Abstract
In this work, a new thickness parameterization which allows for internal ply-drops without intermediate voids is introduced in the Discrete Material and Thickness Optimization (DMTO) method. With the original DMTO formulation, material had to be removed from the top in order to prevent non-physical intermediate voids in the structure. The new thickness formulation relies on a relation between density variables and ply-thicknesses rather than constitutive properties. This new formulation allows internal ply-drops which is essential for composite structures as it is common practice to cover dropped plies as to avoid delaminations. Furthermore, it is demonstrated how the new thickness formulation in some cases improves the convergence characteristics. Finally, it is also shown how solid-shell elements can be utilized within the DMTO method for structural optimization of tapered laminated composite structures.
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References
Albanesi A, Bre F, Fachinotti V, Gebhardt C (2018) Simultaneous ply-order, ply-number and ply-drop optimization of laminate wind turbine blades using the inverse finite element method. Compos Struct 184:894–903. https://doi.org/10.1016/J.COMPSTRUCT.2017.10.051
ANSYS Inc (2017) ANSYS 18 mechanical APDL theory reference. Tech. rep., ANSYS, Inc. Canonsburg, Pennsylvania, USA
Bloomfield MW, Herencia JE, Weaver PM (2009) Enhanced two-level optimization of anisotropic laminated composite plates with strength and buckling constraints. Thin-Walled Struct 47(11):1161–1167. https://doi.org/10.1016/J.TWS.2009.04.008
Bruyneel M (2011) SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim 43(1):17–27. https://doi.org/10.1007/s00158-010-0548-0
Gao T, Zhang WH, Duysinx P (2013) Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Struct Multidiscip Optim 48(6):1075–1088. https://doi.org/10.1007/s00158-013-0948-z
Gill PE, Murray W, Saunders MA (2005) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev 47(1):99–131. https://doi.org/10.1137/S0036144504446096
Haftka RT, Gürdal Z (1992) Elements of structural optimization. Kluwer Academic Publishers
Hvejsel CF, Lund E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43(6):811–825. https://doi.org/10.1007/s00158-011-0625-z
Irisarri FX, Lasseigne A, Leroy FH, Le Riche R (2014) Optimal design of laminated composite structures with ply drops using stacking sequence tables. Compos Struct 107:559–569. https://doi.org/10.1016/J.COMPSTRUCT.2013.08.030
Irisarri FX, Peeters DM, Abdalla MM (2016) Optimisation of ply drop order in variable stiffness laminates. Compos Struct 152:791–799. https://doi.org/10.1016/J.COMPSTRUCT.2016.05.076
Johansen LS, Lund E (2009) Optimization of laminated composite structures using delamination criteria and hierarchical models. Struct Multidiscip Optim 38(4):357–375. https://doi.org/10.1007/s00158-008-0280-1
Liu D, Toroporov VV, Querin OM, Barton DC (2011) Bilevel optimization of blended composite wing panels. J Aircr 48(1):107–118. https://doi.org/10.2514/1.C000261
Lund E (2018) Discrete Material and Thickness Optimization of laminated composite structures including failure criteria. Struct Multidiscip Optim 57(6):2357–2375. https://doi.org/10.1007/s00158-017-1866-2
MUST (2018) The MUltidisciplinary Synthesis Tool (MUST). Department of Materials and Production, Aalborg University
Nikbakt S, Kamarian S, Shakeri M (2018) A review on optimization of composite structures Part I: laminated composites. Compos Struct 195:158–185. https://doi.org/10.1016/J.COMPSTRUCT.2018.03.063
Panda S, Natarajan R (1981) Analysis of laminated composite shell structures by finite element method. Comput Struct 14(3-4):225–230. https://doi.org/10.1016/0045-7949(81)90008-0
Peeters D, Abdalla MM (2016) Optimization of ply drop locations in variable-stiffness composites. AIAA J 54(5):1760–1768. https://doi.org/10.2514/1.J054369
Peeters D, Abdalla M (2017) Design guidelines in nonconventional composite laminate optimization. J Aircr 54(4):1454–1464. https://doi.org/10.2514/1.C034087
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4-5):401–424. https://doi.org/10.1007/s00158-006-0087-x
Sjølund J, Lund E (2018) Structural gradient based sizing optimization of wind turbine blades with fixed outer geometry. Compos Struct 203:725–739. https://doi.org/10.1016/J.COMPSTRUCT.2018.07.031
Sørensen SN, Lund E (2013) Topology and thickness optimization of laminated composites including manufacturing constraints. Struct Multidiscip Optim 48(2):249–265. https://doi.org/10.1007/s00158-013-0904-y
Sørensen R, Lund E (2015) Thickness filters for gradient based multi-material and thickness optimization of laminated composite structures. Struct Multidiscip Optim 52(2):227–250. https://doi.org/10.1007/s00158-015-1230-3
Sørensen SN, Sørensen R, Lund E (2014) DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures. Struct Multidiscip Optim 50(1):25–47. https://doi.org/10.1007/s00158-014-1047-5
Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009–2027. https://doi.org/10.1002/nme.1259
Xu Y, Zhu J, Wu Z, Cao Y, Zhao Y, Zhang W (2018) A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization. Adv Compos Hybrid Mater, 1–18. https://doi.org/10.1007/s42114-018-0032-7
Zhou M, Fleury R, Kemp M (2010) Optimization of composite - recent advances and application. In: 13th AIAA/ISSMO multidisciplinary analysis optimization conference
Acknowledgements
The second author would like to thank Science Foundation Ireland (SFI) for funding Spatially and Temporally VARIable COMPosite Structures (VARICOMP) Grant No. (15/RP/2773) under its Research Professor programme.
Funding
This work was supported by the Innovation Fund Denmark project OPTI_MADE_BLADE, grant no. 75-2014-3.
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Sjølund, J.H., Peeters, D. & Lund, E. A new thickness parameterization for Discrete Material and Thickness Optimization. Struct Multidisc Optim 58, 1885–1897 (2018). https://doi.org/10.1007/s00158-018-2093-1
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DOI: https://doi.org/10.1007/s00158-018-2093-1