Thermal buckling analysis of functionally graded material beams
- 688 Downloads
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.
KeywordsFunctionally graded materials Thermal buckling Euler beam theory
Financial support of the National Elite Foundation to support this research is acknowledged.
- Brush, D.O., Almorth, B.O.: Buckling of Bars, Plates, and Shells. McGraw-Hill, New York (1975)Google Scholar
- Burgreen, D., Manitt, P.J.: Thermal buckling of a bimetallic beams. ASCE J. Eng. Mech. Div. 95(EM1), 421–431 (1969)Google Scholar
- Burgreen, D., Regal, D.: Higher mode buckling of bimetallic beams. J. Eng. Mech. Div. 97(4), 1045–1056 (1971)Google Scholar
- Carter, W.O., Gere, J.M.: Critical buckling loads for tapered columns. J. Struct. Eng. ASCE 88(1), 1–11 (1962)Google Scholar
- Culver, C.G., Preg, S.M.: Elastic stability of tapered beam-columns. J. Struct. Eng. ASCE 94(2), 455–470 (1968)Google Scholar
- Leissa, A.W.: Review of recent developments in laminated composite plates buckling analysis. Compos. Mater. Technol. 45, 1–7 (1992)Google Scholar
- Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials. IOM Communications Ltd., London (1998)Google Scholar
- Timoshenko, S.: Theory of Elastic Stability, Engineering Societies Monograph. McGraw-Hill, New York (1936)Google Scholar
- Yang, B.: Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes. Elsevier Academic Press, Amsterdam (2005)Google Scholar