FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING
Thin-walled plate-shell structural elements are widely used in various sectors of engineering and the national economy, particularly in the aerospace, oil and gas, and power industries, mechanical engineering, construction, etc. The presence of holes in structures of this type leads to a sharp incre...
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Technical Mechanics| _version_ | 1861499660054560768 |
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| author | HART, E. L. TEROKHIN, B. I. |
| author_facet | HART, E. L. TEROKHIN, B. I. |
| author_sort | HART, E. L. |
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| description | Thin-walled plate-shell structural elements are widely used in various sectors of engineering and the national economy, particularly in the aerospace, oil and gas, and power industries, mechanical engineering, construction, etc. The presence of holes in structures of this type leads to a sharp increase in local stresses, which under certain conditions may lead to destructive processes. This is especially true if they are used under extreme conditions, which is common in various sectors of engineering. Reducing stress concentration near holes in thin-walled structures is a pressing problem in solid mechanics. One way to do this is to use advanced functionally graded materials (FGMs) with specific mechanical properties. A gradient in mechanical properties allows one to control the stress and strain field of structural elements and may contribute to stress reduction near local stress concentrators. This FGM feature significantly increases the strength and reliability of structures as a whole.
This paper presents the results of a computer simulation and finite-element analysis of the stress and strain field of thin rectangular FGM plates under various types of loading. The effect of the FGM plate elastic modulus variation law on stress and strain concentration in the vicinity of a hole is investigated. The stress and strain intensity distribution in local stress concentration zones is obtained. Cases of elastic modulus variation in a horizontal and a vertical direction for each of the loading types under consideration are studied. FGM plate heterogeneity parameters are found such that the stress concentration factor can be reduced down to ~19 %. At the same time, a proportional decrease in the strain intensity in the vicinity of the hole is also observed. The FGM plate elastic modulus variation law has a significant effect not only on the magnitude of the stress and strain concentration parameters, but also on the pattern of the stress distribution over the plate. The results of the series of computational experiments show that the use of FGMs in plates is advisable because it allows one to reduce both the stress and the strain intensity around a hole under various types of loading.
REFERENCES
1. Birman V., Byrd L. W. Modeling and analysis of functionally graded materials and structures. Trans. ASME. Appl. Mech. Rev. 2007. V. 60. No. 5. Pp. 195-216.https://doi.org/10.1115/1.2777164
2. Kawasaki A., Watanabe R. Concept and P/M fabrication of functionally gradient materials. Ceramics International. 1997. V. 23, No. 1. Pp. 73-83.https://doi.org/10.1016/0272-8842(95)00143-3
3. Vasiliev V., Morozov E. Advanced Mechanics of Composite Materials and Structures. 4th ed. Amster-dam: Elsevier, 2018. 864 pp.https://doi.org/10.1016/B978-0-08-102209-2.00002-5
4. Helal W. M. K., Shi D. Y. Analysis of functionally graded rectangular plate by ANSYS. Key Engineer-ing Materials. 2013. V. 572. Pp. 505-508.https://doi.org/10.4028/www.scientific.net/KEM.572.505
5. Pidstyhach Ya. S. Selected Works. Kyiv: Naukova Dumka, 1995. 460 pp. (in Ukrainian).
6. Pilkey W. D., Pilkey D. F., Bi Z. Peterson's Stress Concentration Factors. 4th ed. Hoboken: Wiley, 2020. 640 pp.https://doi.org/10.1002/9781119532552
7. Savin G. N. Stress Distribution around Holes. Kiev: Naukova Dumka, 1968. 888 pp. (In Russian).
8. Hudramovich V. S., Hart E. L., Terokhin B. I. Stress concentration around a circular hole in thin plates and cylindrical shells with a radially inhomogeneous inclusion. Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials: Collected work. Springer Cham, 2024. Vol. 204. Chapter 18. Pp. 249-264.https://doi.org/10.1007/978-3-031-54063-9_18
9. Hart E. L., Terokhin B. I. Effect of functionally graded inclusion on stress conservation near a circu-lar hole in thin plates for different boundary conditions. Journal of Optimization, Differential Equa-tions and their Applications. 2025. V. 33. No. 1. Pp. 110-127.https://doi.org/10.15421/142506
10. Hart E. L., Terokhin B. I. Finite-element analysis of stress concentration in thin plates and cylindrical shells with a circular hole surrounded by an inclusion of functionally graded material. Journal of Mathematical Sciences. 2025. V. 291. No. 5. Pp. 703-715.https://doi.org/10.1007/s10958-025-07846-6
11. Hart E. L., Terokhin B. I. Methods for reducing stress concentration around holes in thin plates and cylindrical shells with annular radially inhomogeneous inclusions. International Applied Mechanics. 2025. V. 61. No. 3. Pp. 359-368.https://doi.org/10.1007/s10778-025-01359-0
12. Hart E. L., Hudramovich V. S., Terokhin B. I. Effect of a functionally graded material inclusion on the stress concentration in thin plates and cylindrical shells with a circular opening. Teh. Meh. 2022. No. 4. Pp. 67-78. (in Ukrainian).https://doi.org/10.15407/itm2022.04.067
13. Hudramovich V. S., Hart E. L., Strunin K. A. Modeling of deformation process of a plate with elastic elongated inclusions based on the finite element method. Teh. Meh. 2014. No. 2. Pp. 12-23. (in Russian)
14. 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. Kyiv, KNUBA, 2022. Iss. 108. Pp. 77-86.https://doi.org/10.32347/2410-2547.2022.108.77-86
15. Haque A., Ahmed L., Ramasetty A. Stress concentrations and notch sensitivity in woven ceramic ma-trix composites containing a circular hole. J. Amer. Ceramic Soc. 2005. V. 88. No. 8. Pp. 2195-2201.https://doi.org/10.1111/j.1551-2916.2005.00404.x
16. Sharma D. S. Stress distribution around polygonal holes. Intern. J. Mechanical Sciences. 2012. V. 65. No. 1. Pp. 115-124.https://doi.org/10.1016/j.ijmecsci.2012.09.009
17. Yang Q. Q., Gao C. F., Chen W. T. Stress concentration in a finite functionally graded material plate. Sci. China Phys. Mech. Astron. 2012. V. 55. Pp. 1263-1271.https://doi.org/10.1007/s11433-012-4774-x
18. Sburlati R. Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate. Int. J. Solids Struct. 2013. V. 50. No. 22-23. Pp. 3649-3658.https://doi.org/10.1016/j.ijsolstr.2013.07.007
19. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rec-tangular cutouts. Mechanics Based Design of Structures and Machines. 2024. V. 52. No. 5. Pp. 2411-2439.https://doi.org/10.1080/15397734.2023.2180033
20. 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. V. 50. No. 4. Pp. 732-742.https://doi.org/10.1016/j.ijmecsci.2007.11.009
21. Mohammadi M., Dryden J. R., Jiang L. Stress concentration around a hole in a radially inhomogene-ous plate. Intern. J. Solids Struct. 2011. V. 48. No. 3-4. Pp. 483-491.https://doi.org/10.1016/j.ijsolstr.2010.10.013
22. Enab T. A. Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Eng. Journal. 2014. V. 5. No. 3. Pp. 839-850.https://doi.org/10.1016/j.asej.2014.03.002
23. Rani P., Verma D., Ghangas G. Stress concentration analysis of functionally graded material coated elliptical inclusion under uniaxial tension. Materials Today: Proceedings, 2023. V. 78. Pt. 3. P. 351-358.https://doi.org/10.1016/j.matpr.2022.09.602
24. Abdalla H. M. A., De Bona F., Casagrande D. Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole. Composites. Part C. 2024. V. 15. Art. 100512.https://doi.org/10.1016/j.jcomc.2024.100512
25. Yang Q., Cao H., Tang Y., Li Y., Chen X. Experimental investigation of stress distributions in 3D printed graded plates with a circular hole. Materials. 2021. V. 14, No. 24. Pp. 1-13.https://doi.org/10.3390/ma14247845
26. Bobbio L. D., Bocklund B., Liu Z.-K., Beese A. M. Tensile behavior of stainless steel 304L to Ni-20Cr functionally graded material. Materialia. 2021. V. 18. Art. 101151.https://doi.org/10.1016/j.mtla.2021.101151
27. Zienkiewicz O. C., Taylor R. L., Fox D. D. The Finite Element Method for Solid and Structural Me-chanics. 7th ed. New York: Elsevier, 2014. 624 pp.
28. Timoshenko S. P., Gere J. M. Mechanics of Materials. New York: Van Nostrand Reinhold Company, 1972. 552 pp.
29. Lurie A.I. Theory of Elasticity. Foundations of Engineering Mechanics. Berlin-Heidelberg: Springer, 2005. 1050 рp.https://doi.org/10.1007/978-3-540-26455-2
30. Washizu K. Variational Methods in Elasticity and Plasticity. 2nd ed. Oxford: Pergamon Press, 1975. 412 pp.
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| first_indexed | 2026-04-04T01:00:15Z |
| format | Article |
| id | oai:ojs2.journal-itm.dp.ua:article-171 |
| institution | Technical Mechanics |
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| last_indexed | 2026-04-04T01:00:15Z |
| publishDate | 2026 |
| publisher | текст 3 |
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| spelling | oai:ojs2.journal-itm.dp.ua:article-1712026-04-03T21:15:36Z FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING HART, E. L. TEROKHIN, B. I. thin elastic plate, circular hole, functionally graded material, stress and strain field, uniaxial tension, biaxial tension, pure transverse shear, stress concentration factor, computer simulation , finite-element analysis. Thin-walled plate-shell structural elements are widely used in various sectors of engineering and the national economy, particularly in the aerospace, oil and gas, and power industries, mechanical engineering, construction, etc. The presence of holes in structures of this type leads to a sharp increase in local stresses, which under certain conditions may lead to destructive processes. This is especially true if they are used under extreme conditions, which is common in various sectors of engineering. Reducing stress concentration near holes in thin-walled structures is a pressing problem in solid mechanics. One way to do this is to use advanced functionally graded materials (FGMs) with specific mechanical properties. A gradient in mechanical properties allows one to control the stress and strain field of structural elements and may contribute to stress reduction near local stress concentrators. This FGM feature significantly increases the strength and reliability of structures as a whole. This paper presents the results of a computer simulation and finite-element analysis of the stress and strain field of thin rectangular FGM plates under various types of loading. The effect of the FGM plate elastic modulus variation law on stress and strain concentration in the vicinity of a hole is investigated. The stress and strain intensity distribution in local stress concentration zones is obtained. Cases of elastic modulus variation in a horizontal and a vertical direction for each of the loading types under consideration are studied. FGM plate heterogeneity parameters are found such that the stress concentration factor can be reduced down to ~19 %. At the same time, a proportional decrease in the strain intensity in the vicinity of the hole is also observed. The FGM plate elastic modulus variation law has a significant effect not only on the magnitude of the stress and strain concentration parameters, but also on the pattern of the stress distribution over the plate. The results of the series of computational experiments show that the use of FGMs in plates is advisable because it allows one to reduce both the stress and the strain intensity around a hole under various types of loading. REFERENCES 1. Birman V., Byrd L. W. Modeling and analysis of functionally graded materials and structures. Trans. ASME. Appl. Mech. Rev. 2007. V. 60. No. 5. Pp. 195-216.https://doi.org/10.1115/1.2777164 2. Kawasaki A., Watanabe R. Concept and P/M fabrication of functionally gradient materials. Ceramics International. 1997. V. 23, No. 1. Pp. 73-83.https://doi.org/10.1016/0272-8842(95)00143-3 3. Vasiliev V., Morozov E. Advanced Mechanics of Composite Materials and Structures. 4th ed. Amster-dam: Elsevier, 2018. 864 pp.https://doi.org/10.1016/B978-0-08-102209-2.00002-5 4. Helal W. M. K., Shi D. Y. Analysis of functionally graded rectangular plate by ANSYS. Key Engineer-ing Materials. 2013. V. 572. Pp. 505-508.https://doi.org/10.4028/www.scientific.net/KEM.572.505 5. Pidstyhach Ya. S. Selected Works. Kyiv: Naukova Dumka, 1995. 460 pp. (in Ukrainian). 6. Pilkey W. D., Pilkey D. F., Bi Z. Peterson's Stress Concentration Factors. 4th ed. Hoboken: Wiley, 2020. 640 pp.https://doi.org/10.1002/9781119532552 7. Savin G. N. Stress Distribution around Holes. Kiev: Naukova Dumka, 1968. 888 pp. (In Russian). 8. Hudramovich V. S., Hart E. L., Terokhin B. I. Stress concentration around a circular hole in thin plates and cylindrical shells with a radially inhomogeneous inclusion. Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials: Collected work. Springer Cham, 2024. Vol. 204. Chapter 18. Pp. 249-264.https://doi.org/10.1007/978-3-031-54063-9_18 9. Hart E. L., Terokhin B. I. Effect of functionally graded inclusion on stress conservation near a circu-lar hole in thin plates for different boundary conditions. Journal of Optimization, Differential Equa-tions and their Applications. 2025. V. 33. No. 1. Pp. 110-127.https://doi.org/10.15421/142506 10. Hart E. L., Terokhin B. I. Finite-element analysis of stress concentration in thin plates and cylindrical shells with a circular hole surrounded by an inclusion of functionally graded material. Journal of Mathematical Sciences. 2025. V. 291. No. 5. Pp. 703-715.https://doi.org/10.1007/s10958-025-07846-6 11. Hart E. L., Terokhin B. I. Methods for reducing stress concentration around holes in thin plates and cylindrical shells with annular radially inhomogeneous inclusions. International Applied Mechanics. 2025. V. 61. No. 3. Pp. 359-368.https://doi.org/10.1007/s10778-025-01359-0 12. Hart E. L., Hudramovich V. S., Terokhin B. I. Effect of a functionally graded material inclusion on the stress concentration in thin plates and cylindrical shells with a circular opening. Teh. Meh. 2022. No. 4. Pp. 67-78. (in Ukrainian).https://doi.org/10.15407/itm2022.04.067 13. Hudramovich V. S., Hart E. L., Strunin K. A. Modeling of deformation process of a plate with elastic elongated inclusions based on the finite element method. Teh. Meh. 2014. No. 2. Pp. 12-23. (in Russian) 14. 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. Kyiv, KNUBA, 2022. Iss. 108. Pp. 77-86.https://doi.org/10.32347/2410-2547.2022.108.77-86 15. Haque A., Ahmed L., Ramasetty A. Stress concentrations and notch sensitivity in woven ceramic ma-trix composites containing a circular hole. J. Amer. Ceramic Soc. 2005. V. 88. No. 8. Pp. 2195-2201.https://doi.org/10.1111/j.1551-2916.2005.00404.x 16. Sharma D. S. Stress distribution around polygonal holes. Intern. J. Mechanical Sciences. 2012. V. 65. No. 1. Pp. 115-124.https://doi.org/10.1016/j.ijmecsci.2012.09.009 17. Yang Q. Q., Gao C. F., Chen W. T. Stress concentration in a finite functionally graded material plate. Sci. China Phys. Mech. Astron. 2012. V. 55. Pp. 1263-1271.https://doi.org/10.1007/s11433-012-4774-x 18. Sburlati R. Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate. Int. J. Solids Struct. 2013. V. 50. No. 22-23. Pp. 3649-3658.https://doi.org/10.1016/j.ijsolstr.2013.07.007 19. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rec-tangular cutouts. Mechanics Based Design of Structures and Machines. 2024. V. 52. No. 5. Pp. 2411-2439.https://doi.org/10.1080/15397734.2023.2180033 20. 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. V. 50. No. 4. Pp. 732-742.https://doi.org/10.1016/j.ijmecsci.2007.11.009 21. Mohammadi M., Dryden J. R., Jiang L. Stress concentration around a hole in a radially inhomogene-ous plate. Intern. J. Solids Struct. 2011. V. 48. No. 3-4. Pp. 483-491.https://doi.org/10.1016/j.ijsolstr.2010.10.013 22. Enab T. A. Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Eng. Journal. 2014. V. 5. No. 3. Pp. 839-850.https://doi.org/10.1016/j.asej.2014.03.002 23. Rani P., Verma D., Ghangas G. Stress concentration analysis of functionally graded material coated elliptical inclusion under uniaxial tension. Materials Today: Proceedings, 2023. V. 78. Pt. 3. P. 351-358.https://doi.org/10.1016/j.matpr.2022.09.602 24. Abdalla H. M. A., De Bona F., Casagrande D. Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole. Composites. Part C. 2024. V. 15. Art. 100512.https://doi.org/10.1016/j.jcomc.2024.100512 25. Yang Q., Cao H., Tang Y., Li Y., Chen X. Experimental investigation of stress distributions in 3D printed graded plates with a circular hole. Materials. 2021. V. 14, No. 24. Pp. 1-13.https://doi.org/10.3390/ma14247845 26. Bobbio L. D., Bocklund B., Liu Z.-K., Beese A. M. Tensile behavior of stainless steel 304L to Ni-20Cr functionally graded material. Materialia. 2021. V. 18. Art. 101151.https://doi.org/10.1016/j.mtla.2021.101151 27. Zienkiewicz O. C., Taylor R. L., Fox D. D. The Finite Element Method for Solid and Structural Me-chanics. 7th ed. New York: Elsevier, 2014. 624 pp. 28. Timoshenko S. P., Gere J. M. Mechanics of Materials. New York: Van Nostrand Reinhold Company, 1972. 552 pp. 29. Lurie A.I. Theory of Elasticity. Foundations of Engineering Mechanics. Berlin-Heidelberg: Springer, 2005. 1050 рp.https://doi.org/10.1007/978-3-540-26455-2 30. Washizu K. Variational Methods in Elasticity and Plasticity. 2nd ed. Oxford: Pergamon Press, 1975. 412 pp. текст 3 2026-03-31 Article Article https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/171 Technical Mechanics; No. 1 (2026): Technical Mechanics; 45-53 Институт технической механики Национальной академии наук Украины и Государственного космического агентства Украины; № 1 (2026): Technical Mechanics; 45-53 ТЕХНІЧНА МЕХАНІКА; № 1 (2026): ТЕХНІЧНА МЕХАНІКА; 45-53 Copyright (c) 2026 Technical Mechanics |
| spellingShingle | HART, E. L. TEROKHIN, B. I. FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title | FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title_full | FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title_fullStr | FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title_full_unstemmed | FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title_short | FINITE-ELEMENT ANALYSIS OF THE STRESS AND STRAIN FILED OF THIN FUNCTIONALLY GRADED PLATES WITH A CIRCULAR HOLE UNDER VARIOUS TYPES OF LOADING |
| title_sort | finite-element analysis of the stress and strain filed of thin functionally graded plates with a circular hole under various types of loading |
| topic_facet | thin elastic plate circular hole functionally graded material stress and strain field uniaxial tension biaxial tension pure transverse shear stress concentration factor computer simulation finite-element analysis. |
| url | https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/171 |
| work_keys_str_mv | AT hartel finiteelementanalysisofthestressandstrainfiledofthinfunctionallygradedplateswithacircularholeundervarioustypesofloading AT terokhinbi finiteelementanalysisofthestressandstrainfiledofthinfunctionallygradedplateswithacircularholeundervarioustypesofloading |