Static and vibration analysis of functionally graded beams using refined shear deformation theory
Tóm tắt
Static and vibration analysis of functionally graded beams using refined shear deformation theory is presented. The developed theory, which does not require shear correction factor, accounts for shear deformation effect and coupling coming from the material anisotropy. Governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled axial-flexural response. A two-noded Hermite-cubic element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for functionally graded beams with simply-supported, cantilever-free and clamped-clamped boundary conditions to investigate effects of the power-law exponent and modulus ratio on the displacements, natural frequencies and corresponding mode shapes.
Tài liệu tham khảo
Ching HK, Yen SC (2005) Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites, Part B, Eng 36(3):223–240
Zhong Z, Yu T (2007) Analytical solution of a cantilever functionally graded beam. Compos Sci Technol 67(3–4):481–488
Birsan M, Altenbach H, Sadowski T, Eremeyev V, Pietras D (2012) Deformation analysis of functionally graded beams by the direct approach. Composites, Part B, Eng 43(3):1315–1328
Sankar BV (2001) An elasticity solution for functionally graded beams. Compos Sci Technol 61(5):689–696
Zhu H, Sankar BV (2004) A combined Fourier series–Galerkin method for the analysis of functionally graded beams. J Appl Mech 71(3):421–424
Simsek M, Kocaturk T (2009) Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Compos Struct 90(4):465–473
Khalili SMR, Jafari AA, Eftekhari SA (2010) A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads. Compos Struct 92(10):2497–2511
Alshorbagy AE, Eltaher M, Mahmoud F (2011) Free vibration characteristics of a functionally graded beam by finite element method. Appl Math Model 35(1):412–425
Chakraborty A, Gopalakrishnan S, Reddy JN (2003) A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 45(3):519–539
Li X-F (2008) A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams. J Sound Vib 318(4–5):1210–1229
Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30(3):741–747
Kadoli R, Akhtar K, Ganesan N (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model 32(12):2509–2525
Benatta M, Mechab I, Tounsi A, Bedia EA (2008) Static analysis of functionally graded short beams including warping and shear deformation effects. Comput Mater Sci 44(2):765–773
Ben-Oumrane S, Abedlouahed T, Ismail M, Mohamed BB, Mustapha M, Abbas ABE (2009) A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput Mater Sci 44(4):1344–1350
Simsek M (2009) Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method. Int J Eng Appl Sci 1(3):1–11
Giunta G, Belouettar S, Carrera E (2010) Analysis of FGM beams by means of classical and advanced theories. Mech Adv Mat Struct 17(8):622–635
Li X-F, Wang B-L, Han J-C (2010) A higher-order theory for static and dynamic analyses of functionally graded beams. Arch Appl Mech 80:1197–1212
Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5):1651–1656
Simsek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705
Simsek M (2010) Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos Struct 92(4):904–917
Giunta G, Crisafulli D, Belouettar S, Carrera E (2011) Hierarchical theories for the free vibration analysis of functionally graded beams. Compos Struct 94(1):68–74
Salamat-talab M, Nateghi A, Torabi J (2012) Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. Int J Mech Sci 57(1):63–73
Nateghi A, Salamat-talab M, Rezapour J, Daneshian B (2012) Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory. Appl Math Model 36(10):4971–4987
Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82(3):390–402
Thai H-T, Vo TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 62(1):57–66
Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752
Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton