Simulation of the effect of the elastic modulus of a functionally graded plate material on the stress concentration at a circular hole

Keywords

thin elastic plate, circular hole, functionally graded material, stress-strain state, stress concentration factor, computer simulation, finite element analysis.

Cite as

Hart E. I. and Terokhin B. I. Simulation of the effect of the elastic modulus of a functionally graded plate material on the stress concentration at a circular hole. Physicochemical Mechanics of Materials. 2026. 62(2), 142-149.

https://doi.org/10.15407/pcmm2026.02.142

Abstract

Computer simulation and numerical analysis of the elastic modulus variation of a functionally graded material of a thin, rectangular, non-uniform plate with a circular hole under various loads is performed. The use of functionally graded materials with specific mechanical properties in thin-walled structures can significantly reduce stress and strain concentrations at the hole.

References

1. V. Birman, L.W. Byrd, “Modeling and analysis of functionally graded materials and structures,” Trans. ASME. Appl. Mech. Rev., 60, Is. 5, 195-216 (2007). https://doi.org/10.1115/1.2777164
2. V. Vasiliev, and V. Morozov, Advanced Mechanics of Composite Materials and Structures, Elsevier (2018). https://doi.org/10.1016/B978-0-08-102209-2.00002-5
3. M.B. Shtern, and V.D. Pud, Mechanical and Computer Models for Consolidation of Granular Media Based on Metal and Ceramic Powders under Deformation and Sintering [in Ukrainian], Lutskyi Natsionalnyi Tekhnichnyi Universytet, Lutsk (2010).
4. G.S. Firstov, Yu.N. Koval, J. Van Humbeeck, and P. Ochin, “Martensitic transformation and shape memory effect in Ni3Ta: A novel high-temperature shape memory alloy,” Mater. Sci. and Eng.: A, 481-482, 590-593 (2008). https://doi.org/10.1016/j.msea.2007.03.127
5. V. Skalskyi, and Z. Nazarchuk, O. Stankevych, “Acoustic Emission: Fracture Detection in Structural Materials, Cham: Springer (2022). https://doi.org/10.1007/978-3-031-11291-1
6. Ya. S. Pidtdsryhach, Selected Papers [in Ukrainian], Naukova Dumka, Kyiv (1995).
7. W.D. Pilkey, D.F. Pilkey, and Z. Bi Peterson’s, Stress Concentration Factors, Wiley (2020). https://doi.org/10.1002/9781119532552
8. G.N. Savin, Stress Distribution Around Holes, Washington, NASA; Springfield, Virginia (1970). 997 p.
9. V.S. Hudramovich, E.L. Hart, and B.I. Terokhin, “Stress concentration around a circular hole in thin plates and cylindrical shells with a radially inhomogeneous inclusion,” in Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials: Collected work, Chapter 18, Cham: Springer (2024), pp. 249-264. https://doi.org/10.1007/978-3-031-54063-9_18
10. E.L. Hart, and B.I. Terokhin, “Effect of functionally graded inclusion on stress conservation near a circular hole in thin plates for different boundary conditions,” J. of Optimization, Differential Equations and their Applications, 33, Is. 1, 110-127 (2025). https://doi.org/10.15421/142506
11. E.L. Hart, and B.I. Terokhin, “Finite-element analysis of stress concentration in thin plates and cylindrical shells with a circular hole surrounded by an inclusion of functionally graded material,” J. of Mathem. Sci., 291, Is. 5, 703-715 (2025). https://doi.org/10.1007/s10958-025-07846-6
12. A. Haque, L. Ahmed, and A. Ramasetty, “Stress concentrations and notch sensitivity in woven ceramic matrix composites containing a circular hole – an experimental, analytical, and finite element study,” J. Amer. Ceramic Soc., 88, Is. 8, 2195-2201 (2005). https://doi.org/10.1111/j.1551-2916.2005.00404.x
13. D.S. Sharma, “Stress distribution around polygonal holes,” Int. J. of Mech. Sci., 65, Is. 1, 115-124 (2012). https://doi.org/10.1016/j.ijmecsci.2012.09.009
14. Q.Q. Yang, C.F. Gao, and W.T. Chen, “Stress concentration in a finite functionally graded material plate,” Sci. China Phys. Mech. Astron., 55, 1263-1271 (2012). https://doi.org/10.1007/s11433-012-4774-x
15. R. Sburlati, “Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate,” Int. J. Solids Struct., 50, 22-23, 3649-3658 (2013). https://doi.org/10.1016/j.ijsolstr.2013.07.007
16. D.V. Kubair, and B. Bhanu-Chandar, “Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension,” Intern. J. Mech. Sci., 50, Is. 4, 732-742 (2008). https://doi.org/10.1016/j.ijmecsci.2007.11.009
17. M. Mohammadi, J.R. Dryden, and L. Jiang, “Stress concentration around a hole in a radially inhomogeneous plate,” Intern. J. Solids Structures, 48, Is. 3-4, 483-491 (2011). https://doi.org/10.1016/j.ijsolstr.2010.10.013
18. T.A. Enab, “Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings,” Ain Shams Eng., 5, Is. 3, 839-850 (2014). https://doi.org/10.1016/j.asej.2014.03.002
19. H.M.A. Abdalla, F. De Bona, and D. Casagrande, “Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole,” Compos. Part C: Open Access., 15 (2024). Art. no. 100512. https://doi.org/10.1016/j.jcomc.2024.100512
20. Q. Yang, H. Cao, Y. Tang, Y. Li, and X. Chen, “Experimental investigation of stress distributions in 3D printed graded plates with a circular hole,” Materials, 14, Is. 24, 1-13 (2021). https://doi.org/10.3390/ma14247845
21. L.D. Bobbio, B. Bocklund, Z.-K. Liu, and A.M. Beese, “Tensile behavior of stainless steel 304L to Ni-20Cr functionally graded material: experimental characterization and computational simulations,” Materialia, 18 (2021). Art. no. 101151. https://doi.org/10.1016/j.mtla.2021.101151
22. O. C. Zienkiewicz, R. L. Teylor, and D. D. Fox, The Finite Element Method for Solid and Structural Mechanics, Elsevier, New York (2014).
23. E.L. Hart, “Projection-iterative version of the pointwise relaxation method,” J. of Mathem. Sci., 167, Is. 1, 76-88 (2010). https://doi.org/10.1007/s10958-010-9903-3
24. E.L. Hart, and V.S. Hudramovich, “Projection-iterative schemes for the realization of the finite-element method in problems of deformation of plates with holes and inclusions,” J. of Mathem. Sci., 203, Is. 1, 55-69 (2014). https://doi.org/10.1007/s10958-014-2090-x
25. A.I. Lurie, Theory of Elasticity. Foundations of Engineering Mechanics, Springer, Berlin: Heidelberg (2005). https://doi.org/10.1007/978-3-540-26455-2 https://doi.org/10.1007/978-3-540-26455-2
26. K. Washizu, Variational Methods in Elasticity and Plasticity, Pergamon Press. Ltd., Oxford (1975).