Abstract
The paper addresses the problem of large thermal deflections of a planar shear flexible beam made of functionally graded material. The material properties are varied continuously in the transverse direction according to a power law. Transverse shear strains are taken into account using the first-order shear deformation theory with shear correction factor dependent on the mechanical properties of the material. Under the condition of immovable pinned ends, the problem is reduced to two coupled strongly nonlinear equations written in terms of Legendre’s elliptic integrals. Based on these equations, nonlinear deformations of functionally graded beams with temperature-dependent physical and mechanical properties are studied for uniform and nonuniform temperature fields. Results are given in graphical and tabular forms.
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References
Koizumi M.: The concept of FGM. Ceram. Trans. Funct. Grad. Mater. 34, 3–10 (1993)
Arciniega R.A., Reddy J.N.: Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052 (2007)
Zhao X., Liew K.M.: Geometrically nonlinear analysis of functionally graded shells. Int. J. Mech. Sci. 51, 131–144 (2009)
Lu C.F., Chen W.Q., Xu R.Q., Lim C.W.: Semi-analytical elasticity solutions for bi-directional functionally graded beams. Int. J. Solids Struct. 45, 258–275 (2008)
Wattanasakulpong N., Prusty B.G., Kelly D.W.: Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. Int. J. Mech. Sci. 53, 734–743 (2011)
Yiming Fu., Jianzhe Wang., Yiqi Mao.: Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Appl. Math. Model. 36, 4324–4340 (2012)
Ma L.S., Lee D.W.: Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading. Eur. J. Mech. A/Solids 31, 13–20 (2012)
Zhang D.G.: Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Compos. Struct. 100, 121–126 (2013)
Reissner E.: On one-dimensional finite-strain beam theory: the plane problem. Z. Angew. Math. Phys. 23(5), 795–804 (1972)
Levyakov S.V.: Elastica solution for thermal bending of a functionally graded beam. Acta Mech. 224, 1731–1740 (2013)
Irschik H., Gerstmayr J.: A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli–Euler beams. Acta Mech. 206, 19–29 (2008)
Humer A.: Exact solutions for the buckling and postbuckling of shear-deformable beams. Acta Mech. 224, 1493–1525 (2013)
Hosseini Kordkheili S.A., Naghdabadi R.: Geometrically non-linear thermoelastic analysis of functionally graded shells using finite element method. Int. J. Numer. Methods Eng. 72, 964–986 (2007)
Shen, H.S.: Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC Press, Boca Raton (2009)
Vlachoutsis S.: Shear correction factors for plates and shells. Int. J. Numer. Methods Eng. 33, 1537–1552 (1992)
Byrd, P.F., Friedman, M.D.: Handbook of Elliptic Integrals for Engineers and Scientists. Springer, Berlin (1971)
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Levyakov, S.V. Thermal elastica of shear-deformable beam fabricated of functionally graded material. Acta Mech 226, 723–733 (2015). https://doi.org/10.1007/s00707-014-1218-x
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DOI: https://doi.org/10.1007/s00707-014-1218-x