Abstract
The purpose of this research is to study the limit failure stresses occurring on the rectangular cross section fiber reinforced curved beam subjected to couple moment at the ends of the geometry. Utilizing analytical methods, closed form solutions are obtained for plane stress conditions. Considering different parameters such as the radial thickness and fiber volume of the beam, stress and displacement fields are investigated in detail. Employing different failure criteria, Tsai-Wu and Norris, calculated failure limit moment and failure location differences in the beam are analyzed. Moreover, various transverse Young’s modulus estimation methods available in the literature, Halpin-Tsai, Rule of Mixture, and Chamis, are considered. Effects of these estimations on the aforementioned fields are carefully handled as well. Using the material properties of glass fiber/epoxy constituents, numerical examples are generated by incorporating semi-analytical effective material property calculation models. Achieved numerical results have revealed that the radial thickness of the beam has more influence than fiber volume in terms of failure moment and stresses. Application of different criteria may cause different failure location acquisitions while mildly changing the limit failure moment. Young's modulus estimation influences the radial displacement prominently. In addition to the acquired results, from a general perspective, this study can be used as a benchmark model for failure stress analysis of related structures and may be expanded with appropriate numerical techniques.
Similar content being viewed by others
References
Timoshenko, S., Goodier, J.N.: Theory of elasticity. McGraw Hill, New York (1951)
Conway, H.D.: Elastic-plastic bending of curved bars of constant and variable thickness. J. Appl. Mech. 27(4), 733–734 (1960). https://doi.org/10.1115/1.3644090
Eason, G.: The elastic-plastic bending of a compressible curved bar. Appl. Sci. Res. 9(1), 53–63 (1960). https://doi.org/10.1007/BF00382189
Shaffer, B.W., House, R.N., Jr.: The elastic-plastic stress distribution within a wide curved bar subjected to pure bending. ASME Trans. J. Appl. Mech. 22, 305–310 (1955). https://doi.org/10.1115/1.4011077
Shaffer, B.W., House, R.N., Jr.: Displacements in a wide curved bar subjected to pure elastic-plastic bending. ASME Trans. J. Appl. Mech. 24, 447–452 (1957). https://doi.org/10.1115/1.4011561
Murch, S.A.: On the pure bending of an elastic, perfectly plastic curved bar in the state of plane strain. J. Franklin Inst. 270(4), 301–316 (1960). https://doi.org/10.1016/0016-0032(60)90625-6
Dryden, J.: Bending of inhomogeneous curved bars. Int. J. Solids Struct. 44(11–12), 4158–4166 (2007). https://doi.org/10.1016/j.ijsolstr.2006.11.021
Arslan, E., Eraslan, A.N.: Analytical solution to the bending of a nonlinearly hardening wide curved bar. Acta Mech. 210(1), 71–84 (2010). https://doi.org/10.1007/s00707-009-0195-y
Arslan, E., Eraslan, A.N.: Bending of graded curved bars at elastic limits and beyond. Int. J. Solids Struct. 50(5), 806–814 (2013). https://doi.org/10.1016/j.ijsolstr.2012.11.016
Arslan, E., Sülü, İY.: Yielding of two-layer curved bars under pure bending. ZAMM J. Appl. Math. Mech. 94(9), 713–720 (2014). https://doi.org/10.1002/zamm.201200104
Boresi, A.P., Schmidt, R.J., Sidebottom, O.M.: Advanced mechanics of materials (vol 6). Wiley, New York (1985)
Yang, Y.B., Kuo, S.R.: Effect of curvature on stability of curved beams. J. Struct. Eng. 113(6), 1185–1202 (1987). https://doi.org/10.1061/(ASCE)0733-9445(1987)113:6(1185)
Kang, Y.J., Yoo, C.H.: Thin-walled curved beams. II: analytical solutions for buckling of arches. J. Eng. Mech. 120(10), 2102–2125 (1994). https://doi.org/10.1061/(ASCE)0733-9399(1994)120:10(2102)
Fraternali, F., Bilotti, G.: Nonlinear elastic stress analysis in curved composite beams. Comput. Struct. 62(5), 837–859 (1997). https://doi.org/10.1016/S0045-7949(96)00301-X
Kardomateas, G.A.: Bending of a cylindrically orthotropic curved beam with linearly distributed elastic constants. Q J. Mech. Appl. Math. 43(1), 43–55 (1990). https://doi.org/10.1093/qjmam/43.1.43
Tutuncu, N.: Plane stress analysis of end-loaded orthotropic curved beams of constant thickness with applications to full rings. J. Mech. Des. 120(2), 368–374 (1998). https://doi.org/10.1115/1.2826983
Wang, M., Liu, Y.: Elasticity solutions for orthotropic functionally graded curved beams. Eur. J. Mech. A/Solids 37, 8–16 (2013). https://doi.org/10.1016/j.euromechsol.2012.04.005
Arefi, M.: Elastic solution of a curved beam made of functionally graded materials with different cross sections. Steel Compos. Struct. 18(3), 659–672 (2015). https://doi.org/10.12989/scs.2015.18.3.659
Dadras, P.: Plane strain elastic–plastic bending of a strain-hardening curved beam. Int. J. Mech. Sci. 43(1), 39–56 (2001). https://doi.org/10.1016/S0020-7403(99)00102-2
Eraslan, A.N., Arslan, E.: A computational study on the nonlinear hardening curved beam problem. Int. J. Pure Appl. Math. 43(1), 129–143 (2008)
Eraslan, A.N., Arslan, E.: A concise analytical treatment of elastic-plastic bending of a strain hardening curved beam. ZAMM J. Appl. Math. Mech. 88(8), 600–616 (2008). https://doi.org/10.1002/zamm.200600037
Nie, G., Zhong, Z.: Closed-form solutions for elastoplastic pure bending of a curved beam with material inhomogeneity. Acta Mech. Solida Sin. 27(1), 54–64 (2014). https://doi.org/10.1016/S0894-9166(14)60016-1
Fazlali, M.R., Arghavani, J., Eskandari, M.: An analytical study on the elastic-plastic pure bending of a linear kinematic hardening curved beam. Int. J. Mech. Sci. 144, 274–282 (2018). https://doi.org/10.1016/j.ijmecsci.2018.05.039
Boley, B.A., Barrekette, E.S.: Thermal stress in curved beams. J. Aerosp. Sci. 25(10), 627–630 (1958). https://doi.org/10.2514/8.7814
Mohammadi, M., Dryden, J.R.: Thermal stress in a nonhomogeneous curved beam. J. Therm. Stresses 31(7), 587–598 (2008). https://doi.org/10.1080/01495730801978471
Haskul, M.: Elastic state of functionally graded curved beam on the plane stress state subject to thermal load. Mech. Based Des. Struct. 48(6), 739–754 (2020). https://doi.org/10.1080/15397734.2019.1660890
Arslan, E., Mack, W., Gamer, U.: Elastic limits of a radially heated thick-walled cylindrically curved panel. Forsch Ingenieurwes 77(1–2), 13–23 (2013). https://doi.org/10.1007/s10010-013-0162-6
Arslan, E., Mack, W.: Elastic-plastic states of a radially heated thick-walled cylindrically curved panel. Forsch Ingenieurwes 78(1–2), 1–11 (2014). https://doi.org/10.1007/s10010-014-0170-1
Haskul, M., Arslan, E., Mack, W.: Radial heating of a thick-walled cylindrically curved FGM-panel. ZAMM J. Appl. Math. Mech. 97(3), 309–321 (2017). https://doi.org/10.1002/zamm.201500310
Lekhnitskii, S.G.: Theory of elasticity of an anisotropic body. Mir Publishers, Moscow (1981)
Nahvi, H.: Pure bending and tangential stresses in curved beams of trapezoidal and circular sections. J. Mech. Behav. Mater. 18(2), 123–132 (2007). https://doi.org/10.1515/JMBM.2007.18.2.123
Gao, Y., Wang, M.Z., Zhao, B.S.: The refined theory of rectangular curved beams. Acta Mech. 189(3–4), 141–150 (2007). https://doi.org/10.1007/s00707-006-0413-9
He, X.T., Li, X., Li, W.M., Sun, J.Y.: Bending analysis of functionally graded curved beams with different properties in tension and compression. Arch. Appl. Mech. 89, 1973–1994 (2019). https://doi.org/10.1007/s00419-019-01555-8
Nie, G., Zhong, Z.: Exact solutions for elastoplastic stress distribution in functionally graded curved beams subjected to pure bending. Mech. Adv. Mater. Struct. 19(6), 474–484 (2012). https://doi.org/10.1080/15376494.2011.556835
Pydah, A., Sabale, A.: Static analysis of bi-directional functionally graded curved beams. Compos. Struct. 160, 867–876 (2017). https://doi.org/10.1016/j.compstruct.2016.10.120
Belarbi, M.O., Houari, M.S.A., Hirane, H., Daikh, A.A., Bordas, S.P.A.: On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory. Compos. Struct. 279, 114715 (2022). https://doi.org/10.1016/j.compstruct.2021.114715
J. C. Halpin, Effects of Environmental Factors on Composite Materials. Air Force Materials Lab Wright-Patterson AFB OH (1969).
Jones, R.M.: Mechanics of composite materials. Taylor and Francis, Philadelphia (1999)
Daniel, I.M., Ishai, O.: Engineering mechanics of composite materials. Oxford University Press, New York (2006)
C. C. Chamis, Mechanics of composite materials: past, present and future. In 21st annual meeting of the society for engineering science (No. E-3936) (1984).
Kaw, A.K.: Mechanics of composite materials. CRC Press, Boca Raton (2005)
Funding
None.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Farukoğlu, Ö.C., Korkut, İ. & Motameni, A. Pure bending of fiber reinforced curved beam at the failure limit. Arch Appl Mech 93, 2965–2981 (2023). https://doi.org/10.1007/s00419-023-02420-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-023-02420-5