COMPUTER SIMULATION OF THE EFFECT OF ELLIPTICAL INCLUSION ARRANGEMENT ON THE STRAINING OF A CYLINDRICAL SHELL WITH A CIRCULAR HOLE

Abstract

Thin-walled plate-shell structural elements find wide application in many sectors of engineering and the national economy, particularly in the aerospace and the oil and gas industry, power engineering, mechanical engineering, construction, etc. The integrity and homogeneity of structures can be compromised by the presence of inhomogeneities. Such structures often have various manufacturing defects or design inhomogeneities: holes, cutouts, recesses, inclusions, microcracks, and other similar formations, which act as local stress concentrators. Under real-world operating conditions, an increased stress concentration in the zones of local stress concentrators significantly affects the strength and durability of structural elements, thus making a search for ways to reduce stress concentration a key issue in solid mechanics. When designing up-to-date equipment, optimizing material consumption and extending the service life of components using novel materials and technologies is a priority, which determines their competitiveness in various industries.

This study involves a computer simulation and a finite element analysis of the stress and strain fields of thin-walled cylindrical shells with a small circular through hole and several elliptical inclusions of a different material symmetrically arranged around it. For definiteness, it is assumed that the inclusions are homogeneous and located in the plane of the shell. This paper analyzes the effect of the geometry, the mechanical properties, the number, and the arrangement of the inclusions on the stress and strain fields of the shells in the vicinity of the holes under the action of a uniaxial uniform tensile load applied to the shell ends.  The distributions of the stress and strain intensities in the zones of local stress concentration are obtained. The obtained numerical results are compared with the results for shells without inclusions and with known similar results for plates. It is shown that the use of "stiff" elliptical inclusions contributes to stress concentration reduction by ~ (10 – 36) % depending on their number and arrangement. In the case of two diagonal inclusions, the stress concentration zone shifts, which is in agreement with the results for a similar problem for a plate.

REFERENCES

1. Avdonin A. S. Applied Methods for the Design of Shells and Thin-Walled Structures. Moscow: Mashinostroyeniye, 1969. 402 pp. (In Russian).

2. Balashova S. D., Tavadze E. L. On the convergence of the projection-iteration method for solving an extremal problem with constraints. Mathematical Models and Computational Methods in Applied Problems. Dnipropetrovsk: Dnipropetrovsk State University, 1996. Рp. 128-134. (In Russian).

3. Hart E. L., Rybalko Ya. V. Interaction of a circular hole and the surrounding elliptic inclusions under elastic deformation of a rectangular plate. Problems in Computational Mechanics and Structural Strength. Dnipro: Lira, 2019. V. 30. Pp. 5-18. (In Ukrainian).

4. Hart E. L., Shebanov O. D. Stress concentration around a circular hole in a cylindrical shell in the presence of surrounding elliptical inclusions. Problems in Computational Mechanics and Strength of Structures. Dnipro: Lira, 2024. V. 38. P. 36-50. (In Ukrainian).

5. Hudramovich V. S., Hart E. L., Strunin K. A. Simulation of straining the plate with elastic extended inclusions based on finite element method. Teh. Meh. 2014. No. 2. Pp. 12-23. (In Russian).

6. Guz A. N., Chernyshenko I. S. et al. Theory of Thin Shells Weakened by Holes. Kyiv: Naukova Diumka, 1980. 636 pp. (In Russian).

7. Kraiko A. N. Numerical Methods for Shell Analysis. Moscow: Mashinostroyeniye, 1986. 368 pp. (In Russian).

8. Pidstrygach Ya. S. Selected Works. Kyiv: Naukova Dumka, 1995. 460 рp. (In Ukrainian).

9. Savin G. N. Stress Distribution around Holes. Kyiv: Naukova Dumka, 1968. 888 pp. (In Russian).

10. Shtern M. B., Rud V. D. Mechanical and Computer Models for Consolidation of Granular Media Based on Metal and Ceramic Powders During Deformation and Sintering. V. V. Skorokhod (Ed.). Lutsk: Lutsk National Technical University, 2010. 232 рp. (In Russian).

11. Altenbach H., Altenbach J., Kissing W. Mechanics of Composite Structural Elements. Singapore: Springer, 2018. 503 рp. https://doi.org/10.1007/978-981-10-8935-0

12. Bull J. W. Stress around large circular holes in uniform circular cylinders. J. Strain Anal. Eng. Des. 1982. V. 17. No. 1. Pp. 9-12. https://doi.org/10.1243/03093247V171009

13. Gudramovich V. S., Gart É. L., Strunin K. А. Modeling of the behavior of plane-deformable elastic media with elongated elliptic and rectangular inclusions. Materials Science. 2017. V. 52. No. 6. Рp. 768-774. https://doi.org/10.1007/s11003-017-0020-z

14. Haque A., Ahmed L., Ramasetty A. 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. 2005. V. 88. No. 8. Pp. 2195-2201. https://doi.org/10.1111/j.1551-2916.2005.00404.x

15. Hart E. L., Hudramovich V. S. Projection-iterative modification of the method of local variations for problems with a quadratic functional. J. Appl. Math. Mech. 2016. V. 80. No. 2. Pp. 156-163.
https://doi.org/10.1016/j.jappmathmech.2016.06.005

16. 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. Issue 108. Pp. 77-86. https://doi.org/10.32347/2410-2547.2022.108.77-86

17. 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. Cham: Springer, 2024. V. 204. Chapter 18. Pp. 249-264. https://doi.org/10.1007/978-3-031-54063-9_18

18. Hudramovich V. S., Sirenko V. N., Klimenko D. V., Daniev Yu. F., Hart E. L. Development of the normative framework methodology for justifying the residual resource of starting buildings' constructions of space launch vehicles. Strength of Materials. 2019. V. 51. No. 3. Pp. 333-340.
https://doi.org/10.1007/s11223-019-00079-4

19. Kamalarajah R., Bull J. W., Chizari M. An investigation on circular cut-outs multilayer thin walled pipes. IAENG Transactions on Engineering Sciences. 2018. Pp. 1-13.
https://doi.org/10.1142/9789813230774_0001

20. Kumar R. V., Ramamurthy G., Rao K., Lakshminarayana H. An improved finite element model to study stress concentration around an elliptical cutout in pressure vessel: Validation : Part-I. J. Aerospace Sciences and Technologies. 2007. V. 59. No. 3. Pp. 196-207.
https://doi.org/10.61653/joast.v59i3.2007.711

21. Lekkerkerker J. G. Stress concentration around circular holes in cylindrical shells. AIAA J. 1964. V. 10. Pp. 1466-1472.

22. Lurie A. I. Theory of Elasticity. Foundations of Engineering Mechanics. Berlin, Heidelberg: Springer, 2005. 1050 pр. https://doi.org/10.1007/978-3-540-26455-2

23. Lyashenko B. A., Soroka E., Rutkovskii A. V., Lipinskaya N. V. Determination of discrete-structure parameters of coatings with allowance for residual stresses. Strength of Materials. 2002. V. 34. No. 4. Pp. 402-406. https://doi.org/10.1023/A:1020344724002

24. Murthy M. V. V., Rao K. P., Rao A. K. On the stress problem of large elliptical cutouts and cracks in circular cylindrical shells. Int. J. Solids Struct. 1974. V. 10. No. 11. Pp. 1243-1269.
https://doi.org/10.1016/0020-7683(74)90071-7

25. Nguyen D. H., Wang H. Multi-scale analyses of three dimensional woven composite 3d shell with a cut out circle. Appl. Compos. Mater. 2019. V. 26. Pp. 339-356.
https://doi.org/10.1007/s10443-018-9695-z

26. Oterkus E., Madenci E., Nemeth M. P. Stress analysis of composite cylindrical shells with an elliptical cutout. J. Mech. Mater. Struct. 2007. V. 2. No. 4. Pp. 695-727. https://doi.org/10.2140/jomms.2007.2.695

27. Pierce D. N., Chou S. I. Stresses around elliptic holes in circular cylindrical shells. Exp. Mech. 1973. V. 13. Pp. 487-492. https://doi.org/10.1007/BF02322735

28. Pilkey W. D., Pilkey D. F., Bi Z. Peterson's Stress Concentration Factors. Wiley, 2020. 640 рp.
https://doi.org/10.1002/9781119532552

29. Russo A, Sellitto A, Saputo S, Acanfora V, Riccio A. A numerical-analytical approach for the preliminary design of thin-walled cylindrical shell structures with elliptical cut-outs. Aerospace. 2019. V. 6. No. 5. Pp. 1-15. https://doi.org/10.3390/aerospace6050052

30. Shariati M., Rokhi M. M. Buckling of steel cylindrical shells with an elliptical cutout. Steel Struct. 2010. V. 10. No. 2. Pp. 193-205. https://doi.org/10.1007/BF03215830

31. Sharma D. S. Stress distribution around polygonal holes. International Journal of Mechanical Sciences. 2012. Vol. 65. No. 1. Pp. 115-124. https://doi.org/10.1016/j.ijmecsci.2012.09.009

32. Tennyson R. C. The effects of unreinforced circular cutouts on the buckling of circular cylindrical shells under axial compression. J. Eng. Ind. 1968. V. 90. No. 4. Pp. 541-546.
https://doi.org/10.1115/1.3604686

33. Van Tooren M. J. L., Van Stijn I. P. M., Beukers A. Curvature effects on the stress distribution in sandwich cylinders with a circular cut-out. Compos. Part A: Applied Science and Manufacturing. 2002. V. 33. No. 11. Pp. 1557-1572. https://doi.org/10.1016/S1359-835X(02)00116-1

34. Washizu K. Variational Methods in Elasticity and Plasticity. Oxford, New York: Pergamon Press, 1975. 420 рp.

35. Yazici M., Ozcan R., Ulku S., Okur I. Buckling of composite plates with U-shaped cutouts. J. Compos. Mater. 2003. V. 37. No. 24. Pp. 2179-2195. https://doi.org/10.1177/002199803038109

36. Zienkiewicz O. C., Teylor R. L. The Finite Element Method for Solid and Structural Mechanics. New York: Elsevier, 2005. 632 рp.