Determination of stress concentration factor in the section of the composite plate weakened by the hole, upon contact of the hole with the cylinder


  • Konstantin Rudakov Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine
  • Serhii Babiienko Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine
  • Tatiana Scherban Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine



polymeric composite material, bolted joints, stress concentration factor


Problematic. When designing bolted joints (BJ), it is necessary, to carry out verification strength calculations. In this case, it is advisable to use express analysis: calculations using simple formulas of sufficient accuracy. One of the main strength calculations of BJ is the calculation of the gap section weakened by the hole. For BJ plates made of layered fibre-reinforced polymers (FRP), the problem has not yet been solved.

Research objective. To verify the accuracy of two well-known express analysis formulas for stress concentration factors (SCF) at the contact of the hole with the bolt, using contrasting examples of materials and schemes for reinforcing FRP plates.

Realization technique. Numerical calculations were carried out using the finite element method (contact problem) for a BJ plate made of layered FRP. A 3D orthotropy of each monolayer was assumed. Two simple express analysis formulas were tested. The results are tabulated. The illustrations are provided.

The results of research. Numerical estimates are obtained that characterize the degree of influence of material characteristics and reinforcement patterns in a layered FRP plate and the accuracy of the formulas considered.

Conclusions. A change in the material and the reinforcement scheme of the layered FRP leads to a significant change in the SCF values of the bolt-loaded hole in the section of the plate weakened by the hole, and the considered express analysis formulas have insufficient accuracy for contrast cases of materials and plate reinforcement schemes. More research is needed.

Author Biographies

Serhii Babiienko, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv


Tatiana Scherban, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv



ECSS‑E‑HB‑32‑20, Part 2А. Structural materials handbook – Part 2: Design calculation methods and general design aspects. (2011), available at :

Dvejrin, A.Z. (2014), “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.

Gagauz, P.M., Gagauz, F.M., Karpov, Ya.S. and Krivenda, S.P. (2015), Proektirovanie i konstruirovanie izdelii iz kompozitsionnykh materialov. Teoriya i praktika [Projection and constructing of articles from composite materials. The theory and practice], in Karpova, Ya.S. (ed.), Nats. aerokosm. un-t im. N.E. Zhukovskogo “Khar'k. aviats. in-t”, Kharkov, Ukraine.

Grover, H.J. (1966), NAVAIR 01-1A-13. Fatigue of Aircraft Structures. NAVAL Air Systems Command Department of the NAVY.

Rudakov, K. and Dyfuchyn, Y. (2018), “About calculations of net-tension failure of a bolted joint on the weakened by hole cross-section of composite plate”, Mechanics and Advanced Technologies, vol. 82, no. 1. pp. 58–66.

Savin, G.I. (1979), Mekhanika deformiruemykh tel. Izbrannye trudy [Mechanics of deformable bodies. The Selected transactionses], Naukova dumka, Kiev, Ukraine.

Young, W.C. and Buynas, R.G. (2002), Roark's Formulas for Stress and Strain. Seventh Edition. McGraw-Hill.

Johnson, K.L. (1985), Contact mechanics, Cambridge University Press, Cambridge, Great Britain.

Milton Graeme W. (2004), The Theory of Composites. Cambridge University Press.

Rudakov, Konstantin, Dyfuchyn, Yury and Babienko, Sergey (2019), “Stress concentration factor near loaded hole contacting with the bolt in the monolayer of orthotropic composite material”, Mechanics and Advanced Technologies, vol. 85, no. 1, pp. 41–48.

Echavarrı´a, C., Haller, P. and Salenikovich, A. (2007), “Analytical study of a pin–loaded hole in elastic orthotropic plates”, Composite Structures, vol. 79. pp. 107–112." target="_blank">

De Jong, T. (1977), “Stresses around pin–loaded holes in elastically orthotropic or isotropic plates”. Compos. Mater., vol. 11. pp. 313–331.

Pilkey, W.D. and Pilkey, D.F. (2008), Peterson’s Stress Concentration Factors. Third Edition. John Wiley & Sons, Inc. Hoboken, New Jersey, Canada.

Lehnickij, S.G. (1977), Teorija uprugosti anizotropnogo tela, [Theory of isotropic elasticity], 2nd ed., Glavnaja redakcija fiz-mat. lit-ry izd-va “Nauka”, Moscow, Russia.

Dyfuchyn, Y.N. and Rudakov, K.N. (2016), “Numerical Modelling of Bolted Joints from Composite. The Message 1. Creation of the Mixed 3D-Models”, Journal of Mechanical Engineering NTUU Kyiv Polytechnic Institute”,vol. 77, no. 2, pp. 100–107.

Rudakov, K.N. (2011), FEMAP 10.2.0. Geometricheskoe i konechno-elementnoe modelirovanie konstruktsii [Geometrical and FEM of designs], Kiev, Ukraine, available at :