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Abstrakty
The paper discusses governing differential equation for determining large deflections of slender, non-homogeneous beam subjected to a combined loading and composed of a finite number of laminae, which are made of nonlinearly elastic, modified Ludwick's type of material with different stress–strain relations in tension and compression domain. The material properties are varying arbitrarily through the beam's thickness. When the thickness of laminae is sufficiently small and the variation of mechanical properties is close to continuous, the beam can be considered as made of functionally graded material (FGM). The derived equations are solved numerically and tested on several examples. From a comparison of the results obtained and those found in the literature a good agreement was observed.
Czasopismo
Rocznik
Tom
Strony
700--709
Opis fizyczny
Bibliogr. 20 poz., tab., wykr.
Twórcy
autor
- Laboratory for Nonlinear Mechanics, Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000, Ljubljana, Slovenia
autor
- Laboratory for Nonlinear Mechanics, Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000, Ljubljana, Slovenia
autor
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, United States
Bibliografia
- [1] G. Lewis, F. Monasa, Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment, International Journal of Non-Linear Mechanics 17 (1) (1982) 1–6.
- [2] K. Lee, Large deflections of cantilever beams of non-linear elastic material under a combined loading, International Journal of Non-Linear Mechanics 37 (3) (2002) 439–443.
- [3] M. Brojan, T. Videnic, F. Kosel, Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law, Meccanica 44 (6) (2009) 733–739.
- [4] M. Brojan, M. Sitar, F. Kosel, On static stability of nonlinearly elastic Euler's columns obeying the modified Ludwick's law, International Journal of Structural Stability and Dynamic 12 (6) (2012).
- [5] C. Baykara, U. Güven, I. Bayer, Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment, Journal of Reinforced Plastics and Composites 24 (12) (2005) 1321–1326.
- [6] M. Brojan, M. Cebron, F. Kosel, Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end, Acta Mechanica Sinica 28 (3) (2012) 863–869.
- [7] S. Al-Sadder, N. Shatarat, A proposed technique for large deflection analysis of cantilever beams composed of two nonlinear elastic materials subjected to an inclined tip concentrated force, Advances in Structural Engineering 10 (3) (2007) 319–335.
- [8] S. Suresh, Modeling and design of multi-layered and graded materials, Progress in Materials Science 42 (1–4) (1997) 243–251.
- [9] B.V. Sankar, An elasticity solution for functionally graded beams, Composites Science and Technology 61 (5) (2001) 689–696.
- [10] Z. Zhong, T. Yu, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology 67 (3–4) (2007) 481–488.
- [11] Z. Zhong, T. Yu, Two-dimensional analysis of functionally graded beams, AIAA Journal 44 (12) (2007) 3160–3164.
- [12] G.J. Nie, Z. Zhong, S. Chen, Analytical solution for a functionally graded beam with arbitrary graded material properties, Composites Part B: Engineering 44 (1) (2013) 274–282.
- [13] A. Chakraborty, S. Gopalakrishnan, J.N. Reddy, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences 45 (3) (2003) 519–539.
- [14] X.-F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler– Bernoulli beams, Journal of Sound and Vibration 318 (4–5) (2008) 1210–1229.
- [15] Y.-A. Kang, X.-F. Li, Large deflections of a non-linear cantilever functionally graded beam, Journal of Reinforced Plastics and Composites 29 (12) (2010) 1761–1774.
- [16] Y.-A. Kang, X.-F. Li, Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force, International Journal of Non-Linear Mechanics 44 (6) (2009) 696–703.
- [17] J.H. Jung, T.J. Kang, Large deflection analysis of fibers with nonlinear elastic properties, Textile Research Journal 75 (10) (2005) 715–723.
- [18] T. Kocatürk, M. Şimşek, S.D. Akbaş, Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material, Science and Engineering of Composite Materials 18 (1–2) (2011) 21–34.
- [19] A. Soleimani, Large deflection of various functionally graded beam using shooting method, Applied Mechanics and Materials 110–116 (2012) 4705–4711.
- [20] A. Soleimani, M. Saddatfar, Numerical study of large defection of functionally graded beam with geometry nonlinearity, Advanced Materials Research 403–408 (2012) 4226–4230.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-e32ec06c-784d-4f9c-a908-d18a0e8266cb