Skip to main content
SpringerLink
Log in

Topology optimization-driven design of added rib architecture system for enhanced free vibration response of thin-wall plastic components used in the automotive industry

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

A relentless paradigm switch in the automotive industry is being witnessed, where traditional combustion engines are progressively replacing with electric counterparts. In order to compensate for heavy electric engine technology, plastic components used in the interior parts of electric vehicles seems to be a reasonable strategy aligned with the lightweight trend as the automotive industry’s top priority. Extremely thin plastic components (ultra-lightweight) attached to ribs-based architectures have been identified as an adequate solution offering a good balance between lightweight and structural/vibrational response of the overall composition. Still, they may yield detrimental features regarding thermal-induced deformations (i.e., warpage and shrinkage) associated with the typical mold injection process for their manufacturing. This paper uses topology optimization to determine the precise location of the added rib architecture system for enhanced vibration response of the overall plastic component (thin original plastic part and ribs architecture). Following a constant mass criterion, the topology optimization-driven design of the additional material is replaced with a more convenient ribs-based architecture component, showing a reasonable similarity from a vibration standpoint. The component in its initial state (without some ribs-based architecture) shows a vibration response of 16.69 Hz. Once the topology optimization is applied, a significant improvement is observed since a value of 26.05 Hz is obtained. At a postprocessing stage, the design is analyzed and subjected to typical static loading cases to verify its stiffness properties, getting a significant displacement reduction from 7.68 to 3.51 mm. Finally, the design implementation of a warpage and shrinkage analysis confirmed that the final design was not adversely affected according to standard considerations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Availability of data and materials

The manuscript has no associated data.

Notes

  1. The 3 stems from the three-dimensional nature of the solid \(\mathcal {B}.\)

  2. The eigenvalue problem in (1) can be formulated in terms of the eigenfrequencies \(\nu _j\) (with units of Hz) or in terms of the angular eigenfrequencies \(\omega _j\) (with units of radians per second), both being related through the following relationship, \(\omega _j=2\pi \nu _j\).

  3. Since the pseudo-density dependent fields \({E}_e\) and \(\rho _e\), featuring in both \({K}(\theta )\) and \({M}(\theta )\), depend on the elemental pseudo-density field \(\theta _e\) according to (5), the terms \(\partial {K}/\partial \theta _e\) and \(\partial {M}/\partial \theta _e\) featuring in (10) require the computation of \(\partial {E}_e/\partial \theta _e\) and \(\partial {\rho }_e/\partial \theta _e\), namely

References

  1. Sundmaeker H, Spiering T, Kohlitz S, Herrmann C (2013) Injection mould design: impact on energy efficiency in manufacturing. In: Re-engineering Manufacturing for Sustainability, Springer, pp 269–274

  2. Wadas T, Tisza M (2020) Lightweight manufacturing of automotive parts. IOP Conference Series: Mater Sci Eng 903(1):012036. https://doi.org/10.1088/1757-899x/903/1/012036

  3. Hofer J, Wilhelm E, Schenler W (2012) Optimal lightweighting in battery electric vehicles. World Electric Vehicle Journal 5(3):751–762

    Article  Google Scholar 

  4. Muhammad A, Rahman MR, Baini R, Bin Bakri MK (2021) 8 - applications of sustainable polymer composites in automobile and aerospace industry. In: Rahman MR (ed) Advances in Sustainable Polymer Composites, Woodhead Publishing Series in Composites Science and Engineering, Woodhead Publishing, pp 185–207. https://doi.org/10.1016/B978-0-12-820338-5.00008-4, https://www.sciencedirect.com/science/article/pii/B9780128203385000084

  5. Kamran SS, Haleem A, Bahl S, Javaid M, Prakash C, Budhhi D (2022) Artificial intelligence and advanced materials in automotive industry: Potential applications and perspectives. Materials Today: Proceedings

  6. Peter M, Fleischer J, Sell-Le Blanc F, Jastrzembski JP (2013) New conceptual lightweight design approaches for integrated manufacturing processes: Influence of alternative materials on the process chain of electric motor manufacturing. In: 2013 3rd International Electric Drives Production Conference (EDPC), IEEE, pp 1–6

  7. Mallick PK (2020) Materials, design and manufacturing for lightweight vehicles. Woodhead publishing

  8. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224

    Article  MathSciNet  Google Scholar 

  9. Sigmund O, Maute K (2013) Topology optimization approaches a comparative review. Struct Multidiscipl Optim 48:1031–1055

    Article  Google Scholar 

  10. Zhou M, Rozvany G (1991) The coc algorithm, part ii: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336

    Article  Google Scholar 

  11. Allaire G, Jouve TA (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393

    Article  MathSciNet  Google Scholar 

  12. Wang M, Wang X, Guo D (2003) A level-set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246

    Article  MathSciNet  Google Scholar 

  13. Burger M, Stainko R (2006) Phase-field relaxation of topology optimization with local stress constraints. SIAM J Control Optim 45

  14. Sokolowski J, Zochowski A (1999) On the topological derivative in shape optimization. SIAM J Control Optim 37:1251–1272

  15. Munk DJ, Steven GP (2015) Topology and shape optimization methods using evolutionary algorithms: a review. Struct Multidiscip Optim 52:613–631

    Article  MathSciNet  Google Scholar 

  16. Martin A, Deierlein GG (2020) Structural topology optimization of tall buildings for dynamic seismic excitation using modal decomposition. Struct Multidiscip Optim 216

  17. Zhang G, Khandelwal K (2019) Computational design of finite strain auxetic metamaterials via topology optimization and nonlinear homogenization. Comput Methods Appl Mech Eng 356:490–527

    Article  MathSciNet  Google Scholar 

  18. Martínez-Frutos J, Ortigosa R, Gil AJ (2021) In-silico design of electrode meso-architecture for shape morphing dielectric elastomers. J Mech Phys Solids 157:104594. ISSN 0022-5096. https://doi.org/10.1016/j.jmps.2021.104594

  19. Gonçalves JF, De Leon DM, Perondi EA (2018) Simultaneous optimization of piezoelectric actuator topology and polarization. Struct Multidisc Optim 58:1139–1154. https://doi.org/10.1007/s00158-018-1957-8

  20. Jihong Z, Weihong Z (2006) Maximization of structural natural frequency with optimal support layout. Struct Multidiscip Optim 31:462–469

    Article  Google Scholar 

  21. Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: the 1d and 2d scalar cases. J Sound Vib 289:967–986

    Article  Google Scholar 

  22. Luo Z, Yang J, Chen L (2006) A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures. Aerosp Sci Technol 19:364–373

    Article  Google Scholar 

  23. Yasin S, Mohd N, Mahmud J, Whashilah N, Razak Z (2018) A reduction of protector cover warpage via topology optimization. Int J Adv Manuf Technol 98:2531–2537

  24. Gao H, Li X, Wu Q, Lin M, Zhang Y (2022) Effects of residual stress and equivalent bending stiffness on the dimensional stability of the thin-walled parts. Int J Adv Manuf Technol 119:4907–4924

    Article  Google Scholar 

  25. Karimzadeh R, Hamedi M (2022) An intelligent algorithm for topology optimization in additive manufacturing. Int J Adv Manuf Technol 119:991–1001

    Article  Google Scholar 

  26. Svanberg K (1987) The method of moving asymptotes: a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373

    Article  MathSciNet  Google Scholar 

  27. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158

    Article  MathSciNet  Google Scholar 

  28. Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26):3443–3459

    Article  Google Scholar 

  29. Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784

    Article  Google Scholar 

  30. Autodesk (2022) Topology optimization software. create structures with minimal mass and maximal stiffness. Available at https://www.altair.com/topology-optimization

  31. Altair Engineering (2022) Altair OptiStruct. Altair Engineering Inc., Troy, Michigan, USA, https://www.altair.com/

  32. Autodesk (2022a) Moldflow Insight. Autodesk, Inc., San Rafael, California, USA, http://www.autodesk.com/moldflow

  33. Autodesk (2022b) Autodesk moldflow insight 2021. Available at https://help.autodesk.com/view/MFIA/2021/ENU/

  34. Fung Y, Tong P (2001) Classical and Computational Solid Mechanics. Advanced series in engineering science, World Scientific, https://books.google.com.mx/books?id=hmyiIiiv4FUC

Download references

Funding

The second and fourth authors received support from Cátedras CONACYT program through project no. 674. The fifth author received financial support through the contract 21132/SF/19, Fundación Séneca, Región de Murcia (Spain) and through the program Saavedra Fajardo, as well as the funding by Fundación Séneca (Murcia, Spain) through grant 20911/PI/18.

Author information

Authors and Affiliations

  1. POSGRADO CIATEQ A.C., Centro de Tecnología Avanzada, Circuito de la Industria Poniente Lote 11, Manzana 3, No. 11, Col. Parque Industrial Ex Hacienda Doña Rosa, Lerma de Villada, 52004, Estado de México, Mexico

    Joel Omar Remigio-Reyes

  2. CONACYT-CIATEQ A.C., Centro de Tecnología Avanzada, Eje 126 No. 225, San Luis Potosí, 78395, San Luis Potosí, Mexico

    Isaías E. Garduño & Hugo Arcos-Gutiérrez

  3. CIATEQ A.C., Centro de Tecnología Avanzada, Circuito de la Industria Poniente Lote 11, Manzana 3, No. 11, Col. Parque Industrial Ex Hacienda Doña Rosa, Lerma de Villada, 52004, Estado de México, Mexico

    José Manuel Rojas-García

  4. Computational Mechanics and Scientific Computing Group, Technical University of Cartagena, Campus Muralla del Mar, Cartagena, 30202, Murcia, Spain

    Rogelio Ortigosa

Authors
  1. Joel Omar Remigio-Reyes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Isaías E. Garduño
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José Manuel Rojas-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hugo Arcos-Gutiérrez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Rogelio Ortigosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Isaías E. Garduño.

Ethics declarations

Ethics approval

Not applicable

Consent to participate

Not applicable

Consent for publication

Not applicable

Conflict of interest

The authors declare no competing interests.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Remigio-Reyes, J.O., Garduño, I., Rojas-García, J.M. et al. Topology optimization-driven design of added rib architecture system for enhanced free vibration response of thin-wall plastic components used in the automotive industry. Int J Adv Manuf Technol 123, 1231–1247 (2022). https://doi.org/10.1007/s00170-022-10219-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-10219-x

Keywords

Search

Navigation