Study of influence of the auxiliary factors onto characteristics of elastic-plastic deformation in the stress concentrator of the beam-wall with broken edges
| Назва | Study of influence of the auxiliary factors onto characteristics of elastic-plastic deformation in the stress concentrator of the beam-wall with broken edges |
| Назва англійською | Study of influence of the auxiliary factors onto characteristics of elastic-plastic deformation in the stress concentrator of the beam-wall with broken edges |
| Автори | Valerii Sokov |
| Принадлежність | Admiral Makarov National University Of Shipbuilding, Mykolaiv, Ukraine |
| Бібліографічний опис | Study of influence of the auxiliary factors onto characteristics of elastic-plastic deformation in the stress concentrator of the beam-wall with broken edges / Valerii Sokov // Scientific Journal of TNTU. — Tern.: TNTU, 2024. — Vol 114. — No 2. — P. 60–72. |
| Bibliographic description: | Sokov V. (2024) Study of influence of the auxiliary factors onto characteristics of elastic-plastic deformation in the stress concentrator of the beam-wall with broken edges. Scientific Journal of TNTU (Tern.), vol 114, no 2, pp. 60–72. |
| DOI: | https://doi.org/10.33108/visnyk_tntu2024.02.060 |
| УДК | 539.4 : 629.5 |
| Ключові слова | elastic-plastic deformation, cyclic diagrams, beam with broken edges, finite elements. |
The thin-walled steel beam-wall with broken edges is being investigated, which is a part of many structures. The wall of this beam consists of two prismatic parts with a linear transition from a smaller to a larger wall height, together forming an angular upper edge with the edges of the prismatic parts. The lower linear edge of the wall is attached to the sheathing.The beam-wall is subjected to static and cyclic loads, under which elastic-plastic deformations strains may occur at in the stress concentrator. This leads to failure of static strength and growth of fatigue cracks. The factors influencing the parameters of elastic-plastic deformation at in the stress concentrator of this beam are practically unstudied. The article under discussion presents the results of studying the influence of the beam-wall thickness and load vector balancing on the values of static and cyclic ranges of elastic-plastic deformations strains at in the stress concentrator. It has had been found that load vector balancing significantly improves the results of elastic-plastic deformations strains under single static loading and allows for the use of a larger load increment to achieve the same results as when no balancing is applied. Applying load vector balancing stabilizes the cyclic deformation loop practically from the first cycle. If balancing is absent, stabilization occurs only from the third cycle. Unlike static ones, the values of cyclic ranges do not depend on the application or non-application of balancing and remain practically stable with fixed geometric parameters and loading. Gradual reduction in the thickness of the beam-wall causes an increase in the range (static and cyclic) of elastic-plastic deformations strains at in the stress concentrator. The obtained results will shorten the time required for planning serial calculations of elastic-plastic deformation of a the beam-wall with edge break broken edges to develop appropriate design techniques. | |
| ISSN: | 2522-4433 |
| Перелік літератури |
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2. Sumelka W., & Nowak M. On a general numerical scheme for the fractional plastic flow rule. Mechanics of Materials. Netherlands: Elsevier, 2018, vol. 116, pp. 120–129. Doi: 10.1016/j.mechmat.2017.02.005.
3. Lu D., Liang J., Du X., Ma C., & Gao Z. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule. Computers and Geotechnics. UK: Elsevier BV, 2019, vol. 105, pp. 277–290. Doi: 10.1016/j.compgeo.2018.10.004.
4. Wang J., Liu K., & Zhang D. An improved CE/SE scheme for multi-material elastic–plastic flows and its applications. Computers & Fluids. UK: Elsevier Ltd., 2009, vol. 38 (3), pp. 544–551. Doi: 10.1016/ j.compfluid.2008.04.014.
5. Wells G. N., Sluys L. J., & de Borst R. A p-adaptive scheme for overcoming volumetric locking during plastic flow. Computer Methods in Applied Mechanics and Engineering. Netherlands: Elsevier, 2002, vol. 191 (29–30), pp. 3153–3164. Doi: 10.1016/s0045-7825(02)00252-9.
6. Swedlow, Jerold Lindsay. The thickness effect and plastic flow in cracked plates. Dissertation (Ph.D.). 1965. California Institute of Technology. Doi: 10.7907/0WVE-W364.
7. Beynet P., & Plunkett R. Plate impact and plastic deformation by projectiles. Experimental Mechanics. US: Springer New York, 1971, no. 11, pp. 64–70. Doi: 10.1007/bf02320622.
8. Parton V. 3., Morozov E. M. Mehanika uprugoplasticheskogo razrusheniya. 2-e izd., pererab. i dop. M.: Nauka, Glavnaya redakciya fiziko-matematicheskoj literatury, 1985. 504 p. [In Russian].
9. Zhang Y.-Q., Hao H., & Yu M.-H. A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems. Journal of Applied Mechanics. US: ASME, 2003, vol. 70 (5), pp. 649–654. Doi: 10.1115/ 1.1602484.
10. Runesson K., Saabye Ottosen N., & Dunja P. Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain. International Journal of Plasticity. UK: Elsevier Ltd., 1991, vol. 7 (1–2), pp. 99–121. Doi: 10.1016/0749-6419(91)90007-l
11. Sergei Alexandrov, Yeau-Ren Jeng. A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions. Journal of Mechanics. UK: Cambridge University Press, 2021, vol. 37, pp. 100–107. Available at: https://doi.org/10.1093/jom/ufaa001.
12. Eraslan A. N., Akis T. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica. Austria: Springer-Verlag Wien, 2006, vol. 181, pp. 43–63. Available at: https://doi.org/10.1007/s00707-005-0276-5.
13. Sokov V. M. “Bibliotechnij klas FE VolumeProblemOfTheoryOfElasticity Tetrahedron 10Nodes”: a.s. № 109597 Ukrayini vid 18.11.2021. Avtorske pravo i sumizhni prava. Byuleten no. 68, 2021, pp. 262–263. [In Ukrainian].
14. Sokov V. M. “Bibliotechnij klas FE_VolumeProblemOfTheoryOfElasticity_Tetrahedron_20Nodes”: a. s. № 116226 Ukrayini vid 30.01.2023. Avtorske pravo i sumizhni prava. Byuleten no. 74, 2023, pp. 309–310. [In Ukrainian].
15. Postnov V. A., Harhurim I. Ya. Metod konechnyh elementov v raschetah sudovyh konstrukcij. L.: Sudostroenie, 1974. 344 p. [in Russian]
16. Zienkiewicz O. C., Taylor R. L. The Finite Element Method for Solid and Structural Mechanics: 6-th ed. Elsevier, 2005. 648 p.
17. Sokov V. M. Study of influence of the thickness in the stress raiser of the ship structure assembly in plastic stage. Suchasni tekhnolohii proektuvannia, pobudovy, ekspluatatsii i remontu suden, morskykh tekhnichnykh zasobiv i inzhenernykh sporud: proceedings of all-Ukrainian scientific and technical conference with international participation (Mykolaiv, 17–18 may 2023 y.). Mykolaiv: NUOS, 2023. pp. 103–107. |
| References: |
1. Andrew John Abbo B.E. Finite Element Algorithms For Elastoplasticity And Consolidation: 3-rd ed. A Thesis submitted for the Degree of Doctor of Philosophy at the University of Newcastle. 2005. 285 p.
2. Sumelka W., & Nowak M. On a general numerical scheme for the fractional plastic flow rule. Mechanics of Materials. Netherlands: Elsevier, 2018, vol. 116, pp. 120–129. Doi: 10.1016/j.mechmat.2017.02.005.
3. Lu D., Liang J., Du X., Ma C., & Gao Z. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule. Computers and Geotechnics. UK: Elsevier BV, 2019, vol. 105, pp. 277–290. Doi: 10.1016/j.compgeo.2018.10.004.
4. Wang J., Liu K., & Zhang D. An improved CE/SE scheme for multi-material elastic–plastic flows and its applications. Computers & Fluids. UK: Elsevier Ltd., 2009, vol. 38 (3), pp. 544–551. Doi: 10.1016/ j.compfluid.2008.04.014.
5. Wells G. N., Sluys L. J., & de Borst R. A p-adaptive scheme for overcoming volumetric locking during plastic flow. Computer Methods in Applied Mechanics and Engineering. Netherlands: Elsevier, 2002, vol. 191 (29–30), pp. 3153–3164. Doi: 10.1016/s0045-7825(02)00252-9.
6. Swedlow, Jerold Lindsay. The thickness effect and plastic flow in cracked plates. Dissertation (Ph.D.). 1965. California Institute of Technology. Doi: 10.7907/0WVE-W364.
7. Beynet P., & Plunkett R. Plate impact and plastic deformation by projectiles. Experimental Mechanics. US: Springer New York, 1971, no. 11, pp. 64–70. Doi: 10.1007/bf02320622.
8. Parton V. 3., Morozov E. M. Mehanika uprugoplasticheskogo razrusheniya. 2-e izd., pererab. i dop. M.: Nauka, Glavnaya redakciya fiziko-matematicheskoj literatury, 1985. 504 p. [In Russian].
9. Zhang Y.-Q., Hao H., & Yu M.-H. A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems. Journal of Applied Mechanics. US: ASME, 2003, vol. 70 (5), pp. 649–654. Doi: 10.1115/ 1.1602484.
10. Runesson K., Saabye Ottosen N., & Dunja P. Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain. International Journal of Plasticity. UK: Elsevier Ltd., 1991, vol. 7 (1–2), pp. 99–121. Doi: 10.1016/0749-6419(91)90007-l
11. Sergei Alexandrov, Yeau-Ren Jeng. A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions. Journal of Mechanics. UK: Cambridge University Press, 2021, vol. 37, pp. 100–107. Available at: https://doi.org/10.1093/jom/ufaa001.
12. Eraslan A. N., Akis T. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica. Austria: Springer-Verlag Wien, 2006, vol. 181, pp. 43–63. Available at: https://doi.org/10.1007/s00707-005-0276-5.
13. Sokov V. M. “Bibliotechnij klas FE VolumeProblemOfTheoryOfElasticity Tetrahedron 10Nodes”: a.s. № 109597 Ukrayini vid 18.11.2021. Avtorske pravo i sumizhni prava. Byuleten no. 68, 2021, pp. 262–263. [In Ukrainian].
14. Sokov V. M. “Bibliotechnij klas FE_VolumeProblemOfTheoryOfElasticity_Tetrahedron_20Nodes”: a. s. № 116226 Ukrayini vid 30.01.2023. Avtorske pravo i sumizhni prava. Byuleten no. 74, 2023, pp. 309–310. [In Ukrainian].
15. Postnov V. A., Harhurim I. Ya. Metod konechnyh elementov v raschetah sudovyh konstrukcij. L.: Sudostroenie, 1974. 344 p. [in Russian]
16. Zienkiewicz O. C., Taylor R. L. The Finite Element Method for Solid and Structural Mechanics: 6-th ed. Elsevier, 2005. 648 p.
17. Sokov V. M. Study of influence of the thickness in the stress raiser of the ship structure assembly in plastic stage. Suchasni tekhnolohii proektuvannia, pobudovy, ekspluatatsii i remontu suden, morskykh tekhnichnykh zasobiv i inzhenernykh sporud: proceedings of all-Ukrainian scientific and technical conference with international participation (Mykolaiv, 17–18 may 2023 y.). Mykolaiv: NUOS, 2023. pp. 103–107. |
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