Application of the Southwell Method to Determine the Critical Load of Compression Rods Made of Nonlinear Materials

• Autorzy: Marcinowski Jakub , Sadowski Mirosław

Identyfikatory

DOI

10.59440/ceer/194260

• Języki publikacji: EN

Abstrakty

EN

Experimental determination of the critical force of a compression bar made of linear material does not pose major problems. The widely used Southwell method is also applicable to bars with cross-sections varying in length. The purpose of the research undertaken was to demonstrate that this method can also be successfully applied to bars made of elastic materials exhibiting nonlinear σ(ε) characteristics. Using analytical relationships for a rod satisfying the assumptions of Euler-Bernoulli theory, F(δ) relationships were derived for a rod with an initial arc imperfection, and Southwell diagrams were constructed on this basis. Nonlinear equilibrium paths F(δ) were also determined numerically using the COSMOS/M program for this purpose. For the pre-assumed different nonlinear characteristics, full confirmation of the validity of the application of the Southwell method for determining the critical force was obtained.

Słowa kluczowe

EN

bar buckling; critical force; Southwell method; nonlinear material; analytical method; numerical method

PL

wyboczenie prętów; siła krytyczna; metoda Southwella; materiał nieliniowy; metoda analityczna; metoda numeryczna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: Civil and Environmental Engineering Reports
• Rocznik: 2024
• Tom: Vol. 34, no. 4
• Strony: 168--184
• Opis fizyczny: Bibliogr. 37 poz., rys., tab., wykr. wzory

Twórcy

autor

Marcinowski Jakub

• University of Zielona Gora, Faculty of Building, Architecture and Environmental Engineering, Poland

• https://orcid.org/0000-0001-6834-0843

autor

Sadowski Mirosław

• University of Zielona Gora, Faculty of Building, Architecture and Environmental Engineering, Poland

• https://orcid.org/0009-0007-7886-7666

Bibliografia

• 1. Ambartsumyan, SA 1986. Elasticity Theory of Different Moduli. China Railway Publishing House, Beijing.
• 2. Ariaratnam, ST 1961. The Southwell Method for Predicting Critical Loads of Elastic Structures, Quart. J. Mech. and Appl. Math., 14, 137-153.
• 3. Awrejcewicz, J, Krysko, VA, Sopenko, AA, Zhigalov, MV, Kirichenko, AV, Krysko, AV 2017. Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields. Chaos Solit. Fract. 104, 635-654. https://doi.org/10.1016/j.chaos.2017.09.008.
• 4. Balduzzi, G, Morganti, S, Auricchio, F and Reali, A 2017. Non-prismatic Timoshenko-like beam model: Numerical solution via isogeometric collocation. Computers and Mathematics with Applications 74 1531-1541.
• 5. Baykara, C, Guven, U and Bayer, I 2005. Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment. Int. J. Eng. Sci. 24(12), 1321-1326. https://doi.org/10.1177/0731684405049857.
• 6. Bert, CW 1977. Models for fibrous composites with different properties in tension and compression. ASME J. Eng. Mater. Technol. 99, 344-349. https://doi.org/10.1115/1.3443550.
• 7. Birger, A 1951. Some general methods of solution for problems in the theory of plasticity. Prikl. Mat. Mekh. 25(6).
• 8. Blostotsky, B, Efraim, E, Stanevsky, O, Kucherov, L and Zakrassov, A 2016. Extended options and improved accuracy for determining of buckling load with Southwell plot method. The Ninth International Conference on Material Technologies and Modeling MMT-2016.
• 9. Bo-Hao, Z, Yan-Lin, G and Chao, D 2013. Ultimate bearing capacity of asymmetrically double tapered steel columns with tubular cross-section, Journal of Constructional Steel Research 89 52 62.
• 10. Chen, LY, Lin PD, Chen LW 1991. Dynamic stability of thick bimodulus beam. Comput. Struct. 41(2), 257-263. https://doi.org/10.1016/0045-7949(91)90429-P.
• 11. Dinnik, AN 1935. Stability of elastic systems, NTI NKTP USSR, Moscow, Leningrad.
• 12. Goel, M, Bedon, Ch, Singh, A, Khatri, A and Gupta, L 2021. An Abridged Review of Buckling Analysis of Compression Members in Construction. Buildings 2021, 11, 211. https://doi.org/10.3390/buildings11050211.
• 13. Jakubowicz, A, Orłoś, Z 1978. Strength of materials. Scientific and Technical Publishing House, Warsaw. 14. Jones, RM 1977: Stress-strain relations for materials with different moduli in tension and compression. AIAA J. 15(1), 16-23. https://doi.org/10.2514/3.7297.
• 15. Krysko, AV, Awrejcewicz, J, Bodyagina, KS and Zhigalov, MV 2021. Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials. Acta Mech 232, 3441 3469 (https://doi.org/10.1007/s00707-021-03010-8).
• 16. Lü, CF, Chen, WQ, Xu, RQ, Lim, CW 2008. Semi-analyical elasticity solutions for bi-directional functionally graded beams. Int. J. Sol. Struct. 45, 258-275. https://doi.org/10.1016/j.ijsolstr.2007.07.018.
• 17. Łubiński, M, Filipowicz, A, Żółtowski, W 1986. Metal structures. Part I. Fundamentals of design. Arkady Publishing House, Warsaw.
• 18. Mandal, P, Calladine, CR 2002. Lateral-torsional buckling of beams and the South well plot. International Journal of Mechanical Sciences, Prof Publishing, 44 (12) 2557-2571.
• 19. Marcinowski, J 2017. Stability of elastic structures. Bar structures, arches, shells. Lower Silesian Educational Publishing House, Wrocław.
• 20. Marcinowski, J and Sadowski, M 2021. Designing of steel CHS columns showing maximum compression resistance. Civil And Env. Eng. Reports CEER; 31 (1): 0079-0092.
• 21. Marcinowski, J and Sadowski, M 2020. Using the erfi function in the problem of the shape optimization of the compressed rod. Int. J. of Applied Mechanics and Engineering, vol. 25, No.2, pp.75-87.
• 22. Marcinowski, J, Sadowski, M and Sakharov, V 2022. On the applicability of Southwell’s method to the determination of the critical force of elastic columns of variable cross sections. Acta Mech 233, 4861-4875 (https://doi.org/10.1007/s00707-022-03345-w).
• 23. Marques, L, Taras, A, da Silva, LS and Rebelo, C 2012. Development of a consistent buckling design procedure for tapered columns. Journal of Constructional Steel Research 72 61-74.
• 24. Mihai, A, Goriely, A 2017. How to characterize an on linear elastic material? A review on nonlinear constitutive parameters inisotropic finite elasticity. rspa.royalsocietypublishing.org (http://dx.doi.org/10.1098/rspa.2017.0607).
• 25. Pavilaynen, G 2015. Elastic-plastic deformations of a beam with the SD-effect. AIP Conf. Proc. 1648, 300007. https://doi.org/10.1063/1.4912549.
• 26. Pavilaynen, GV 2015. Mathematical model for the bending of plastically anisotropic beams. Vest. St. Petersburg Univ. Math. 48, 275-279.
• 27. Rusiński, E 1994. Finite element method: the COSMOS/M system, Publishing House of Communications, Warsaw.
• 28. Rykaluk, K 2012. Issues on stability of metal structures. Lower Silesian Educational Publishing House, Wrocław.
• 29. Sadowski, M 2018. Spatial shaping of bars compressed with maximum buckling capacity. Doctoral dissertation, Zielona Góra.
• 30. Serna, MA, Ibáñez, JR and López, A 2011. Elastic flexural buckling of non-uniform members: Closed-form expression and equivalent load approach. Journal of Constructional Steel Research 67 1078-1085.
• 31. Shatnawi, AS and Al-Sadder, S 2007. Exact large deflection analysis of non-prismatic cantilever beams of nonlinear bimodulus material subjected to tip moment. J. Reinf. Plast. Compos. 26(12), 1253-1258. https://doi.org/10.1177/0731684407079754.
• 32. Singer, J 1989. On the Applicability of the South well Plot to Plastic Buckling. Experimental Mechanics, 29(2), 205-208.
• 33. Southwell, RV 1932, On the analysis of experimental observations in problems of elastic stability. Proc Royal Soc, Ser A 135, pp. 601-616.
• 34. Timoshenko, S and Gere, JM 1963. Theory of Elastic Stability. McGraw Hill Book Company, Inc., 2nd Ed.
• 35. Valsangkar, AJ, Britto, AM and Gunn, MJ 1981. Application of the Southwell plot method to the inspection and testing of buried flexible pipes. Proc. Instn Ciu. Engrs, Part 2,1982,73, 217-221.
• 36. Van Tran, TT and Shapiro, D 2019. Nonlinear deformation analysis for precast-prestressed concrete beam systems. FORM-2019 Web Conf. 97, 03039.
• 37. Wang, CT 1948. Inelastic Column Theories and an Analysis of Experimental Observations, J. Aero. Sci., 15, 283-292.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)