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Establishment and experimental verification of a theoretical model for axial nonlinear stiffness of bolt connected members

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Abstract

This work presents a new universal mathematical calculation model of connected members based on real deformation of bolted joints. For this model, a finite element simulation analysis of stiffness was carried out of connected members based on multiple size parameters of the three-dimensional entity model of bolted joint. Moreover, deformation of bolt hole edges with bolt head (nut) which influences stiffness sensitivity greatly was used as the reference; a new universal mathematical calculation model of bolted connected members was constructed based on Levenberg-Marquardt optimization algorithm. Subsequently, a finite element simulation verification of the proposed new model was conducted. The absolute error was about 4 % and the maximum absolute error was 5.66 %; experimental verification was also conducted on the proposed model.

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Abbreviations

K me :

Stiffness of connected members

F b :

Axial force of bolt

δ me :

Deformation under the action of forces

d h :

Diameter of bolt diameter

d he :

Diameter of bolt head

t m :

Thickness of connected members

K mo :

Stiffness of hollow cylinder

βme :

Correction factor of stiffness

a :

Thickness of bolt head

d b :

Effective large diameter of bolt

E m :

Elasticity modulus of connected members

E b :

Elasticity modulus of bolt

K FEA-M :

Calculated stiffness in finite element analysis

\({\overline d}_{he}\) :

Dimensionless parameter of dhe

\({\overline a}\) :

Dimensionless parameter of a

\({\overline d}_{h}\) :

Dimensionless parameter of dh

\({\overline E}_{m}\) :

Dimensionless parameter of Em

\({\overline t}_{m}\) :

Dimensionless parameter of tm

K me-t :

Stiffness of connected members

K me-u :

Stiffness of the upper part of connected members

K me-d :

Stiffness of the lower part

K to-me :

Final calculated stiffness of connected members

F m :

Guarantee load median of bolts of some specification

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Heze University, Heze, 274015, China

    Shikun Lu

  2. Faculty of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Shikun Lu

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  1. Shikun Lu
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Correspondence to Shikun Lu.

Additional information

Shikun Lu holds a Doctorate from Xi’an University of Technology. He currently teaches at Heze University. His research interests include mechanical bonding surfaces, mechanical vibration and stiffness of bolted connections, stirling engines, and more.

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Lu, S. Establishment and experimental verification of a theoretical model for axial nonlinear stiffness of bolt connected members. J Mech Sci Technol 39, 1901–1913 (2025). https://doi.org/10.1007/s12206-025-0317-z

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  • DOI: https://doi.org/10.1007/s12206-025-0317-z

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