Computer simulation of the stress-strain state of thin plates and cylindrical shells with a circular hole reinforced by an inclusion from functionally graded material

Authors

DOI:

https://doi.org/10.32347/2410-2547.2023.110.63-80

Keywords:

elastic plate, thin-walled cylindrical shell, circular hole, annular inclusion, functionally graded material, stress-strain state, stress concentration factor, FEM analysis

Abstract

Computer simulation and FEM analysis of the stress-strain state of thin plates and thin-walled cylindrical shells, weakened by a circular hole in the presence of an annular inclusion of a functionally graded material (FGM) surrounding it, have been carried out. The influence of the dimensions of the FGM-inclusion and the law of change of its elastic modulus on the concentration of the parameters of the stress-strain state of plates and shells in the vicinity of the hole is studied. The distribution of stress and strain intensities in the zones of local stress concentration is obtained. It has been established that when using a radially inhomogeneous FGM-inclusion with certain mechanical properties, it is possible to reduce the stress concentration factor by more than 35%. The law of change in the modulus of elasticity of the FGM-inclusion and the width of the inclusion have a significant effect not only on the concentration of the parameters of the stress-strain state of the plate and shell, but also on the nature of the stress distribution over their surfaces. The results of a series of large-scale computational experiments show that the use of an FGM annular inclusion makes it possible to reduce the intensity of both stresses and deformations around the hole.

Author Biographies

Eteri Hart, Dnipro National University named after Olesya Honchara

doctor of physical and mathematical sciences, professor, professor of the department of theoretical and computer mechanics

Bohdan Terokhin, Dnipro National University named after Olesya Honchara

postgraduate

References

Avdonin A.S. Prikladnie metodi rascheta obolochek i tonkostennih konstrukcii (Applied methods for calculating shells and thin-walled structures). – M., 1969. – 402 р.

Bazhenov V., Perelmuter A., Vorona Yu. Structural mechanics and theory of structures. History essays. – LAP LAMBERT Academic Publishing. Beau Bassin, Mauritius, 2017. – 580 p.

Lukianchenko O., Kostina O. The finite element metod in problems of the thin shells theory. – LAP LAMBERT Academic Publishing, Beau Bassin, Mauritius, 2019. – 134 p.

Peterson R. Koeffitsiyenty kontsentratsii napryazheniy (Stress concentration factors). – M., 1977. – 302 р.

Savin G.N. Raspredeleniye napryazheniy okolo otverstiy (Stress distribution around holes). – Kyiv, 1968. – 888 p.

Guz A.N., Chernyshenko I.S., Chekhov Val. N. et al. Metody rascheta obolochek. V 5 t. T. 1. Teoriya tonkikh obolochek, oslablennykh otverstiyami (Shell calculation methods. In 5 vols. Vol. 1. Theory of thin shells weakened by holes). – Kyiv, 1980. – 636 p.

Gudramovich V.S., Gart É.L., Strunin K.A. Modeling of the behavior of plane-deformable elastic media with elongated elliptic and rectangular inclusions // Materials Science. – 2017. – Vol. 52, Iss. 6. – P. 768–774.

Hart E.L., Hudramovich V.S. Computer simulation of the stress-strain state of plates with reinforced elongate rectangular holes of various orientations // Strength of materials and theory of structures: Scientific-and-technical collected articles. – Kyiv: KNUBA, 2022. – Iss. 108. – P. 77–86.

Hart E.L., Hudramovich V.S., Terokhin B.I. Vplyv vklyuchennya iz funktsionalʹno-hradiyentnoho materialu na kontsentratsiyu napruzhenʹ v tonkykh plastynakh ta tsylindrychnykh obolonkakh z kruhovym otvorom (Effect of a functionally graded material inclusion on the stress concentration in thin plates and cylindrical shells with a circular opening) // Tekhnichna mekhanika. – 2022. – № 4. – P. 67–78.

Hart E.L., Terokhin B.I. Computer simulation of the stress-strain state of the plate with circular hole and functionally graded inclusion // Journal of Optimization, Differential Equations and their Applications. – 2021. – Vol. 29, Iss. 1. – P. 42–53.

Hart E.L., Terokhin B.I. Vybir ratsionalʹnykh parametriv pidkriplyuyuchykh elementiv pry kompʺyuternomu modelyuvanni povedinky tsylindrychnoyi obolonky z dvoma pryamokutnymy otvoramy (Choice of rational parameters of reinforcement elements in computer simulation of behavior of a cylindrical shell with two rectangular holes) // Problemy obchyslyuvalʹnoyi mekhaniky i mitsnosti konstruktsiy: zb. nauk. pratsʹ. – Dnipro: Lira, 2019. – Vol. 30. – P. 19–32.

Hudramovych V.S., Hart E.L., Marchenko O.A. Vplyv formy pidkriplenʹ na napruzheno-deformovanyy stan tsylindrychnoyi obolonky z vydovzhenymy pryamokutnymy otvoramy (About the influence of the form of reinforcement on the stress-strain state of a cylindrical shell with elongated rectangular holes) // Problemy obchyslyuvalʹnoyi mekhaniky i mitsnosti konstruktsiy: zb. nauk. pratsʹ. – Dnipro, 2017. – Vol. 27. – P. 52–64.

Hudramovich V.S., Hart E.L., Marchenko O.A. Reinforcing inclusion effect on the stress concentration within the spherical shell having an elliptical opening under uniform internal pressure // Strength of Materials. – 2021. – Vol. 52, No. 6. – P. 832–842.

Analiticheskiye resheniya smeshannykh osesimmetrichnykh zadach dlya funktsional'no-gradiyentnykh sred (Analytical solutions of mixed axisymmetric problems for functionally graded media) / S.M. Aizikovich [et al.]. – M., 2011. – 192 p.

Yang Q., Gao C.-F., Chen W. Stress analysis of a functional graded material plate with a circular hole // Arch. Appl. Mech. – 2010. – Vol. 80. – P. 895–907.

Linkov A., Rybarska-Rusinek L. Evaluation of stress concentration in multi-wedge systems with functionally graded wedges // Intern. J. Engng Sci. – 2012. – Vol. 61. – P. 87–93.

Kubair D.V., Bhanu-Chandar B. Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension // Intern. J. Mech. Sci. – 2008. – Vol. 50. – P. 732–742.

Mohammadi M., Dryden J. R., Jiang L. Stress concentration around a hole in a radially inhomogeneous plate // Intern. J. Solids Structures. – 2011. – Vol. 48. – P. 483–491.

Zienkiewicz O.C, Taylor R.L. The finite element method for solid and structural mechanics. – New York: Elsevier, 2005. – 632 p.

Washizu K. Variational Methods in Elasticity and Plasticity. – Oxford-New York: Pergamon Press, 1975. – 420 p.

Downloads

Published

2023-06-26

Issue

Section

Статті