Concentration of stresses near the hole in contact with rigid cylinder in composite plate, taking into account lateral clearances




bolted joints, clearance between bolt and hole, stress concentration factor, polymer composite material


Problems. When designing bolted joints (BJ), it is necessary, in particular, to carry out their verification calculations for strength.  At the same time, it is desirable to use express analysis: calculations by simple formulas of sufficient accuracy. For BJ of plates made of layered polymer composite materials (PCM), the problem has not yet been solved.

The aim of the study. The task is to test the accuracy of three known formulas for quick calculation of the value of the stress concentration factor (SCF) in zone of contact of bolt-hole with a rigid cylinder (bolt). The study was carried out on contrasting examples of materials and schemes of reinforcement of plates made of PСM, taking into account possible clearance between bolt and hole in the real range: from zero to 1% of diameter.

Methodology of implementation. Numerical calculations were made using the finite element method (contact problem) for the BJ of plates made of layered PCM. 3D orthotropy of each monolayer was provided. Three simple formulas of express analysis were tested. The results are summarized in the tables and many illustrations are given.

Research results. Numerical estimates of depending of the SCF in zone of the surface of the bolt-hole from considered factors are obtained.  The factors are the material characteristics, the schemes of reinforcement of plates made of layered PСM and the values of the clearance between bolt and hole in the plates, as well as the accuracy of the considered formulas.

Conclusions. Changing the material and the scheme of reinforcement of plate made of layered PСM leads to a significant change in the values ​​of maximum stresses and SCF in zone of the bolt-loaded hole in the weakened by hole cross section of a plate. Considered formulas of the express analysis have insufficient accuracy for consideration of contrast properties of materials and schemes of reinforcement of a plate. Changing size of clearance between bolt and hole in the range from zero to 1% of the diameter leads to relatively small changes in SCF: up to 10% maximum. Additional research is needed.


  1. ECSS-E-HB-32-20, Part 2А. Structural materials handbook – Part 2: Design calculation methods and general design aspects, 2011. Available:
  2. E.T. Vasilevskij et al., “System of experimental support for strength calculation of composites mechanical joints”, Otkrytye informacionnye i komp'juternye integrirovannye tehnologii, No. 47, pp. 42–52, 2010.
  3. A.Z. Dvejrin, “Review and analysis of problem state of experiment-calculated support of design of aircraft units from polymer composites with mechanical junction of parts”, Otkrytye informacionnye i komp'juternye integrirovannye tehnologii, No. 66, pp. 5–19, 2014.
  4. P.M. Gagauz et al., “Proektirovanie i konstruirovanie izdelii iz kompozitsionnykh materialov. Teoriya i praktika: uchebnik; pod obshch. red. Ya.S. Karpova" [Projection and constructing of articles from composite materials. The theory and practice: the textbook], 2015. Kharkov, Ukraine: Nats. aerokosm. un-t im. N.E. Zhukovskogo “Khar'k. aviats. in-t”.
  5. H.J. Grover, NAVAIR 01-1A-13. Fatigue of Aircraft Structures. NAVAL Air Systems Command Department of the NAVY,
  7. K. Rudakov and Y. Dyfuchyn, “About calculations of net-tension failure of a bolted joint on the weakened by hole cross-section of composite plate”, Mechanics and Advanced Technologies, No. 1(82). pp. 58–66, 2018.
  8. G.I. Savin, Mekhanika deformiruemykh tel. Izbrannye trudy [Mechanics of deformable bodies. The Selected transactionses], Naukova dumka, Kiev, Ukraine, 1979.
  9. W.C. Young, and R.G. Buynas, Roark's Formulas for Stress and Strain. Seventh Edition. McGraw-Hill, 2002.
  10. K.L. Johnson, Contact mechanics. Cambridge University Press, Cambridge, Great Britain, 1985.
  11. W. Milton Graeme, The Theory of Composites. Cambridge University Press, 2004.
  12. K. Rudakov, Y. Dyfuchyn, S. Babienko, “Stress concentration factor near loaded hole contacting with the bolt in the monolayer of orthotropic composite material”, Mechanics and Advanced Technologies, No. 1(85). pp. 41–48, 2019.
  14. C. Echavarrı´a, P. Haller and A.Salenikovich, “Analytical study of a pin–loaded hole in elastic orthotropic plates”, Composite Structures, Vol.79. pp. 107–112, 2007.
  15. T. DeJong, “Stresses around pin–loaded holes in elastically orthotropic or isotropic plates”, J. Compos. Mater., Vol. 11,
  16. pp. 313–331, 1977.
  17. C. Echavarría, H. Cañola and W. Echeverri, “Analysis of bolted ultra-high performance concrete joints”, Lámpsakos, No. 24, julio-diciembre, pp.15–22, 2020.
  18. Crews, John H., Hong, Jr.C.S. and I.S. Raju, Stress-Concentration Factors for Finite Orthotropic Laminates with a Pin-Loaded Hole. NASA Technical Paper 1862, 1981.
  19. W.D. Pilkey and D.F. Pilkey, Peterson’s Stress Concentration Factors. Third Edition. John Wiley & Sons, Inc. Hoboken, New Jersey, Canada, 2008.
  20. Lehnickij, S.G. Teorija uprugosti anizotropnogo tela, [Theory of anisotropic elasticity], 2nd ed., Glavnaja redakcija fiz-mat. litry izd-va “Nauka”, 1977. Moscow, Russia.
  21. K. Rudakov and V. Maslyey, “To definition of elasticity modules of plate from unidirectional high-modules carbon
  22. fibre”, Mechanics and Advanced Technologies, No. 3(87). pp. 7–15, 2019.
  23. Y.N. Dyfuchyn and K.N. Rudakov, “Numerical Modelling of Bolted Joints from Composite. The Message 1. Creation of the Mixed 3D-Models”, Journal of Mechanical Engineering NTUU “Kyiv Polytechnic Institute”, No. 2 (77), pp. 100–107, 2016.
  24. 192
  25. K. Rudakov, and Y. Dyfuchyn, “Express estimation of stress concentration factor near the hole loaded with a bolt in a plate from a layered polymeric composite material. Impact of monolayers stacking sequence”, Mechanics and Advanced Technologies, No. 1(88). pp. 7–18, 2020.
  26. K. Rudakov, S. Babiienko and T. Scherban “Determination of stress concentration factor in the section of the composite plate weakened by the hole, upon contact of the hole with the cylinder”, Mechanics and Advanced Technologies, No. 2(89). pp. 48–54, 2020.
  27. K.N. Rudakov, FEMAP 10.2.0. Geometricheskoe i konechno-elementnoe modelirovanie konstruktsii [Geometrical and FEM of designs]. Kiev, Ukraine, 2011. Available:



How to Cite

K. Rudakov, Y. Dyfuchyn, and T. Bakhtovarshoiev, “Concentration of stresses near the hole in contact with rigid cylinder in composite plate, taking into account lateral clearances”, Mech. Adv. Technol., vol. 5, no. 2, pp. 183–192, Nov. 2021.