Article

Received 09.09.2021

Revised 13.01.2022

Accepted 15.02.2022

Retrieved from Vol. 26, No. 1, 2022

Pages 226 -233

Kirilyuk, V., Levchuk, О., Gavrilenko, V., & Viter, M. (2022). Mathematical and computer simulation of the stress state caused by the displacement of a rigid circle disc in a piezoelectric space. The National Transport University Bulletin, 26(1), 226-233. https://doi.org/10.33744/2308-6645-2022-1-51-226-233

Mathematical and computer simulation of the stress state caused by the displacement of a rigid circle disc in a piezoelectric space

V. Kirilyuk О. Levchuk V. Gavrilenko Mykhailo Viter

Using the mathematical model that takes into account the coupling of force and electric fields in piezoelectric bodies, the stress distribution that occurs when a rigid thin circle disk moves along the axis of symmetry of an electroelastic transversely isotropic material is studied. The exact solution of the space problem of electroelasticity is obtained on the basis of the solution representing of the static equations of electroelasticity for a transversely isotropic body through harmonic functions and using a harmonic potential of a special type. As special cases, from the found analytical solution follow the expressions for evaluating the stress state in an elastic transversely isotropic material for the displacement of a circle hard disk. Computer simulation have been carried out, the influence of the coupling of the force and electric fields on the distribution of stresses under a rigid circle disk.

 

mathematical model; computer simulation; piezoelectric space; hard circle disk; electrical and stress state; stress distribution; field coupling effect
  1. Dai L., Guo W., Wang X. (2006) Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids. Int. J. Solids and Struct., 6 (43), 1818–1831.
  2. Hodes A.Y., Loboda V.V. (2017) A contact zone approach for an arc crack at the interface between two electrostrictive materials. Int. J. Solids Structures, 1 (128), 262–271.
  3. Kaloerov S.A. (2007) Determination of intensity factors for stresses, induction and field strength in multi-connected electro-elastic anisotropic media. Int. Appl. Mech., 6 (43), 77–84.
  4. Karnaukhov V.G., Kozlov V.I., Karnaukhova T.V. (2019) Critical electric load on a hinged thermoviscoelastic rectangular plate with piezoelectric sensors and actuators. Int. Appl. Mech., 6 (55), 596–600.
  5. Kirilyuk V.S. (2006) On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space. Int. Appl. Mech., 11 (42), 1256–1269.
  6. Kirilyuk V.S. Levchuk O.I. (2019) Stress state of an orthotropic piezoelectric body with a triaxial ellipsoidal inclusion subject to tension crack. Int. Appl. Mech., 3 (55), 305–310.
  7. Kyryliuk V.S., Levchuk O.I. (2021) Stress state of an orthotropic electroelastic medium with an arbitrarily oriented elliptic crack under uniaxial tension. Int. Appl. Mech., 1 (57), 53–62.
  8. Podil'chuk Yu.N. (1998) Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions. Int. Appl. Mech., 7 (34), 623–628.
  9. Podil'chuk Yu.N. (2003) Exact analytical solutions of static electroelastic and thermoelectroelastic problems for a transversely isotropic body in curvilinear coordinate systems crack. Int. Appl. Mech., 2 (39), 132–170.
  10. Zhao M.H. (2016) Extended displacement discontinuity method for analysis of cracks in 2D piezoelectricsemiconductors. International Journal of Solids and Structures, 1 (94–95), 50–59.
  11. Selvadurai, A.P.S. (1979.) On the displacement of a penny-shaped rigid inclusion embedded in a transversely isotropic elastic medium. Solid Mechanics Archives, 3 (4), 163–172.
  12. Selvadurai, A.P.S. (1980) Asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic elastic medium of infinite extent. Int. J. Eng. Sci., 7 (18), 979–986.

https://doi.org/10.33744/2308-6645-2022-1-51-226-233