimized structure
- v e :
-
Unit volume
- x min :
-
Minimum limits of the relative density of the element
- x max :
-
Maximum limits of the relative density of the element
- λ 1 :
-
Lagrange multiplier
- λ 2 :
-
Lagrange multiplier
- λ 3 :
-
Lagrange multiplier
- λ 4 :
-
Lagrange multiplier
- a e :
-
Relaxation factor
- b e :
-
Relaxation factor
- k :
-
Iteration algebra
- δ 1 :
-
Damping coefficient
- σ s :
-
Yield point
- σ b :
-
Tensile strength
- S :
-
Span length of main girder
References
D. D. Zhang, Y. Lv, Q. L. Zhao and F. Li, Development of lightweight emergency bridge using GFRP-metal composite plate-truss web, Engineering Structures, 196(109291) (2019) 1–22.
T. Evangelos and S. Martin, Messing with boundaries — quantifying the potential loss by preset par-ameters in topology optimization, Procedia CIRP, 84 (2019) 979–985.
X. D. Huang, Z. H. Zuo and Y. M. Xie, Evolutionary topological optimization of vibrating continuum structures for natural frequencies, Computers and Structures, 88(5–6) (2010) 357–364.
R. Ortigosa, D. Ruiz and A. J. Gil, A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method, Computer Methods in Applied Mechanics and Engineering, 364(112924) (2020) 1–24.
G. Ghanshyam, J. Vimal, K. Vivek and P. V. Savsani, Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics, Journal of Computational Design and Engineering, 5(2) (2018) 198–214.
M. Milomir, M. Mile and R. Radovan, Optimization of a pentagonal cross section of the truck crane boom using La-grange’s multipliers and differential evolution algorithm, Meccanica, 46 (2011) 845–853.
G. David, W. William and F. Mohamed, High-resolution nongradient topology optimization, Journal of Computational Physics, 372 (2018) 107–125.
N. P. Garcia-Lopez, M. Sanchez-Silva and A. L. Medaglia, A hybrid topology optimization methodology combining simulated annealing and SIMP, Computers and Structures, 89(15–16) (2011) 1512–1522.
B. Xu, L. Zhao, W. Y. Li, J. J. He and Y. M. Xie, Dynamic response reliability based topological optimization of continuum structures involving multi-phase materials, Composite Structures, 147 (2016) 134–144.
J. Davin et al., Developing topology optimization with additive manufacturing constraints in ANSYS®, IFAC-PapersOnLine, 51(11) (2018) 1359–1364.
R. Christian, F. W. Wang and S. Ole, Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis, Computer Methods in Applied Mechanics and Engineering, 339 (2018) 115–136.
X. W. Wu, B. Chen, D. Zhang and J. Li, The research on optimal design of large metallurgical crane, Procedia Engineering, 24 (2011) 783–787.
X. C. Jiang, H. Wang, Y. Li and K. J. Mo, Machine learning based parameter tuning strategy for MMC based topology optimization, Advances in Engineering Software, 149(102841) (2020) 1–11.
C. S. Edwards, H. A. Kim and C. J. Budd, An evaluative study on ESO and SIMP for optimising a cantilever tie—beam, Structural and Multidisciplinary Optimization, 34 (2007) 403–414.
H. T. Qiao, S. J. Wang, T. J. Zhao and H. Tang, Topology optimization for lightweight cellular material and structure simultaneously by combining SIMP with BESO, Journal of Mechanical Science and Technology, 33 (2019) 729–739.
A. Li, C. Liu and S. Z. Feng, Topology and thickness optimization of an indenter under stress and stiffness constraints, Journal of Mechanical Science and Technology, 32 (2018) 211–222.
H. P. Panganiban, W. C. Kim, T. J. Chung and G. W. Jang, Optimization of flatbed trailer frame using the ground beam structure approach, Journal of Mechanical Science and Technology, 30 (2016) 2083–2091.
S. Ole and M. Kurt, Topology optimization approaches, Structural and Multidisciplinary Optimization, 48 (2013) 1031–1055.
Acknowledgments
This work was supported by the 13th Five-Year National Key Research and Development Projects [2017YFC0703906], the Shanxi Provincial Key Research and Development Project [201903D121067], and the Fund for Shanxi “1331Project” Key Subjects Construction [1331KSC].
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Yangyang Zhang is a graduate student of the Taiyuan University of Science and Technology. His research interests include optimization design of engineering structure and hoisting machinery.
Yixiao Qin is a Professor and Doctoral Supervisor in the Taiyuan University of Science and Technology. He received his Ph.D. degree from the Shanghai Institute of Applied Mathematics and Mechanics. He is a Standards Committee and International fellow. His research interests include optimization design of engineering structure.
Jinpeng Gu is a Doctor of the Taiyuan University of Science and Technology. His research interests include mechanical vibration and green logistics.
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Zhang, Y., Qin, Y., Gu, J. et al. Topology optimization of unsymmetrical complex plate and shell structures bearing multicondition overload. J Mech Sci Technol 35, 3497–3506 (2021). https://doi.org/10.1007/s12206-021-0722-x
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DOI: https://doi.org/10.1007/s12206-021-0722-x