0
Technical Brief

Simultaneous Discrete Topology Optimization of Ply Orientation and Thickness for Carbon Fiber Reinforced Plastic-Laminated Structures

[+] Author and Article Information
Chi Wu

School of Automotive Studies,
Tongji University, Shanghai 201804, China;
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle
Thermal Management Systems,
Tongji University,
Shanghai 201804, China;
School of Aerospace, Mechanical and Mechatronic
Engineering,
The University of Sydney,
Sydney 2006, NSW, Australia

Yunkai Gao

School of Automotive Studies,
Tongji University,
Shanghai 201804, China;
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle
Thermal Management Systems,
Tongji University,
Shanghai 201804, China
e-mail: gaoyunkai@tongji.edu.cn

Jianguang Fang

School of Civil and Environmental Engineering,
University of Technology Sydney,
Sydney 2007, NSW, Australia
e-mail: fangjg87@gmail.com

Erik Lund

Department of Materials and Production,
Aalborg University,
Fibigerstraede 16,
Aalborg East 9220, Denmark

Qing Li

School of Aerospace, Mechanical and Mechatronic
Engineering,
The University of Sydney,
Sydney 2006, NSW, Australia

1Corresponding authors.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 24, 2018; final manuscript received December 4, 2018; published online January 11, 2019. Assoc. Editor: Samy Missoum.

J. Mech. Des 141(4), 044501 (Jan 11, 2019) (6 pages) Paper No: MD-18-1251; doi: 10.1115/1.4042222 History: Received March 24, 2018; Revised December 04, 2018

This study developed a discrete topology optimization procedure for the simultaneous design of ply orientation and thickness for carbon fiber reinforced plastic (CFRP)-laminated structures. A gradient-based discrete material and thickness optimization (DMTO) algorithm was developed by using casting-based explicit parameterization to suppress the intermediate void across the thickness of the laminate. A benchmark problem was first studied to compare the DMTO approach with the sequential three-phase design method using the free size, ply thickness, and stacking sequence of the laminates. Following this, the DMTO approach was applied to a practical design problem featuring a CFRP-laminated engine hood by minimizing overall compliance subject to volume-related and functional constraints under multiple load cases. To verify the optimized design, a prototype of the CFRP engine hood was created for experimental tests. The results showed that the simultaneous discrete topology optimization of ply orientation and thickness was an effective approach for the design of CFRP-laminated structures.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Patel, S. , and Ahmad, S. , 2017, “ Probabilistic Failure of Graphite Epoxy Composite Plates Due to Low Velocity Impact,” ASME J. Mech. Des., 139(4), p. 044501. [CrossRef]
Beer, M. , Gloy, Y.-S. , Raina, M. , and Gries, T. , 2014, “ Construction of a Carbon Fiber Reinforced Weft Guide Bar for a Crochet Knitting Machine,” ASME J. Mech. Des., 136(6), p. 064501. [CrossRef]
Peel, L. D. , Mejia, J. , Narvaez, B. , Thompson, K. , and Lingala, M. , 2009, “ Development of a Simple Morphing Wing Using Elastomeric Composites as Skins and Actuators,” ASME J. Mech. Des., 131(9), p. 091003. [CrossRef]
Lee, J.-M. , Lee, K.-H. , Kim, B.-M. , and Ko, D.-C. , 2016, “ Design of Roof Panel With Required Bending Stiffness Using CFRP Laminates,” Int. J. Precis. Eng. Manuf., 17(4), pp. 479–485. [CrossRef]
Sadagopan, D. , and Pitchumani, R. , 1997, “ A Combinatorial Optimization Approach to Composite Materials Tailoring,” ASME J. Mech. Des., 119(4), pp. 494–503. [CrossRef]
Ghiasi, H. , Fayazbakhsh, K. , Pasini, D. , and Lessard, L. , 2010, “ Optimum Stacking Sequence Design of Composite Materials—Part II: Variable Stiffness Design,” Compos. Struct., 93(1), pp. 1–13. [CrossRef]
Huang, G. , Wang, H. , and Li, G. , 2016, “ An Efficient Reanalysis Assisted Optimization for Variable-Stiffness Composite Design by Using Path Functions,” Compos. Struct., 153, pp. 409–420. [CrossRef]
Adams, D. B. , Watson, L. T. , Gürdal, Z. , and Anderson-Cook, C. M. , 2004, “ Genetic Algorithm Optimization and Blending of Composite Laminates by Locally Reducing Laminate Thickness,” Adv. Eng. Software, 35(1), pp. 35–43. [CrossRef]
Coburn, B. H. , and Weaver, P. M. , 2016, “ Buckling Analysis, Design and Optimisation of Variable-Stiffness Sandwich Panels,” Int. J. Solids Struct., 96, pp. 217–228. [CrossRef]
Schläpfer, B. , and Kress, G. , 2014, “ Optimal Design and Testing of Laminated Light-Weight Composite Structures With Local Reinforcements Considering Strength Constraints—Part I: Design,” Composites, Part A, 61, pp. 268–278. [CrossRef]
Zhou, M. , Fleury, R. , and Kemp, M. , 2010, “ Optimization of Composite—Recent Advances and Application,” AIAA Paper No. 2010-9272.
Allaire, G. , and Delgado, G. , 2016, “ Stacking Sequence and Shape Optimization of Laminated Composite Plates Via a Level-Set Method,” J. Mech. Phys. Solids, 97, pp. 168–196. [CrossRef]
Peeters, D. , van Baalen, D. , and Abdallah, M. , 2015, “ Combining Topology and Lamination Parameter Optimisation,” Struct. Multidiscip. Optim., 52(1), pp. 105–120. [CrossRef]
Lund, E. , and Stegmann, J. , 2005, “ On Structural Optimization of Composite Shell Structures Using a Discrete Constitutive Parametrization,” Wind Energy, 8(1), pp. 109–124. [CrossRef]
Stolpe, M. , and Svanberg, K. , 2001, “ An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization,” Struct. Multidiscip. Optim., 22(2), pp. 116–124. [CrossRef]
Wu, C. , Fang, J. , and Li, Q. , 2018, “ Multi-Material Topology Optimization for Thermal Buckling Criteria,” Comput. Methods Appl. Mech. Eng. (in press).
Lund, E. , 2017, “ Discrete Material and Thickness Optimization of Laminated Composite Structures Including Failure Criteria,” Struct. Multidiscip. Optim., 57(6), pp. 2357–2375. [CrossRef]
Sjølund, J. H. , Peeters, D. , and Lund, E. , 2018, “ A New Thickness Parameterization for Discrete Material and Thickness Optimization,” Struct. Multidiscip. Optim., 58(5), pp. 1885–1897. [CrossRef]
Niu, B. , Olhoff, N. , Lund, E. , and Cheng, G. , 2010, “ Discrete Material Optimization of Vibrating Laminated Composite Plates for Minimum Sound Radiation,” Int. J. Solids Struct., 47(16), pp. 2097–2114. [CrossRef]
Sørensen, R. , and Lund, E. , 2015, “ Thickness Filters for Gradient Based Multi-Material and Thickness Optimization of Laminated Composite Structures,” Struct. Multidiscip. Optim., 52(2), pp. 227–250. [CrossRef]
Wang, F. , Lazarov, B. S. , and Sigmund, O. , 2011, “ On Projection Methods, Convergence and Robust Formulations in Topology Optimization,” Struct. Multidiscip. Optim., 43(6), pp. 767–784. [CrossRef]
Gersborg, A. R. , and Andreasen, C. S. , 2011, “ An Explicit Parameterization for Casting Constraints in Gradient Driven Topology Optimization,” Struct. Multidiscip. Optim., 44(6), pp. 875–881. [CrossRef]
Bendsoe, M. P. , and Sigmund, O. , 2013, Topology Optimization: Theory, Methods, and Applications, Springer Science & Business Media, Berlin.
Wu, C. , Gao, Y. , Fang, J. , Lund, E. , and Li, Q. , 2017, “ Discrete Topology Optimization of Ply Orientation for a Carbon Fiber Reinforced Plastic (CFRP) Laminate Vehicle Door,” Mater. Des., 128, pp. 9–19. [CrossRef]
Jorge, N. , and Stephen, J. W. , 1999, Numerical Optimization, Springer-Verlag, New York.
Kulikov, G. , and Plotnikova, S. , 2005, “ Equivalent Single-Layer and Layerwise Shell Theories and Rigid-Body Motions—Part I: Foundations,” Mech. Adv. Mater. Struct., 12(4), pp. 275–283. [CrossRef]
Sigmund, O. , 2007, “ Morphology-Based Black and White Filters for Topology Optimization,” Struct. Multidiscip. Optim., 33(4–5), pp. 401–424. [CrossRef]
Youming, T. , Weipeng, H. , and Mingyang, S. , 2016, “ Topology Optimization and Lightweight Design of Engine Hood Material for SUV,” Funct. Mater., 23(4), p. 631. http://dspace.nbuv.gov.ua/handle/123456789/121499

Figures

Grahic Jump Location
Fig. 2

Iteration histories of objective function, and discrete indicators Mcnd and Mdnd

Grahic Jump Location
Fig. 3

Loading and boundary conditions for the stiffness analysis of the CFRP-laminated engine hood: (a) load case 1: torsional rigidity, (b) load case 2: front bending stiffness, (c) load case 3: rear bending stiffness, (d) load case 4: lateral stiffness (1, 2, and 3 denote the translational, and 4, 5, and 6 denote the rotational degrees-of-freedom around the x-, y-, and z-axes, respectively)

Grahic Jump Location
Fig. 4

Convergence histories of the objective function and discreteness

Grahic Jump Location
Fig. 5

Thickness distribution and stacking sequence of CFRP inner panel

Grahic Jump Location
Fig. 6

The experimental setup for the tests of the optimized CFRP hood

Grahic Jump Location
Fig. 1

Optimization of (a) the DMTO approach and (b) the three-phase design method

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In