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Numerical Investigation of Member Stiffness in Composite Sandwich Bolted Connections

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Strength of Materials Aims and scope

Member stiffness in bolted connections has been widely studied for homogenous and isotropic materials contrary to composite sandwich ones. Therefore, a numerical simulation based on the augmented Lagrangian algorithm to solve contacts problems is conducted in ANSYS software to investigate various preloaded sandwich bolted joints with carbon and glass laminate skins and two types of foam cores. Tested samples show a rise of the ratio of maximum shear stress to maximum principal stress when the applied preload increases considerably which improves the risk of core failure, additionally, an analytical approximation of stiffness at preload is proposed, for that, a search algorithm is used to deduce the expression of the equivalent elastic modulus of tested joint members and a distance correlation method is applied to determine the theoretical formulation of the introduced stiffness model whose accuracy is optimized through analyzing results of root mean square error (RMSE) of its mathematical approximations , the convergence of the chosen model is ensured for all tested samples except the ones having the most rigid skins with the greatest elastic modulus (209 GPa). Furthermore, the equation introduced by Zhang and Poirier concerning the tension load causing a bolted joint separation is adapted and validated with a percent error less than 13%.

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Abbreviations

ρ :

material density (kg/m3)

E :

Young’s modulus of bolted members in the case of an homogenous joint material (MPa)

E b :

Young’s modulus of bolt (MPa)

E a :

Young’s modulus along the axis a (MPa), a ∈ {X, Y, Z}

v :

Poisson’s ratio

v ab :

Poisson’s ratio in the ab-plane, with ab ∈ {XY, XZ, YZ}

G ab :

shear modulus in the ab-plane (MPa), with ab ∈ {XY, XZ, YZ}

E eq :

equivalent elastic modulus (MPa)

\({E}_{{z}_{skins}},{E}_{{z}_{core}}\) :

Young’s moduli of skins and core along the Z-axis (MPa)

\({E}_{{x}_{skins}}\) :

Young’s modulus of skins along the X-axis (MPa)

σ y :

yield stress (MPa)

σ t :

tensile strength (MPa)

α skins :

volume fraction of the two skins

α core :

volume fraction of the core

ε eq :

strain produced by preload

σ eq :

stress produced by preload (MPa)

d :

diameter of bolt (mm)

D :

diameter of bolt head (mm)

l :

thickness of joint member (mm)

l s :

thickness of sandwich member (mm)

l skins :

thickness of sandwich skins (mm)

\({A}_{d,{l}_{s}}\) :

characteristic constant for stiffness (m)

\({A}_{d,8,{l}_{skins}},{A}_{d,14,{l}_{skins}}\) :

characteristic constants for stiffness depending on core thickness (m)

F i :

bolt preload (kN)

F :

tension load (kN)

F sep :

the minimum tension load causing the joint separation (kN)

α :

proportional factor

F res :

residual force (kN)

F num :

the minimum numerical load causing joint separation (kN)

F c :

a load that is 13% less than Fsep (kN)

Nδ i :

member deformation caused by Fi (mm)

δ m , res :

member deformation caused by Fres (mm)

δ m , F :

member deformation caused by F (mm)

δ m , :

deformation caused by member rotation (mm)

δ m :

resulting member deformation (mm)

\({\delta }_{{m}_{Num}}\) :

numerical member deformation measured without preload (mm)

dCor(X, Y):

distance correlation coefficient

(X k, Y k):

statistical sample

n :

number of correlated samples

\(\widehat{A},\widehat{B}\) :

double centered distance matrices

K j :

joint stiffness (kN/mm)

K :

member stiffness (kN/mm)

K ana :

analytical stiffness (kN/mm)

K b :

bolt stiffness (kN/mm)

K r :

member stiffness when joint is tensioned without bolt preload (kN/mm)

p K :

percentage difference between Kana and K

A, B :

distance matrices

References

  1. J. C. Lee, D. H. Park, H. S. Jung, et al., “Design for carbon fiber lamination of PMI foam cored CFRP sandwich composite applied to automotive rear spoiler,” Fiber Polym, 21, 156–161 (2020).

    Article  CAS  Google Scholar 

  2. G. J. Bi, J. P. Yin, Z. J. Wang, et al., “Impact resistance analysis of a composite double-layer honeycomb sandwich structure,” Strength Mater, 53, No. 1, 126–133 (2021). https://doi.org/https://doi.org/10.1007/s11223-021-00268-0

    Article  CAS  Google Scholar 

  3. A. J. M. Ferreira, “On the shear-deformation theories for the analysis of concrete shells reinforced with external composite laminates,” Strength Mater, 35, No. 2, 128–135 (2003). https://doi.org/https://doi.org/10.1023/A:1023706410615

    Article  CAS  Google Scholar 

  4. J. Grünewald, P. Parlevliet, and V. Altstädt, “Manufacturing of thermoplastic composite sandwich structures: a review of literature,” J Thermoplast Compos Mater, 30, No. 4, 437–464 (2015).

    Article  Google Scholar 

  5. A. V. Yarovaya, “Bending of circular sandwich plate on elastic foundation,” Strength Mater, 37, No. 6, 598–605 (2005). https://doi.org/https://doi.org/10.1007/s11223-006-0007-8

    Article  CAS  Google Scholar 

  6. S. Zhu, G. Shao, Y. Wang, et al., “Mechanical behavior of the CFRP lattice core sandwich bolted splice joints,” Compos B-Eng, 93, 265–272 (2016).

    Article  Google Scholar 

  7. S. Satasivam and Y. Bai, “Mechanical performance of bolted modular GFRP composite sandwich structures using standard and blind bolts,” Compos Struct, 117, 59–70 (2014).

    Article  Google Scholar 

  8. M. Zabihpoor, R. Moslemian, M. Afshin, and M. H. Nazemi, “Failure analysis of bolted joints in foam-core sandwich composites,” J Reinf Plast Compos, 27, No. 15, 1635–1647 (2008).

    Article  CAS  Google Scholar 

  9. R. Roy, K. H. Nguyen, Y. B Park, et al., “Testing and modeling of Nomex™ honeycomb sandwich panels with bolt insert,” Compos B-Eng, 56, 762–769 (2014).

    Article  CAS  Google Scholar 

  10. C. Zhao, W. Zheng, J. Ma, and Y. Zhao, “Shear strengths of different bolt connectors on the large span of aluminium alloy honeycomb sandwich structure,” Appl Sci, 7, No. 5, 450 (2017).

    Google Scholar 

  11. Ya. S. Karpov, “Jointing of high-loaded composite structural components. Part 1. Design and engineering solutions and performance assessment,” Strength Mater, 38, No. 3, 234–240 (2006). https://doi.org/https://doi.org/10.1007/s11223-006-0036-3

    Article  CAS  Google Scholar 

  12. C. T. McCarthy and M. A. McCarthy, “Design and failure analysis of composite bolted joints for aerospace composites,” in: P. E. Irving and C. Soutis, Polymer Composites in the Aerospace Industry, Limerick, Ireland (2015), pp. 295–334.

    Chapter  Google Scholar 

  13. J. Xu, Y. Lan, X. Zhang, and K. Du, “Numerical and experimental study on stiffened composite panel repaired by bolted joints under compressive load,” J Appl Math Phys, 6, No. 8, 1763–1771 (2018).

    Article  Google Scholar 

  14. M. Pakdil, “Failure analysis of composite single bolted-joints subjected to bolt pretension,” Indian J Eng Mater Sci, 16, No. 2, 79–85 (2009).

    Google Scholar 

  15. F. Sen, O. Sayman, R. Ozcan, and R. Siyahkoc, “Failure response of single bolted composite joints under various preload,” Indian J Eng Mater Sci, 17, No. 1, 39–48 (2010).

    Google Scholar 

  16. D. Sivakumar, L. F. Ng, J. W. Ng, and M. Z. Selamat, “Failure analysis of hybrid fibre reinforced plastics for bolted joint under thermal effect,” J Mech Eng, 1, No. 1, 141–156 (2017).

    Google Scholar 

  17. C. D. Coman and D. M. Constantinescu, “Preload effects on failure mechanisms of hybrid metal-composite bolted joints,” Mater Sci Forum, 957, 293–302 (2019).

    Article  Google Scholar 

  18. O. Sayman and O. Ahishali, “Failure analysis of bolted aluminum sandwich composite plates under compressive preload,” J Reinf Plast Compos, 27, No. 1, 69–81 (2008).

    Article  CAS  Google Scholar 

  19. M. Kumar, J. S. Saini, H. Bhunia, and S. R. Chowdhury, “Aging of bolted joints prepared from electron-beamcured multiwalled carbon nanotube-based nanocomposites with variable torques,” Polym Compos, 42, No. 8, 4082–4104 (2021).

    Article  CAS  Google Scholar 

  20. S. A. Nassar and A. Abboud, “An improved stiffness model for bolted joints,” J Mech Des, 131, No. 12, 121001 (2009).

    Google Scholar 

  21. N. Haidar, S. Obeed, and M. Jawad, “Mathematical representation of bolted-joint stiffness: a new suggested model,” J Mech Sci Technol, 25, No. 11, 2827–2834 (2011).

    Article  Google Scholar 

  22. Y. Yang, Y-Q. Wang, X. Liu, et al., “A stiffness model for unidirectional composite bolted joints,” in: Proc. of the 21st Int. Conf. on Composite Materials (ICCM/21) (Xi’an, China, 2017).

  23. O. E. Canyurt and T. Sekercioglu, “A new approach for calculating the stiffness of bolted connections,” Proc Inst Mech Eng L, 230, No. 2, 426–435 (2016).

    CAS  Google Scholar 

  24. N. Yildirim, Experimental Determination of the Stiffness of Connected Parts in Preloaded Bolted Joints, MSc Thesis, METU, Turkey (1988).

  25. O. Zhang and J. A. Poirier, “New analytical model of bolted joints,” J Mech Des, 126, No. 4, 721–728 (2004).

    Article  Google Scholar 

  26. P. Joho, Vis a Tete Hexagonale [Hexagonal Head Screw].

  27. T. F. Lehnhoff, K. I. Ko, and M. L. McKay, “Member stiffness and contact pressure distribution of bolted joints,” J Mech Des, 116, No. 2, 550–557 (1994).

    Article  Google Scholar 

  28. J. Wileman, M. Choudhury, and I. Green, “Computation of member stiffness in bolted connections,” J Mech Des, 113, No. 4, 432–437 (1991).

    Article  Google Scholar 

  29. S. de Siqueira Santos, D . Y. Takahashi, A. Nakata, and A. Fujita, “A comparative study of statistical methods used to identify dependencies between gene expression signals,” Brief Bioinform, 15, No. 6, 906–918 (2014).

  30. A. Bhattacharjee, “Distance correlation coefficient: an application with Bayesian approach in clinical data analysis,” J Mod Appl Stat Methods, 13, No. 1, 354–366 (2014).

    Article  Google Scholar 

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Authors and Affiliations

  1. EMISys Research Team, E3S Research Center, Mohammadia School of Engineers Mohammed V University in Rabat, Rabat, Morocco

    O. Soukaina & M. Hamid

  2. QSM Research Team, Mohammadia School of Engineers, Mohammed V University in Rabat, Rabat, Morocco

    H. Bachir

Authors
  1. O. Soukaina
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  2. M. Hamid
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  3. H. Bachir
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Correspondence to O. Soukaina.

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Translated from Problemy Mitsnosti, No. 5, p. 122, September – October, 2023

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Soukaina, O., Hamid, M. & Bachir, H. Numerical Investigation of Member Stiffness in Composite Sandwich Bolted Connections. Strength Mater 55, 986–1005 (2023). https://doi.org/10.1007/s11223-023-00590-9

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