Thermal buckling analysis of functionally graded material beams
Source abstract
Abstract
Buckling of beams made of functionally graded material under various types of thermal loading is considered. The derivation of equations is based on the Euler–Bernoulli beam theory. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of power law across the thickness of beam. Using the nonlinear strain–displacement relations, equilibrium equations and stability equations of beam are derived. The beam is assumed under three types of thermal loading, namely; uniform temperature rise, nonlinear, and linear temperature distribution through the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped and simply-supported edges. In each case of boundary conditions and loading, a closed form solution for the critical buckling temperature for the beam is presented. The formulations are compared using reduction of results for the functionally graded beams to those of isotropic homogeneous beams given in the literature.
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Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Load-Bearing Analysis · Structural Analysis and Optimization
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References (30)
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1. Aydoglu, M.: Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions. Compos. Sci. Technol. 67(6), 1096–1104 (2007)10.1016/j.compscitech.2006.05.021 ↗
2. Brush, D.O., Almorth, B.O.: Buckling of Bars, Plates, and Shells. McGraw-Hill, New York (1975)
3. Burgreen, D., Manitt, P.J.: Thermal buckling of a bimetallic beams. ASCE J. Eng. Mech. Div. 95(EM1), 421–431 (1969)10.1061/JMCEA3.0001106 ↗
4. Burgreen, D., Regal, D.: Higher mode buckling of bimetallic beams. J. Eng. Mech. Div. 97(4), 1045–1056 (1971)10.1061/JMCEA3.0001431 ↗
5. Carter, W.O., Gere, J.M.: Critical buckling loads for tapered columns. J. Struct. Eng. ASCE 88(1), 1–11 (1962)
6. Culver, C.G., Preg, S.M.: Elastic stability of tapered beam-columns. J. Struct. Eng. ASCE 94(2), 455–470 (1968)
7. Forray, M.: Thermal stresses in rings. J. Aerosp. Sci. 26(5), 310–311 (1959)10.2514/8.8053 ↗
8. Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates. AIAA J. 40(1), 162–169 (2002a)10.2514/2.1626 ↗
9. Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates bases on higher order theory. J. Therm. Stress. 25(7), 603–625 (2002b)10.1080/01495730290074333 ↗
10. Javaheri, R., Eslami, M.R.: Buckling of functionally graded plates under in-plane compressive loading. ZAMM 82, 277–283 (2002c)10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y ↗
11. Ke, L.L., Yang, J., Kitipornchai, S.: Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end-shortening. Compos. Struct. 90, 152–160 (2009a)10.1016/j.compstruct.2009.03.003 ↗
12. Ke, L.L., Yang, J., Kitipornchai, S., Xiang, Y.: Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mech. Adv. Mater. Struct. 16(6), 488–502 (2009b)10.1080/15376490902781175 ↗
13. Khdeir, A.A.: Thermal buckling of cross-ply laminated composite beams. J. Acta Mech. 149, 201–213 (2001)10.1007/BF01261672 ↗
14. Lanhe, W.: Thermal buckling of a simply supported moderately thick rectangular FGM plate. Compos. Struct. 64, 211–218 (2004)10.1016/j.compstruct.2003.08.004 ↗
15. Leissa, A.W.: Review of recent developments in laminated composite plates buckling analysis. Compos. Mater. Technol. 45, 1–7 (1992)
16. Li, S.R., Zhang, J.H., Zhao, Y.G.: Thermal post-buckling of functionally graded material Timoshenko beams. Appl. Math. Mech. 27(6), 803–810 (2006)10.1007/s10483-006-0611-y ↗
17. Mossavarali, A., Eslami, M.R.: Thermoelastic buckling of plates with imperfections based on a higher order displacement field. J. Therm. Stress. 25(8), 745–771 (2002)10.1080/01495730290074513 ↗
18. Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates. Int. J. Solids Struct. 35(33), 4457–4476 (1998)10.1016/S0020-7683(97)00253-9 ↗
19. Rastgo, A., Shafie, H., Allahverdizadeh, A.: Instability of curved beams made of functionally graded material under thermal loading. Int. J. Mech. Mater. Des. 2, 117–128 (2005)10.1007/s10999-005-4446-3 ↗
20. Reddy, J.N., Khdeir, A.A.: Buckling and vibration of laminated composite plates using various plate theories. AIAA J. 27(12), 1808–1817 (1989)10.2514/3.10338 ↗
21. Samsam Shariat, B.A., Eslami, M.R.: Effect of initial imperfections on thermal buckling of functionally graded plates. J. Therm. Stress. 28(12), 1183–1198 (2005)10.1080/014957390967884 ↗
22. Samsam Shariat, B.A., Eslami, M.R.: Thermomechanical stability of imperfect functionally graded plates based on higher order theory. AIAA J. 44(12), 2929–2936 (2006)10.2514/1.19492 ↗
23. Samsam Shariat, B.A., Eslami, M.R.: Buckling of thick functionally graded plates under mechanical and thermal loads. Compos. Struct. 78, 433–439 (2007)10.1016/j.compstruct.2005.11.001 ↗
24. Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials. IOM Communications Ltd., London (1998)
25. Tauchert, T.R.: Thermally induced flexure, buckling and vibration of plates. Appl. Mech. Rev. 44(8), 347–360 (1991)10.1115/1.3119508 ↗
26. Timoshenko, S.: Theory of Elastic Stability, Engineering Societies Monograph. McGraw-Hill, New York (1936)
27. Wang, C.M., Wang, C.Y., Reddy, J.N.: Exact Solutions for Buckling of Structural Members. CRC Press, Boca Raton (2004)10.1201/9780203483534 ↗
28. Yang, B.: Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes. Elsevier Academic Press, Amsterdam (2005)
29. Zhao, F.Q., Wang, A.M., Liu, H.Z.: Thermal post-buckling analyses of functionally graded material rod. Appl. Math. Mech. 28(1), 59–67 (2007)10.1007/s10483-007-0107-z ↗
30. Zhao, X., Lee, Y.Y., Liew, K.M.: Mechanical and thermal buckling analysis of functionally graded plates. Compos. Struct. 90, 161–171 (2009)10.1016/j.compstruct.2009.03.005 ↗