Abstract
In this work, a hybrid topology optimization scheme based on the moving morphable component (MMC) method is presented for the design of stiffened membrane structure. The stiffened membrane structure is composed of a base membrane, reinforcing stiffeners, and functional cells. For an accurate and effective simulation of the structure, a hybrid structure model with multiple element types is constructed. In this study, MMC components used as the basic elements for the topology description will include several different types: bar elements for the stiffeners and continuum elements for the base membrane and functional cells. The base membrane is modeled using bi-modulus material. With this approach, the distribution of element types in different parts can be changed as the components are moved around during the optimization process. Some numerical examples are presented to validate the effectiveness of the proposed scheme.
References
1.
Zhou
, M.
, and Rozvany
, G. I. N.
, 1991
, “The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization
,” Comput. Methods Appl. Mech. Eng.
, 89
(1–3
), pp. 309
–336
. 2.
Wang
, M. Y.
, Wang
, X.
, and Guo
, D.
, 2003
, “A Level Set Method for Structural Topology Optimization
,” Comput. Methods Appl. Mech. Eng.
, 192
(1–2
), pp. 227
–246
. 3.
Allaire
, G.
, Jouve
, F.
, and Toader
, A. M.
, 2004
, “Structural Optimization Using Sensitivity Analysis and a Level-Set Method
,” J. Comput. Phys.
, 194
(1
), pp. 363
–393
. 4.
Huang
, X.
, and Xie
, Y. M.
, 2010
, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications
, John Wiley & Sons
, West Sussex, UK
.5.
Xie
, Y. M.
, and Steven
, G. P.
, 1994
, “Optimal Design of Multiple Load Case Structures Using an Evolutionary Procedure
,” Eng. Comput.
, 11
(4
), pp. 295
–302
. 6.
Kang
, P.
, and Youn
, S. K.
, 2016
, “Isogeometric Topology Optimization of Shell Structures Using Trimmed NURBS Surfaces
,” Finite Elem. Anal. Des.
, 120
, pp. 18
–40
. 7.
Okuizumi
, N.
, Satou
, Y.
, Mori
, O.
, Sakamoto
, H.
, and Furuya
, H.
, 2021
, “Analytical Investigation of Global Deployed Shape of a Spinning Solar Sail Membrane
,” AIAA J.
, 59
(3
), pp. 1075
–1086
. 8.
Sakamoto
, H.
, Park
, K. C.
, and Miyazaki
, Y.
, 2006
, “Distributed and Localized Active Vibration Isolation in Membrane Structures
,” J. Spacecr. Rockets
, 43
(5
), pp. 1107
–1116
. 9.
Wei
, P.
, Ma
, H.
, and Wang
, M. Y.
, 2014
, “The Stiffness Spreading Method for Layout Optimization of Truss Structures
,” Struct. Multidiscip. Optim.
, 49
(4
), pp. 667
–682
. 10.
Zegard
, T.
, and Paulino
, G. H.
, 2013
, “Truss Layout Optimization Within a Continuum
,” Struct. Multidiscip. Optim.
, 48
(1
), pp. 1
–16
. 11.
Li
, B.
, Hong
, J.
, and Ge
, L.
, 2017
, “Constructal Design of Internal Cooling Geometries in Heat Conduction System Using the Optimality of Natural Branching Structures
,” Int. J. Therm. Sci.
, 115
, pp. 16
–28
. 12.
Gaynor
, A. T.
, Guest
, J. K.
, and Moen
, C. D.
, 2013
, “Reinforced Concrete Force Visualization and Design Using Bilinear Truss-Continuum Topology Optimization
,” J. Struct. Eng.
, 139
(4
), pp. 607
–618
. 13.
Li
, B.
, Liu
, H.
, Yang
, Z.
, and Zhang
, J.
, 2019
, “Stiffness Design of Plate/Shell Structures by Evolutionary Topology Optimization
,” Thin-Walled Struct.
, 141
, pp. 232
–250
. 14.
Zegard
, T.
, and Paulino
, G. H.
, 2014
, “GRAND—Ground Structure Based Topology Optimization for Arbitrary 2D Domains Using MATLAB
,” Struct. Multidiscip. Optim.
, 50
(5
), pp. 861
–882
. 15.
Zhou
, K.
, and Li
, X.
, 2008
, “Topology Optimization for Minimum Compliance Under Multiple Loads Based on Continuous Distribution of Members
,” Struct. Multidiscip. Optim.
, 37
(1
), pp. 49
–56
. 16.
Amir
, O.
, and Sigmund
, O.
, 2013
, “Reinforcement Layout Design for Concrete Structures Based on Continuum Damage and Truss Topology Optimization
,” Struct. Multidiscip. Optim.
, 47
(2
), pp. 157
–174
. 17.
Li
, Y.
, Wei
, P.
, and Ma
, H.
, 2017
, “Integrated Optimization of Heat-Transfer Systems Consisting of Discrete Thermal Conductors and Solid Material
,” Int. J. Heat Mass Transfer
, 113
, pp. 1059
–1069
. 18.
Cao
, M.
, Ma
, H.
, and Wei
, P.
, 2018
, “A Modified Stiffness Spreading Method for Layout Optimization of Truss Structures
,” Acta Mech. Sinica
, 24
(6
), pp. 1072
–1083
. 19.
Jewett
, J. L.
, and Carstensen
, J. V.
, 2019
, “Experimental Investigation of Strut-and-Tie Layouts in Deep RC Beams Designed With Hybrid Bi-Linear Topology Optimization
,” Eng. Struct.
, 197
, p. 109322
. 20.
Guo
, X.
, Zhang
, W.
, and Zhong
, W.
, 2014
, “Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework
,” ASME J. Appl. Mech.
, 81
(8
), p. 081009
. 21.
Zhang
, W.
, Yuan
, J.
, Zhang
, J.
, and Guo
, X.
, 2016
, “A New Topology Optimization Approach Based on Moving Morphable Components (MMC) and the Ersatz Material Model
,” Struct. Multidiscip. Optim.
, 53
(6
), pp. 1243
–1260
. 22.
Zhang
, W.
, Jiang
, S.
, Liu
, C.
, Li
, D.
, Kang
, P.
, Youn
, S. K.
, and Guo
, X.
, 2020
, “Stress-Related Topology Optimization of Shell Structures Using IGA/TSA-Based Moving Morphable Void (MMV) Approach
,” Comput. Methods Appl. Mech. Eng.
, 366
, p. 113036
. 23.
Hoang
, V. N.
, and Jang
, G. W.
, 2017
, “Topology Optimization Using Moving Morphable Bars for Versatile Thickness Control
,” Comput. Methods Appl. Mech. Eng.
, 317
, pp. 153
–173
. 24.
Sun
, J.
, Tian
, Q.
, Hu
, H.
, and Pedersen
, N. L.
, 2018
, “Topology Optimization of a Flexible Multibody System With Variable-Length Bodies Described by ALE–ANCF
,” Nonlinear Dyn.
, 93
(2
), pp. 413
–441
. 25.
Norato
, J. A.
, Bell
, B. K.
, and Tortorelli
, D. A.
, 2015
, “A Geometry Projection Method for Continuum-Based Topology Optimization With Discrete Elements
,” Comput. Methods Appl. Mech. Eng.
, 293
, pp. 306
–327
. 26.
Zhang
, S.
, and Norato
, J. A.
, 2017
, “Optimal Design of Panel Reinforcements With Ribs Made of Plates
,” ASME J. Mech. Des.
, 139
(8
), p. 081403
. 27.
Wein
, F.
, Dunning
, P. D.
, and Norato
, J. A.
, 2020
, “A Review on Feature-Mapping Methods for Structural Optimization
,” Struct. Multidiscip. Optim.
, 62
(4
), pp. 1597
–1638
. 28.
Du
, Z.
, and Guo
, X.
, 2014
, “Variational Principles and the Related Bounding Theorems for Bi-Modulus Materials
,” J. Mech. Phys. Solids
, 73
, pp. 183
–211
. 29.
Zhang
, W.
, Song
, J.
, Zhou
, J.
, Du
, Z.
, Zhu
, Y.
, Sun
, Z.
, and Guo
, X.
, 2018
, “Topology Optimization With Multiple Materials via Moving Morphable Component (MMC) Method
,” Int. J. Numer. Methods Eng.
, 113
(11
), pp. 1653
–1675
. 30.
Svanberg
, K.
, 1987
, “The Method of Moving Asymptotes—A New Method for Structural Optimization
,” Int. J. Numer. Methods Eng.
, 24
(2
), pp. 359
–373
. 31.
Li
, Z.
, Shi
, T.
, and 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
, pp. 59
–70
. 32.
Chu
, S.
, Townsend
, S.
, Featherston
, C.
, and Kim
, H. A.
, 2020
, “Simultaneous Layout and Topology Optimization of Curved Stiffened Panels
,” AIAA J.
, 59
(7
), pp. 2768
–2783
. 33.
Chu
, S.
, Townsend
, S.
, Featherston
, C.
, and Kim
, H. A.
, 2021
, “Simultaneous Size, Layout and Topology Optimization of Stiffened Panels Under Buckling Constraints
,” AIAA Scitech 2021 Forum
, Virtual Event
, June 15–19, 2020
, pp. 1
–18
.34.
Chu
, S.
, Featherston
, C.
, and Kim
, H. A.
, 2021
, “Design of Stiffened Panels for Stress and Buckling via Topology Optimization
,” Struct. Multidiscip. Optim.
, 64
(5
), pp. 3123
–3146
. 35.
Shen
, L.
, Ding
, X.
, Hu
, T.
, Zhang
, H.
, and Xu
, S.
, 2021
, “Simultaneous Optimization of Stiffener Layout of 3D Box Structure Together With Attached Tuned Mass Dampers Under Harmonic Excitations
,” Struct. Multidiscip. Optim.
, 64
(2
), pp. 721
–737
. 36.
Savine
, F.
, Irisarri
, F. X.
, Julien
, C.
, Vincenti
, A.
, and Guerin
, Y.
, 2021
, “A Component-Based Method for the Optimization of Stiffener Layout on Large Cylindrical Rib-Stiffened Shell Structures
,” Struct. Multidiscip. Optim.
, 64
(4
), pp. 1843
–1861
. 37.
Ma
, X.
, Wang
, F.
, Aage
, N.
, Tian
, K.
, Hao
, P.
, and Wang
, B.
, 2021
, “Generative Design of Stiffened Plates Based on Homogenization Method
,” Struct. Multidiscip. Optim.
, 64
(6
), pp. 3951
–3969
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